Table 12. Standardized regression coefficients for cases of declared statistical significance—Con.

Dependence pattem of Y,—Con.

Northeast North Central South West
Independent variable Group
Male Female | Male Female Male: Female | Male Female
Per capita income:
MM Xo -133} 207} 021] 296]... | 186
WW Xa, <All 364] 298} -.811 +182
MW Xea +-304| 155] 265] .532 051
WW Xa5 973) 135] 300] -.510 --561
WX, | -2.432]  -.318] 199] 1.493 1.852
MW Xa6 1.637 -372|  -.918 “1.194
Education no response . 1X. .
Income no response... 1 Xz bees
Previous farm residence no response 1 Xie 123
Color I Xe -.089| _-.149 -
Dependence pattern of Y,
Northeast North Central South West
independent variable Group
Male | Female | Male | Female | Male | Female | Male | Female
Lineor .. 1x, -3.630| -3.798| -4.180] -3.536] -3.535] -4.770| -4.417|  -4.639
Quadratic . 1x, 6.066] 6.581 6.008} 6.085} 8.560] 7.330) 6.045
Age cubic... 1x, -2.893|  -3.238 -2.874| -2.894]  -4.209|  -3.416| — -2.833
Opposite of rurality. xX, . bees tees sees
SMSA’ city .. VX, 130
Urbonizetion. 1X,
Unmarriedness . 1x,
Child impedance . 1x
S.P. other than at work. WX,
S.P. occupation status . W Xo
S.P. occupation moderoteness of status . WX,
Head other than at work . WX,
Heod’s occupation status. WX,
S.P. completed high school . WX.
S.P. education status .. WX
No previous farm residenc 1 Xe
No response or DK on health 1X,
Poomess of health .. Xa
Presence of impairments. IX,
Per capita income:
Linear I Xz0
WW Xs,
We Xa
MW Xs
Quadratic . WX.
Cubie WE Xu
Education no response . 1X,
Income no respons 1X
Previous farm resi 1 Xs
Color . 1 Xv
Dependence pattern of Y,
Northeast North Central South West
Group
Male Female Male Female | Male Female | Male Female
Lineor .. 1x, -3.480 -2.769| ....] -2.880
Quodratic . 1X, 6.801 5.069 5.453
Age cubic ... 1X, “3.377 “2.719
Opposite of rurality 1X, 2
‘SMSA' city 1X, +151

90



me quote from notes summarizing my hunches as
to styles of recreation participation:

Activity Groupings by Cultural Context

I Backwoods—The relevant standards are escape
from formality of interpersonal relations and
observance of rules for gaining approval which
are mutually exclusive with those used in
work~a-day situations. The activities which in
many cases seem to answer to these role
specifications are: Camping, fishing, hunting,
nature walks, hiking, mountain climbing, and
canoeing.

Il Boat culture—Originally this was named Mobil-
ity Culture and would have covered motorcycles
and sports cars, as well as boats and auto-
mobiles, but the relevant activities distinguished
on the questionnaire list are simply: Boating
and water skiing. Gregory Stone used the
term ‘highway culture” to describe the features
of shiny, long-tail fins, speed, showmanship,
and the element of risk involved and these seem
to underly the activities considered.
Country Club to Picnic Ground Complex—These
are activities of moderate to heavy public
setting with rather elaborate ‘‘rules of the
game’’ and traditions with widely distributed
and agreed-upon standards of excellence. Here
we include: Sailing, swimming, bicycling,
horseback riding, outdoor games or sports,
and picnicking.

Be

IV Passive Pursuits—Driving for pleasure, walking
for pleasure, sightseeing, attending outdoor
concerts, and attending sporting events.

It is clear that the fourth activity grouping (passive
pursuits) is reflected in P, the first varimax factor.
The second grouping (boat culture) appears to be
factor W, while the first grouping (backwoods) is
varimax factor B, The third grouping and factor A
may be identified. Although the correspondences
are apparent, considerable reappraisal will need to
be done to redefine the ‘‘cultura] contexts.”’

Table 5 summarizes the activities which charac-
terize each factor and the rationale by which their
names were chosen is apparent from the listings.

Figure 2 is a further attempt to characterize the
factors, Activities far from the center are those
which clearly form part of only one factor; those
nearer the center have ties to many factors.

The backwoods factor has a variance of 1.32
(see bottom table 4) which indicates that itis ‘‘roughly
worth about one and one-third ‘activity.’’? Therefore,
its status is not too well supported and, as will be
seen, its reappearance among the region by sex
patterns is sporadic.

The rather loosely phrased statement including
‘one and one-third activity’? deserves comment.
The correlation matrix, table 3, exhibits each activity
with a variance of unity (1.0). All are standardized
The sum of the variances (i.e. 15) is conserved
through the extraction of the latent vectors and roots,
while the varimax rotations also preserve this total

81

variance, This means that variability among persons
with respect to the concocted variables, i.e. among
their factor scores, is obtained by a reapportioning of
the original variance and not by an artificial change
of scale.

Personally, I have been wary of attributing much
importance to factor analytic results that are new
and suggestive. Too often they may be a figment
of an unstable rotation problem, When an independent
replication of the study again yields the same pattern
naturally and without forcing, one can begin to feel
confidence in the results. Consequently, I consider
the following data on regional and sex comparisons
of factor patterns to be of great utility, although
the statistical theory used is not rigorous.

Fifteen by fifteen (activity variables) correlation
matrices were computed for each of the 16 region
by sex by color subpopulations. Each of the eight
region by sex subpopulation matrices for the white
sample persons were subjected to the factor analysis
program, The matrices for the nonwhite persons
were not analyzed due to the small sample sizes.
The results of the eight analyses appear in table 6. 3/

Table 7 shows the eigen-values of the five largest
roots for each of the eight subpopulation correlation
matrices. There is considerable uniformity among
the eight sets, and it seems obvious that on the basis
of variance alone the first four factors do not differ
greatly from one subpopulation to the next. The
Western and the Southern females show the largest
sums of the first four roots indicating some greater
degree of homogeneity of outdoor recreation styles
there than among, say, the Northeastern or North
Central females, The males are similar with respect
to this sum across the four regions.

The factor patterns in each of the subpopulations
were compared to the total population pattern. First,
an attempt was made to locate the corresponding
P, W, B, and A factors. These identifications appear
in table 6. Next, a search for discrepancies between
the total population loadings and the subpopulation
patterns was made, and the results appear in table 8.

Among the Northeast males there was a more serious
problem of correspondence of factor patterns. The
first factor for Northeast males, call it 1-NEM,
appears to be the W-factor with a bit more nature
walks (45 loading on 1-NEM versus 05 loading on
W-factor for the population) and walking for pleasure
(12 versus -16) and less sightseeing (-18 versus 07).

Factor 2-NEM is a driving-picnicking factor but
with more physically demanding activities represented
than the P-factor has. That is, games and sports,
swimming and horseback riding are prominent in
2-NEM but not in the P-factor. The other candidate
for passive factor is 4-NEM, which has very low

2/These onalyses were not contemplated in the original proposal.
When the correlation matrices were first produced | asked the
State College computing center ot Raleigh to do the factor
analyses using a quartimax program. This they generously ar-
ranged to do. Then it turned out that the data were in error due
to the loss of the few cases. The results produced at Roleigh
were nonetheless sufficient to show the value of such anclyses
and also to show the superiority of the varimox over the quorti-
max for this problem.



The level of passive pursuits may be expected to
rise as the educational level does and also as the
population ages.

The backwoods factor is only lightly dependent on
any of the variables of the study, but it is at least
as sensitive to the occupational, educational, and
income variables as it is to the demographic type.

Only among southern and western males does it
appear that a rise in income may be followed by a
rise in level of backwoods activity; elsewhere the
backwoods scores may be expected to drop.

The water related activities scores need further
study before even a tentative guess may be offered
on their future course.



The matrix B tells all there is to know about the
dependent variables, the factor scores, but the ex-
planation is rather unpalatable. The units are num-
bers of standard deviations (away from zero, rather
than the mean in this case). The means and stand-
ard deviations of the factor scores for each region
by sex subpopulation appear in table 9. The differ-
ences among these means exhibit the nature of the
dependence of the factor scores on region and sex.

REGRESSION ANALYSIS

Within each region by sex subpopulation the pattern
of dependence of the four activity scores upon the 29
other variables is exhibited in the multiple correla-
tion coefficients and regression coefficients. These
appear in tables 10 and 12.

Unfortunately, the regression program did not
compute standardized regression coefficients and the
independent variables were not standardized before
performing the regression. Since the interpretations
are to be made largely in terms of the standardized
coefficients, it was necessary to compute these on a
desk calculator. The number of them being large
and time short, these computations were not checked,
so some caution should be exercised in utilizing
them.

The major problem in interpreting these regres-
sion coefficients is the fact that we tend to focus
upon only one or two coefficients at a time. They
were in fact computed in three ‘‘batches’’ or runs,
The first run deleted Xg through Xj5 and Xgq through
Xg5 the second run deleted only Xgq through Xp5 and
the final run allowed all variables to enter. Variable
Xgg was never part of the regression since it was
a constant,

Regression coefficients computed in table 12 always
refer to the regression equation for which the fewest
variables possible appear. Thus although three esti-
mates of the coefficient of X) in the equation for Y3,
say, are available we will only use the coefficient
estimated by the first run where Xj is one of 16 other
variables. It also appeared as one of 23 and of 29
variables,

The sign and size of a regression coefficient
thus indicate what peculiar contribution should be
added or subtracted and how much, depending on a
person’s X-score so as to best predict or guess his
Y-score, and this is a contribution over and above
what contributions other X-scores of the same person

make to the guessed Y-score. In a ‘‘linear’’ world
the regression coefficients show how much to be added
or subtracted for a given Xg score, or separation
from urban centers, say, no matter what age, occupa-
tional status or whatnot the person is. Thus, the
statement ‘‘all other things equal’ has its proper
meaning if, in fact, the factor scores can be repre-
sented as linear functions of the X-scores. The
rather low proportions of variance removed seem
to suggest that this is not the case.

A further precaution in interpreting the coefficients
or perhaps another way of saying the same thing is
a hypothesis somewhat facetiously offered by
M. G. Kendall ‘‘that if enough variables are used in
a regression system every system is almost collinear,
and consequently the matrix determining the co-
efficients is ill-conditioned.’’4/ It is not clear as
to how many is “enough”, but surely 29 is pushing
that boundary line.

Table 10 of percentages of variance removed
yields the rather distressing finding that although
the rate of ‘‘explanation of variance’? may rise to
about 40 percent for Y3, it is usually within 10 to
20 percent. These percentages have an appealing
interpretation as a ratio of number of days ex-
plained by number of days of variation in the popu-
lation recreation pattern. The Y variables are in
units of square roots of different days of participa-
tion and their variances are thus in days of participa-
tion,

Roughly speaking, if ‘30 percent of the variance
is removed”? this is saying that although knowing the
population pattern of participation would allow us to
be able to guess a person’s number of days of
participation to within, say, 10 days with a certain
rate of correctness we could, by using the back-
ground information on him as represented by the
independent variables, guess his participation to within
(100-30) percent of 10, that is 7 days, with the
same success. Thus, knowledge of the variables
of group I (age primarily) allows one to reduce
the uncertainty, expressed in the form of aconfidence
interval, about a North Central female’s active factor
score (Y3) to 100V1 - .2872 percent = 84.43 percent
of its former length, or expressed as a confidence
interval concerning number of days of ‘‘preparedness’’

Vin a discussion reported on page 58 of « paper by H. Wold,
“Journal of the Royal Statistical Society,” ser

Table 9. Means and standard deviations of the 4 factor scores for region-by-sex populations

Northeast North Central South West
Male Female | Mole Female | Male Female | Male Female

y. 1.04 1.16 97 1.20 68 83 -89) 1.09

* 98 1.05 1.01 1.05 89 92 92 99
y. 58 26 .70 +38 65 29 66 AS

’ 1.21 73 AW 73 1.08 90 1.18 ww
Y -52 33 42 7 Al 18 33

. Stondard dey 7 93 1.15 90 1.10 19 1.07
Y Meon ... +07 03 12 13 +01 +03 7 3

‘ Standard de 1.06 90 1.08 79 1.06 73 1.28 1.24

86



6. Boating
8. Water Skiing

5. Driving for
Pleasure

12, Picnicking

14. Sightseeing
15. Outdoor Events

13. Walking for Pleasure

11, Nature walks
7. Swimming
9. Games, Sports
4, 4, Horseback Riding 1. Camping
4. tip, 3. Bicycling 10. Hiking
‘So,
fn

Figure 2. Pictorial representation of total population factor pattern

REGION, SEX, AND COLOR DIFFERENCES

Computation of the dependent variable scors

If X represents the 15 by N = 3,647 matrix of stand-
ardized activity scores (square roots of number of
different days), then XX'/N = R, the 15 by 15correla-
tion matrix (prime denotes transpose). R appears in
table 3c. Next a 15x15 matrix, P, was computed
such that P'R =Dp,P', where Dp,is a 15x15
diagonal matrix of latent roots of R ordered, from
top to bottom, by size. The last 11 columns of P
were discarded leaving the 15 x4 matrix, called A
say, with the property A!R = D,A' where D, is 4x4
diagonal and contains as elements the first four latent
roots of R.

A, the so-called principal axes factor loadings,
became the input to the varimax rotation routine

83.

whereby a 4x4 matrix T was found such that T'T =
I and such that the rotated factor loadings AT = Ar
satisfied a criterion of simple structure, namely
maximization of the sum of their fourth powers. The
factor loadings exhibit the correlations between the
four ‘underlying factors’? and the 15 observed vari-
ables. In order to find for each individual a score on
the underlying factors we proceeded to make three
trials and two errors.

At first the elements of the matrix Ay itself were
employed as weights to obtain Z'=X'Ay where Z is
a 4 by N matrix of ‘‘underlying factor scores.’’
However, the correlation matrix of these factor
scores becomes ZZ'/N = AyXX'Ay/N, T'A'RAT =
T'D,A'AT=T'D2T, This is not in general diagonal
and the underlying factor scores are thus not orthogo-
nal,

Finally, we took as weighting matrix B = AD,!T.
Note that these dependent variable scores, namely



Table 5. Activities favored by persons with high scores on the factor

Factor High Moderate Opposed
P-factor Driving for pleasure | Walking for pleasure | None
Passive pursuits Sightseeing Picnicking
Nature walks
Outdoor events
W-factor Boating Swimming Walking for pleasure
Water related Water skiing Camping
activities Fishing
A-factor Games, sports Swimming
Physically demanding | Bicycling Horseback riding
activities Outdoor events
B-factor Hiking Nature walks Outdoor events
Backwoods activities | Camping Driving for pleasure

total variance and on which driving is little represented
(26 as compared with 73 on the P-factor).

Factor 3-NEM has high loadings on hiking and
bicycling with a negative loading on driving. There
are moderate loadings on camping and fishing. The
importance of these contrasts among modes of trans-
portation and the associated activities may hold up
in further investigation but it is only suggestive at
present. In short, the NEM factor pattern is aberrant
and is worthy of further questioning but not within
the confines of the present study.

In the North Central region the factor pattern for
males and most of that for females conform to the
population-as-a-whole pattern. For males, walking
for pleasure is less a part of the P-factor than it
is for females and this is true in other regions also.
In the North Central region swimming is more a part
of the B-factor for both sexes, The B-factor is the
least satisfactorily identified of the factors, and
particularly for the females. However, since its
common variance is only 1.25, it is also true that,
whatever the fourth factor is, it is not too important.

In the South, also, conformity to the overall
pattern is noticeable especially among the males.
For them, picnicking is less a part of the P-factor
and more a part of the W-factor and bicycling appears
to move from the A-factor to the B, relative to the
population as a whole. For the females, the total
Population P- and B-factors cannot be too clearly
identified. Fishing and picnicking occur in the B-
factor of Southern females while these activities are
not part of the total population B-factor. In this case
the common variance, 1.96, is sizeable.

In the West both the male and the female patterns
show that fishing occupies there a different position
than in the population as a whole. It disappears from
the W-factor and appears in the B-factor. In general
the W-factor becomes more specialized—to camping
and fishing.

Meaning of the correlation coefficients among
activity scores

The correlation coefficients of table 3c represent
a composite index of association between two activi-

82

ties, The mean square contingency coefficients, also
shown in table 3c, reflect one component of the
association. Insofar as participants (whether ‘‘light’’
or “‘heavy’’) in one activity are also participants in
the other activity, the @ value or mean square
contingency coefficient will be large. The correlation
coefficients (r values) are large both for this reason
and also insofar as, among participants, the heavy
participators in one activity are also heavy partici-
pators in the other.

For example, from table 3c we find that 934 = .2267
while rg4 = .1454. Thus, although participators in
bicycle riding are somewhat more likely to be partici-
pators in horseback riding than not, these who are
frequently bicyclers are not the most active horse-
back riders. On the other hand @,, = .3004 while
Tg7 = -3934. This suggests that over and above the
£80 that participation itself is associated between
swimming and boating the days spent in these activi-
ties are also associated.

Either of these indices, § or r, could, in the sense
of both computational admissibility and rationale, be
used as a basis for the factor analyses. If # is used,
exclusive attention would be concentrated upon the act
of moving from none to some participation which
seems important enough from a social psychological
standpoint to justify such attention. The added aspect
of association between the square root of the number
of days participated may be more a function of the
bundles of facilities provided and other situational
features of the participation than of the so-called
desires of the person.

In comparision with the r values actually used in
the factor analyses, the J values show the following
general differences:

They are larger than r for sightseeing, walking
for pleasure and horseback riding than bicycling
and nature walks.
They are smaller for boating, swimming, fish-
ing, water skiing, picnicking, and driving for
pleasure.
Notice the cluster of water-related activities, whose
intercorrelation can be explained by the common
recreation setting, with smaller 9 values thanr.



Table 8. Subpopulotion factor loadings relative to total population loadings (numbers in parentheses equal
absolute value of difference between subpopulation and total population loadings)

P-factor W-factor A-factor B-factor
Northeast
M (See Text)
F Camp up (28) Camp down (28) Horse ride down (23)| Fish down (23)
Hike up (23) W. Ski down (39) Horse ride up (53)
O. Events down (31) Swim up (21)
W. Ski up (47)
Games up (27)
N, Walk down (25)
North Central
M P, Walk down (22) | Bicycle up (28) Swim up (21)
N. Walk up (22)
| N. Walk up (29) Fish down (35)
F Bicycle down (33)
Swim up (38)
N. Walk down (24)
Picnic up (23)
P, Walk down (34)
©, Events up (23)
South
M Picnic down (22) Picnic up (32) Bicycle down (48) Bicycle up (45)
Games up (33)
0, Events up (23)
F Swim up (23) Horse up (28) Fish up (44)
Games up (23) Swim down (21) Bicycle down (21)
N. Walk down (25) Drive up (31)
Picnic down (30) N. Walk up (31)
Sightsee down (24) Picnic up (40)
Sightsee up (29)
O, Events up (29)
West
P. Walk down (24) Fish down (35) Fish up (72)
Hike up (64) Bicycle down (72)
P. Walk up (42) Hike down (82)
0, Events down (27) N. Walk down (36)
P. Walk down (67)
Sightsee down (21)
O. Events up (37)
F Horse ride up (44) Fish down (60) Horse down (62) Fish up (76)
Drive down (49) Bicycle up (23) Swim down (33) Bicycle down (52)
Swim down (32) Horse ride up (28) | W. Ski up (40) Hike down (54)
Hike up (25) Drive up (75) Hike up (41) N. Walk down (23)
P. Walk up (22) Swim up (35) N. Walk up (34) P. Walk down (26)
©, Events down (37) | Sightsee down (21)
O, Events up (29)
Y'=X'B, have covariance matrix YY'/N= trial and error were expended to achieve this degree

T'D}1A' XX'AD,/T/N =I, the identity matrix. Also,
as for correlations between Y’s and X’s, we find
We X¥'=RADYT = AT =A,, the factor loadings, as
is proper,

In point of fact, the activity scores were never
standardized by origin, only by scale (and one further

85

of standardization).

This accounts for the fact that

the grand means of the Y variables as they stand are

not zeros,

If M be taken to represent the 15 x N

score matrix of unstandardized measurements andD,
be the diagonal matrix of standard deviations, then
the matrix X* = Ds~1M was actually used in compu-
tations in place of the X as described above.



APPENDIX A

DEPENDENCE OF RECREATION PARTICIPATION ON BACKGROUND
CHARACTERISTICS OF SAMPLE PERSONS IN THE SEPTEMBER 1960

NATIONAL RECREATION SURVEY
BY CHARLES PROCTOR

TRANSFORMATIONS AND MARGINAL
TABULATIONS

Table 1 shows the numbers of cases by region, sex,
and color divisions. Analysis was conducted on
3,647 unduplicated cases.

Many of the independent variables were, at this
stage, in qualitative form in accordance with the
code key. Table 2 indicates how the independent
variables X, through Xgq were constructed from the
data supplied by the Census Bureau. The activity
variables Yj through Yy5 were constructed in each
ease by taking the square root of the number of
different days of participation.

This square root transformation was an attempt
to reduce the skewness of the original distribution

Toble 1. Numbers of cases (sample persons) behind
computations for factor analysis and regression
analysis and adjusted distribution of sample
persons (adjusted sample persons) behind
tabulations done by Census Bureau

Semple persons ‘Adjusted sample
persons
Region and color Sex Sex
Total Total
Male | Female Male | Female
Northeast:
White....... | 427] 528] 955] 536) 622] 1,158
Nonwhite.... | 28) 36] 64} 36] 45/81
Total 455| 5641 1,019| 572) 667 | 1,239
North Central:
White . 500| 526] 1,026) 579| © 602] 1,181
Nonwhite , 33 36 69 44 45 89
Total ..... 533| 562} 1,095} 623) 647 | 1,270
South:
White . 422) 417/839] 525) 507 | 1,032
Nonwhite. 82| 120] 202| 108] 152] 260
Total 504} 537} 1,041} 633) 659 | 1,292
West:
White ze} 250| 468} 268} 309] 577
n 13} 24] 14{ 17] 31
Total ..... 229] 263| 492| 282) 326] 608
U.S. Totol {1,721 | 1,926 | 3,647 {2,110 | 2,299 } 4,409

Note: The number of mole and female adjusted sample persons
are estimated from totals, and may differ slightly from the
actual.

77

so that the usual statistical tests which assume
normal distributions might not be too misleading.
Also it reflects my judgement that the difference
between two people, one reporting no days, the other
with 1 day in some activity, is not ‘equal’? to the
difference between one reporting having spent 20
days and another 21. It seems preferable to equate
differences of “from none to 1’? with such gaps as:
“from 9 to 16” or ‘from 16 to 25,’ etc.

Table 3a shows the means and table 3bthe standard
deviations of the 15 activity variables for region by
sex by color subpopulations.

FACTOR ANALYSIS OF ACTIVITY
INTERCORRELATIONS

If the patterns of recreation participation of two
people are compared, one will find differences and,
depending on his point of view, similarities. The
purpose of the factor analysis is to fixon a particular
point of view for determining similarities. Thus,
if one of the persons camps and the other goes on
nature walks they are similar from the point of
view which contrasts backwoods against the more
developed setting, which is one of the four factors
to be introduced shortly.

The factors themselves are defined as linear
combinations of the 15 participation scores. This
is an operational definition assigning to each sample
person a score on all four factors. The theoretical
definition is turned around to read that the participation
scores manifest the factor scores. Thus, knowing
a person’s factor scores, we can guess what activities
he favors and which he tends to avoid.

The computational exercise which is used to convert
the 15 by 15 correlation matrix (see table 3c) of
participation scores into a matrix of factor loadings
will by necessity yield ‘‘some’’ set of loadings. 1/
But whether these numerical factor loadings identify
an important, useful, or fruitful collection of factors
is not guaranteed. In the present case three kinds

VEach factor analysis began by inputting the correlation matrix
“with ones on the diagonal”’. The machine than printed out the
eigen-values and vectors after which the first four eigen-
vectors [or principal axis factor Idadings as they are known in
factor analysis literature] became the input to a varimax rota
tion program. This scheme of rotation has the machine trying
various directions of rotations so as to produce either very

large (in absolute value) or very small (hovefully near zero)
factor loadings.



Table 11. Significance of regression removal by 3 groups of independent variables

Groups of independent Northeast North Central South West No. of
variable variables Male | Female| Male | Femole| Mole | Female | Mole | Female | No's
Y, 1. All else except. No ” * * a ” No * 2
Il. Occupation and educ: ” ” No ” ile * No ” 2
I. Income No ** No No No * No No 6
Y, I. All else except—......... “ * “ “ “ a a “* 0
Il. Occupation ond education. TM ial ” No * No No No 4
II. Income ” * * * No ”* No No 3
Y, 1. All else except os ns = ros rs 7 = 4
Il. Occupation and education. . No No ” No * No No No 6
11. Income. No No No No No No No No 8
Y. 1. All else except— - No * No * No No * 4
Jl. Occupation and education. . No * No * No Neo No No 6
Hil. Income . * iid No * No N * No 4

of this dependence is that among West males, where
the coefficients are quite large, the linear relationship
is positive—the higher the income the higher the back-
woods factor score, However, in the Northeast and
among North Central females this is not the case.

The smallness of some of the linear income
coefficients there suggests that they are responding to
happenings in the extremes of the income distribution
more so than to the whole range. This is true of the
Northeast females family income coefficients, which
suggest that very high family incomes lead to a
decrease in levels of Y4. This is contrasted with
the Northeast males where the cubic coefficient is
small and where high incomes characterize a re-
surgence of the backwoods factor since it is the
quadratic coefficient which operates.

In instances where they are statistically significant
the coefficients of Y4 on age tell a story similar to
the dependence of Y3 on age, albeit ona flatter curve.
The isolated variables with statistically significant
coefficients can, of course, be interpreted but were
quite unexpected to me. Child impedance once again
appears to be an inappropriate title since southern
males seem more likely to have high backwoods
scores with younger children about. Completion of
high school among North Central females seems
tied to lower Y4 scores. Among Northeast females
the presence of a head of household who is other
than at work is associated with higher backwoods
factor scores, and for Northeast males those in
SMSA and those in less urbanized settings have
lower backwoods scores.

Pattern of Dependence of Yj =
the Passive Pursuits Factor

The major variable affecting Yj scores appears
to be education—either as X14, completion of high
school, or X15, educational status in general. The
more educated persons have higher passive pursuits
scores. The members of the health complex, X1g
and X19, also have significant coefficients in the not
surprising direction—poorer health goes with less
passive pursuit activities.

Age appears among the North Central region
persons as positively related to Y4 scores and a less
urban setting tends to less passive pursuits, also in

the North Central region, To complete the North
Central picture a no response among females on
income is associated with a lower passive pursuits
score. This along with the same case inthe Northeast
region suggests that the Y score may be to some
extent a function of response conditions. Perhaps
the education effect is also acting upon these response
conditions and so upon Yj, rather than directly upon
Yi.

Also among Northeast females income appeared
to be significantly related to Y, and the negative
nature of this relationship is apparent from the co-
efficients. The size of the cubic coefficient suggests
the tortured path of a regression curve trying to
be flat throughout most of its range with a twist
at either extreme. Also among Northeast females
those for which the head of household was other
than at or looking for work and of lower X10 (occu-
pation status variable) had higher Y, scores, while
all other things equal, the nonwhites had lower levels
of Y1 scores than the whites among Northeast females.

For southern females the statistically notable
coefficients suggest that:

Being not on a farm depresses the Y] score as
does being further from centers, having younger
children about, and being of a moderate occu-
pational status while a head of household who is
other than looking for or at work elevates the
passive pursuits score.

Among western females moderateness of status
is tied to higher Y] scores while the S.P. other
than looking for or at work also leads to high Yj
scores.

Pattern of Dependence of Y 9:
the Water Related Factor

Investigation of the details of this pattern is left for
the reader. There is a fertile field for exploration
as the liberal sprinkling of asterisks in table II,
over Yo cells, attests. The more universally apparent
determinants of Yp scores seem to be:

Color—nonwhites have lower scores.
Urbanization—those away from urban centers
have higher scores.

S.P. occupational status—high status males have
higher scores.

88


Table 10. Percentages of variance as represented by squares of multiple correlation coeff
independent variables:
Group | —Everything except . . .
Group I! —Occupation and education (X, through X,,) and
Group IIl—Income (X,, through X,,)

Dependent Sowce Northeast North Central South
variable Mole | Female| Male | Female | Male | Female
Y, | Group ! alone. 3.26] 10.56} 14.83) 15.49] 8.72, 16.91
Group I! over Group |. 412} 3.91) 1.93] 3.05] 3.45] 6.81
Group II! over | ond I 1.00] 2.98] = 147{ 1.39] 1.52] 4.32
Total removed 2.0.2.2... cece 8.38] 17.45 18.23] 19.93] 13.68] 28.04
Y, {Group | alone... 16.58, 681| 15.67; 9.87) 12.92] 9.69
Group II over Group |. 4.87 3.59 2.94 1.12 3.75 42
Group II] over | and II. 3.04 3.97 2.10 2.16 94 3.73
Total removed ......2...0e sees 26.48} 14.36] 20.71{ 13.14) 17.61/ 13.83
Y, Group | clone ... 35.28 3.27 35.07 28.72 32.02 27.83
| Group II over Group |. 84 ww 3.57 1.19 1.98 -80
Group II! over | and II. AD 95 A7|_1.03] 1.53] 1.00]
Total removed .....00.22eeee 36.54] 33.33{ 39.11] 30.94] 35.53 29.63
Y, {Group | alone... e7e] 279) sat} 3.47] 9.91] 1.66]
Group 1! over Group |. 1.46{ 3.08] 1.97} 2.95] 1.97 28
Group II! over | and It. 3.07| 2.27 80] 2.67 23) 1.66
Total removed . 13.31] 814] 818] 9.09] 121] 3.60

or “‘proneness’’ or whatnot for active outdoor recrea-
tion pursuits, it would be reduced to 71.28 percent
of its former length.

Table 11, the results of significance tests of vari-
ances removed, gives, so to speak, a signal to go
ahead and examine regression coefficients within
certain groups of independent variables in certain
subpopulations for certain factor scores. Table 12
shows the results of this search by reporting stand-
ardized regression coefficients whenever warranted
by table 11 and by an associated t value of over 1.96.

Patterns of Dependence: Y 3
e Active Factor

Factor three, the active factor, is dependent almost
exclusively on age which presumably indexes physical
fitness, absence of cultural inhibitions and a con-
stellation of tensions favorable to such activities.
The only other variables of somewhat universal
influence are Xg, called child impedance, an evident
misnomer in this instance, and Xjg, no previous
farm residence,

In the South, particularly, previous farm residence
seems to inhibit the active pursuits while, in the
North Central region particularly, the presence of
younger children encourages them. Among males
in the North Central and the South a sample person
being employed effects some restriction on his
participation in activities of this type. In the West
nonwhite persons had higher levels of Y3 than
whites.

Other evidences of dependence are more or less
isolated, such as:

Males on rural farms in the North Central
region had a higher level of Y3 than those not
on rural farms.

In the Northeast, males in SMSA’s had higher
levels of Y than those not in SMSA’s.

Among males in the North Central region those
with the head of household working and those
with less than a high school education had higher
levels of Yg3 than other North Central males.
Among southern males poorness of health was
associated with lower levels of Y3.

Since the signs and sizes of the partial regression
coefficients for Yg on Xz, Xo, and Xg are quite
similar from one to the other subpopulation. Figure 3
exhibits only one specimen curve, that for South
females.

The scale along which Y3 is measured is in terms
of standard deviations so that 40 is a rather extreme
quantity and in itself rather meaningless as is fre-
quently the case with predictions for extreme values
of the independent variable. It does suggest, however,
that the distribution of Y3 values is quite positively
skewed, and also cautions against the too literal
interpretation of the prediction equation. Remember
that the entire equation involves all other variables
in group 1 and that the Y3 scores represent only the
additional adjustment due to age over or below that
predicted on the basis of the other variables, The
strategy is however quite clear—if the sample person
is young throw caution to the winds and guess that
his active factor score is high.

Dependence Pattern of Y 4 : the Backwoods Factor

The pattern of dependence of Y3 is clearer than for
others of the Y’s, while that for Y4 is muddier. The
presence of the income variables is indicated although
at a barely significant level. The interesting feature

87



Table 6. Varimax rotated factor loadings for 8 sub-

populations with population factors identified

(entries are in hundredths)

Table 6. Varimax rotated factor loadings for 8 sub-
populations with population factors identified
(entries are in hundredths)—Con.

NORTHEAST—WHI TE

SOUTH-WHITE—-Con.

Voriabh Males Females Males Females
eres if 2[3v[ afi] 2 fav[a 2[3¥] 4 2[ 3 [4¥
2} 16{ 44] -26} 1a] 31] 43) -15 10 77\ -05| 13 -13} 09) 69
65} 11] 30] -06} 72] 09) -18] 11 n 52] 36| -10 -05] 05) 71
Mn] 16| 67} 04] -09{ 10} 09) 74 12 05| 27) 20 28| 23) 37
-12| 48] 27] 19] -07| -10] 58) 26 13 20] 60| -02 -08} 03) 19
+06} 66] -34) 26] -02] 62/ -12] 23 4 13] 71) -03 12] 08] 49
79} 15] 13] 00} 75} 06) 23] 08 15 03} 44) 48 ni} 39} 03
x * 0 % bed 3 2 s Population factor B/ PLA wi al B
311 62] 17] -09} 2a} 12/31] 69 Varionce 1.84] 1.82 11.63 2.17|2.00 | 1.96
06} 02} 75] 20] -14) 32) 60} 10 ;
45} 05} 08| 52] 16] 58] 15] 01 WEST-WHITE
20] 64] 13} -03] 30) 39| -04/ 36 Males | Females
12) 02) 03} 73] -04} 62] 08) 13 Vv 2 av
-18) 43) 08] 57] 14] 67) 03) 02 2434 2412 i4
: 18{ 51] 12| 05} 21] 08] -09) 62 121 06! 74 al os} 72
Population factor (See|text) Ww P B A 00 22! 75 00; 18 79
Varionce (2.39 | 2.31 | 1.61 |1.38 | 1.68] 2.02] 1.51] 1.86 15) 51, -48 16} 52] -28
02] 57) 21 36} -13| 06
NORTH CENTRAL-WHITE 76) -14; -02 83) -09)  -01
Mal Fonal n} 1; 20 80} 19] 10
j ales males -05| 64; 01 7a} 21| 12
Voriabl
srieble 1f2[3 [4 [0 [2v[av[a 07] -05, 16 61] 44] 09
03] 59! -06 2} si] 12
39| 61} -08] 08] 37] 01] 46) 09 19} 20. -11 00} 66} 17
59} 08} 19] 03/ 48/ 21] -32] -06 66] 04; 04 01} 46{ 17
21} 20] -13) 71} -o1] 12] -09] 78 32} 33. 10 15] 28} 10
-10} 04] 13) 57] 21] -20) 22) 53 29} 03; -41 02} 11] 00
12) 01] 72] 13] 12] 69} -09| -o1 68] 18; -01 04} 09} 01
79| ov} 21} 08) 70} 18} 07] 31 32) 51. 0 12} 07} 03
47| 30) 25] 51] 39] 18) 29] 58 . i vl A
oy| o2| oa| ob] ey] orl os] og Population factor Pi) Ai. ¥ B
16| 16 21} 73] 04] 39) 02 55 Variance 1.87} 1.88 1-66 2.57|2.02 | 1.35
o7} 71] -11] 33) -09} 11) 77] 08 1
-o1] 62| 35] -01 20] 40! 16] at Vindicotes thot o sign reversal has been performed on the
23| 07| 58] 08| 37) 52] 19| 12 vorimox output.
-17] 43} 31| 13] -13} 60] -08] 26
13] 31] 62} -02| 01] 67] 34) -12
14; -22) 58) 43) 18) 50) -03} 24 Table 7. Eigen=values of the lnrgest 5 vectors by levels
lati Ww
Population factor! W | B | P | A PiBIA Te) ae an Son] Sm
Vorionce ...... 2.02] 1.76 | 2.02|1.98 |1.75] 2.27] 1.25| 1.96
Total population—
SOUTH-WHITE White and non-
Von toler Foncles 3.47) 1.51 1.11] 7.30] 0.92
sre vf{2)yvjafif2]s fay Northeast (white)
3.67] 1.64 1.2: 7.69| 1.04
1. 38) 46/ 04) -09/ -12) 41) 17] 51 3.24] 1.41 1.25 7.07| 99
2. 59| 03} 02] 03} -08} 41] 01 47 North Central (wi
3. 704) 69) 09] 21] 09) 02) 79) 03 3.81] 1.50 1.17] 7.79] .97
4. 09] -10] -07] 59] -05] 11) 77] 10 3.56) 1.46 1.06! 7.23} 1.00
5. oi} -17] 73} 22] 75} 06) 02) 14 South (white) :
6. at| 09) 01] 06) 11] 87] -03) 09 64) 1.18! 7.49} 1.06
7. 35] 20) 09) 60) 49) 50) 33) .05 1.81 1.09} 8.14} 1.01
8. 68] 00) -03] 15] -01] 83] 09] -06 Mest (white)
9. 4} 37] 1] 70) 44) 08) 65) 20 1.68! 1.57] 1.24] 7.76) .98
See footnote at end of table. 1.86] 1.29] 1.19] 8.52] 98



0.0 0.5 1.0 1.5

2.0 2.5 3.0 3.5

First

Second

Third

Fourth

Fifth

Sixth

Seventh
Eighth
Ninth

Tenth

ORDER OF SIZE OF ROOT

Eleventh

of Original Variables

1.0 Equals Variance

Twelfth
Thirteenth

Fourteenth

Fifteenth

Figure 1, Size of latent roots plotted against order of size

variable. This indicated that the nonerror variance
represented by the fifth, sixth, to the fifteenth vectors
was specific rather than common. Consequently, the
decision to use four latent vectors as the basis for
varimax rotation was confirmed.2/ The principal
axes (or latent vector) and varimax factor matrices
for the first four factors are shown intable 4.

The first principal axes factor loadings are all
positive, while there is a mixture of signs (albeit
an unbalanced mixture) for all varimax factors,
Notice also the close parity with respect to commu-
nality among the first three varimax factors. A
single ‘general factor’ could make sense in that
people active in any one kind of outdoor recreation
are people who are generally active in outdoor
recreation. However, this is just not important
enough in comparison with the possibility that certain
people might favor one type of activity while others
show a different style.

2A technique suggested by Bartlett and reported in M. G.
Kendall, “A Course in Multivariate Analysis," Hafner, New
York, 1957, pp. 95-98 for deciding if the latent roots are ef-
fectively differentiated was applied to the present data. All
values to the thirteenth were found significant, so by this
means we would be entitled to claim that four is modest
enough. For example, A,,=0.50606102 and A,, =0.45207721
were found os fourteenth and fifteenth roots. The test sto-
tistic to determine if a thirteenth factor is differentiated wos
found to be 11.05 with « distribution under the null hypothesis
of a 1 degree of freedom cl

80

The hypotheses of styles of outdoor recreation
participation were elaborated in discussions with
Abbott L. Ferriss and H. Douglas Sessoms. Let

Table 4. Principal axis and varimax rotated factor
loadings for total population

Factor loadings /

Activity Principal axis Vorimax
1f[2]3]4[rel[wia [es
Camping . 41| 31| -05} -51| 03) 39] 02/ 61
Fishing 40| 41) 20) 05} 05| 60} 08} 03
Bicycling 44| -11| -57} 09] 04] -07| 69) 24
Horseback 1 32] 05| -34) 18] -03| 08] 49} 05
Driving for pleasure] 43| -44} 41| 15| 73] 08] 05] -17
Booting 58| 50| 25] 04{ 12| 78) 14) 08
Swimming. 70; 12] -11! 17) 26} 43) 54 09
Water skiing . 41] 54} 22} 00] -02| 71| 04) 08
Games, sports. 61} -08 | -36] 28] 21] 13] 72] 04
Hiking... 42| 01] -35] -53] 09] 05/ 25] 71
Nature walks... | 47) -25] 03] -32] 46) 05] 12] 40
Picnicking ..... | 57] -11 | 22] 12] 49| 32] 23] -03
Wolkingforpleasure| 35| -46 | 03} -22) 53|-16/ 12) 26
Sightseeing... 45| -40| 35] -26) 70] 07| -07| 20
Outdoor events... | 49| -18| 04| 42| 39] 17| 44| -26
Variance ....... [3.47 [1-51 [1.21] 1.11 [2.06 [2.01 [1.91] 1.32

VAI entries in the body of the table are in hundredths.



Table 12. Standardized regression coeffi

jents for cases of declared statistical significance~Con.

Dependence pattern of Y,-Con.

Northeast

North Central South West

Independent bl Grou
independent variable ry Male

Female | Male Female Male Female Male Female

Urbanization .
Unmarriedness .
Child impedances
S.P. other than at work.
S.P. occupation status .
S.P. occupation moderateness of status ...
Head other than ot work ..
Head's occupation status.
S.P. completed high school .
S.P. educotion status ....
No previous farm residence .
No response or DK on health
Poorness of health ..
Presence of impairments .
Per copita income:

Linear

Quadratic .

Cubic.
Family incom

Linear

Quadratic .

Cubic...
Education no response .
Income no response
Previous form residence no response

141

> 6K DE DC EE KK DE DK DE DE

MW Xo 086
WX, 825
MX -.703
MX, -.323
WX 26
MW Xa, -.079

+278)
873]

+075}
594]
--495|

x,

x,

x

1X,
1 X,

1X,

Color 1x

189

-.003
201
+222

616
-1.700
1.067

359
-782
+277

689
1.408
949

Poorness of health—those with poor health have
lower scores,
Income—the picture is mixed.

Notice the peculiar pattern among the Northeast
males with regard to both occupational status and
income, The coefficient for X19 is positive and that
for X13 is negative; thus the sample person with a
relatively high occupational status for whom the head
of household has a relatively low occupational status
is guessed to have a high Y2 score. On income
likewise there is a reversal of direction from per
capita to family, The reasons for these two odditi:
are probably somewhat distinct.

SUMMARY AND CONCLUSIONS

As in most statistical analyses, the results of this
one should point out critical or crucial differences
and similarities from person to person. Discovery
of the similarities allows for more efficient sum-
maries of the otherwise confusing details, while
the recognition of differences suggests or confirms
the presence of paths of causal influence. The
summarizing portion of the analysis, the factor
analysis, was rather extensively commented on
earlier, but a few words of reminder may not be
wasted before resuming work with the regression
analysis.

On section II, The appearance of the same four
aspects of the pattern of reported recreation activity,
recognizable as passive pursuits, water related,
active and backwoods factor scores, was quite con-
sistent even in the face of moving the analysis from

region to region and accross the sexes, Thus, we
advocate and illustrate the use of this four-part
description of a person’s pattern of recreation activ-
ity.

Nonetheless, it must be remembered that only 50
percent of the variance provided by the original 15
activity scores has been represented by the 4 factors
and there were only 15 activities included for which
the time span covered is only the 3 summer months,
One should also remember that there were peculiari~
ties in factor pattern in each region (section II) and
that the correlation coefficient is not the only index
of association with a legitimate claim to initiate a
factor analysis.

If one person has a low score on, say, the second
factor while another has a high score, we know
that they differ with respect to their reports of
activities during the summer. In particular the
greater is the difference in Y2 score the more
likely is it that differences between the persons
will be found in water related activities. It is these
differences, then, which become the starting point for
the regression analysis.

On section II, The sex differences were most
pronounced for the Y2 scores, the regional differ-
ences most extreme for Y4, and the region by sex
interaction was apparent in Y3. In particular, the
males showed considerably higher water related
activities factor scores than the females in all
regions. Although the North Central region was
higher and the Northeast region lower in average
Y2 scores the regional differences were moderate.



The backwoods factor scores were highest in the
West and lowest in the North Central with the other
two regions on a par closer to the North Central
than the western level. The passive pursuits scores
also differed quite a bit from region to region,
ranging from highest in the North Central and North-
east, lower in the West and lowest in the South,
Females in all regions had higher average Yj scores
than males,

Although females have generally lower average
active factor scores than males, the regional pe-
culiarities in this respect are interesting. The dif-
ference is most pronounced in the South, nearly as
much in the Northeast, less in the North Central,
and for practical purposes absent in the West. The
regional averages, however, show that the highest
average occurs in the Northeast with the other
regions near one another and arranged from North
Central through the West to the South,

The extent to which the recognition of differences
such as these can or should be used to forsee future
patterns of use of outdoor recreation facilities is not
too clear. One frequent application of such bald
statements is as a check upon one’s own impressions
and hypotheses about recreation participation. For
example, that backwoods scores are highest in the
West is not surprising to me but that they are lowest
in the North Central region is, Having been reared
in Michigan, I know that camping opportunities are
extensive in the North Central region, but now I
suspect that opportunities alone are by no means a
sufficient explanation of levels of participation of
this kind.

The region by sex interaction for the Y3 scores
suggests that the sex role in active recreation may
well differ quite a bit from region to region. There
is agreement, however, from region to region that
women engage in more passive pursuits and men in
more water related activities. It is this last finding
which I would like to check more carefully.

This suggests another use of the findings—that of
serving as a guide to more careful examination
of the original detailed data. Such broad patterns
as have been noticed with regard to the four factor
scores may be verified further and amplified by
looking at table 3a or the original tabulations.

On section IV. After having applied the elaborate
regression computations, it is apparent that the
technique is helpful in performing a screening opera-
tion on all causal connections leading from independent
to dependent variables but falls far short of being
very precise concerning the amount of influence. In
short, table 11 is useful but table 12 is not so much
80.

The finding that Yo, water related, and to a lesser
extent Y4, backwoods, and Y1, passive, but not Y3,
active, are influenced by income levels confirms my
own beliefs and perhaps others about the way income
might influence recreation participation. But a
glance at the regression coefficients for predicting
or explaining Yj, say, on Xgq through X95 confuses
the issue. The pattern of signs of the linear, quadratic
and cubic components sometimes appears as+, -,
+and at others -,+, - as one goes from region to
region, from males to females and from per capita
to family income.

93

The reason in computational language is “‘colinear-
ity’? as mentioned by Kendall, and quoted previously.
In behavioral terms the reason is that the independent
variables do not act independently of one another.
They are inhibited or encouraged by concurrent
states of affairs and influence one another as well
as the dependent variable, if this choice of ‘deus ex
machine” description be pardoned.

For Northeast males the dependence pattern of
Y2 on per capita income has signs -,+ , ~ and on
family income +, -,+. One is tempted to say that,
since the “significance” of the coefficients for
family income is greater, boating is primarily en-
couraged by the greater resources of the whole
family while the presence of a high per capita income
and what it implies about the family are actually
a dampening influence on boating. This is obviously
extending the guesswork beyond these data them-
selves but does at least raise the question.

An interesting and important feature of this particu-
lar dependence pattern are the coefficients on the
sample person’s occupational status, Recall that
these are computed from a regression run (group II)
in which income did not figure. I am quite sure
that in explaining these coefficients, the fact that
income and occupational status are interrelated is
quite relevant.

These coefficients show that water related scores
are higher when the head’s occupation is high while
if the sample person’s occupation is lower, his Y2
score is higher. The sample person’s occupation will
differ from the head’s occupation only if he is not
also the head and this means usually that he is
younger. Of course, the age effect on Yo (an inverse
effect) has been partialed out, so the occupational

coefficients .437 (on S,P. occupation status) suggests
that:

If two persons, A and B, are male nonheads of
households in the Northeast region and equal in other
characteristics, and A’s occupation is lower on the
census listing (has a higher code number) than B’s,
then chances are that A has a higher water related
factor score than B.

In the North Central region and in the South also
among males the S,P.’s occupation status coefficient
is positive. In the West, although not significant,
the coefficient is negative. This suggests that occu-
pation has a different kind of influence in the West.

Hypothesizing and explaining with such a great
amount of detail are very time consuming and usually
lead to more doubts than convictions. Consequently,
we will turn to a broader viewpoint. In the future it
may be reasonable to expect that the level of partici-
pation in such activities as are closely dependent
upon demographic variables, place of residence and
health conditions will not change. Those activities
which are more closely associated with occupation,
education, and income might be more unstable.

If this be so, then the level of Y 3 scores, the
active factor scores, will remain steady in the future.
An aging of the population would depress the general
level, but other influences from increasing presence
of young children and diminishing numbers of rural
backgrounds would be offsetting.



Table 3a. Heans of the 15 activity variables by region, color, and sex

Northeost North Central South West
White Nonwhite White Nonwhite White Nonwhite
Female) Male | Female} Male | Female Male | Female|Mole | Female} Male | Female
0.106 | 0.051| 0.056 |0.189] 0.098 0.068 | 0.008 | 0.432] 0.361 | 0.241 0.154
-267 | .413 139] 1.004 435, 1.136 -427| 867) .383) .273 294
+282} .221] 0.000; .373 326 490 -507) .226) .396 | 1.414 516
+121 | 080; .039] .110] 096 190} 0.000] 208} .191] .746} — .596
1.750 | 1.257 -874| 1.734) 1.980 1.172 991] 1.321] 1.626 | 1.393 981
+356 | 122 -166| .687 460 093, 025 365) .097 077
1.609 | .876 +573}1.239) 1.144 -788 372} 1.275) 1.482} 1.438 840
+036 |0.000; 0.000) .157 053 0.000} 0.000 -193] 0.000} 0.000
-701 | 1.216 «391 | 1.129 744 830 -518| -803} .660| 2.748} 1.290
107 | .036 039] .096 073 054 -026| .192| .191| .091 133,
+360 | .172 +235) 226 332 AW 162] .220) 341} .339 352
1.158 | .832 B71) 951) 1.143 A435 561) .866| 1.083 | 1.038 780
1.484 11.533] 1.282] .722|  .892 -746 | 1.260) .747| 1.301] .639] — -451
913 | A411} .387{ 913] 1.094 +344} 503] 1.167} 1.144] .840) — .747
501] .928 219] .700 -682 697 A79| .597) 559 | 1.490 +399

Table 3b. Standard deviations of the 15 activity v

ariobles by region, color, and sex

Northeast North Central South West
White Nonwhite White Nonwhite White Nonwhite
Female |Male | Female |Mole | Female Male |Female|Male |Female|Male | Female
0.541 |0.267| 0.333 )0.691| 0.484 0.362 | 0.091 |0.973 } 0.928 |0.798| 0,555
B47 | .645 -424 | 1.439 948 1.736 | 1,001 | 1.341 +899 | 467 810
1.207 | .993) 0.000 |1.514] 1.160 1.660 | 1.586 1.372 |3.146] 1.340
649 | 423 +236) .544 625 -981 | 0.000 +814 41.670] 2.148
2.036 | 1.833 | 1.507 |2.142] 2.130 1.837 | 3.627 | 1.672 | 7.781 11.835} 2.010
-962 | .364 -507 {1.230 956 449 - 157 1.086 | -828 | .302 277
2.077 {3.114} 1.003 ]1.842] 1.732 1.432 -993 11.811 | 1.935 |2.031 1.49
+273 |0.000| 0.000; .590 294 0.000 | 0.600 699 |0.000} 0.000
1.417 | 1.977 918 |1.969 | 1.436 1.746 | 1.541 | 1.638 | 1.462 |3.492| 2.714
457 | -189 236 | .477 +38 +289 +203 -620 | .302 480
+969 | 583 586 | .733 766 AIS, 541 -789) 611 930
1.287 | .955 B90 11.115} 1.156 662 71 1.156 |1.103 | 1.158
2.182 [1.927 | 1.896 ]1.729] 1.717 1.587 | 2.089 }1.581 | 1.988 | 1.500 883
1.287 | .845 .748 |1.288] 1.309 641 +942 | 1.373} 1,230 11.060 947
949 | 1.137 -616 |1.167} 1.228 1.223 | 1.079 973 41.749 813

. Intercorrelations over all sample persons among activity variables (in lower left-hand triongle) and mean
square contingency coefficients for the same variables, when only some versus no participation is
distinguished (in the upper right-hand triangle)

Y, | Ys | % | Ye | Ye | Ye Yu Yue Activity
Y, 2265} .1072| .1453 | .0263} .2189|.1764 |. -1323 |. -1456| 0104] Comping.
Y,- -0960] .1163 | .0761 | .2858 | .1967 |. -1616 |. -1053] 1126] Fishing,
Y, 0920 -2267 | 1013} .1408 }.2665 |. 1424 |. -1348 | .17551 Bicycling.
Y,- 0639) .1454| -0658 | .3413 |.1883 |. -1220 |. -1126 | .1648|Horseback riding.
Y,. .0733| .0911].0759 1747 |.1925 |. 2499 | -3984 | .2407 | Driving for pleasure.
Y. -3707 | .1229].1082 | .1244 3004 |. -1831 -1989 | .2156| Seating.
Y,. -2065] .2813] .2202 | .2002 |.3934 3437 |. -2290 } .2442|Swimming.
Y,. -1596 | .0579}.0981 | .0635 | .4655 |.2847 117}. 0689 | .1258 |Water skiing.
Y, -1431 | .3622].1859 | .1626 |.2244 |.4201 }. 2872 | . :2217|.3179|Gomes, sports
Yio -0840 | .2167|.1183 | .0578 |.1524 |.2284 |. 1255 |. -1415 4.1175 |Hiking.
Yue +1185 | .1662].0942 | .1658 |.1573 |.2286 |. 2062 2956 |.1668 |Nature walks.
Yue -1799 | .13051.1066 | .2706 |.2392 |. 3820 |. 3188 |.2279 |Picnicking.
Yue -0087 | .1561].0321 | .2240 | 0692 |.1628 |. 21379 +2878 | - Walking for pleasure.
Y -0626 | .0843}.0686 | 3574 |.1418 .1811 |. -2508 -2506 |Sightseeing.
Y 1546 | .1625].1154 | -2657 |.1763 |.2687 |. 2278 +1806 [Outdoor events.



Table 2. Construction of independent variables in recreation regression computations

Definition

Voriable Possible values
X, Linear age .... 121099...

X, Quadratic age 144 to 9,801

X, -Cobic age. 1,728 10 970,299.

X, -Rurality . :

X, —SMA city .

X, —Urbanization. 1t0 8.2... cece eee

~Married
'» Child impedanc:

—Meaningfulness of response on employment status
of S.P.
X,o5.P.'s occupation (status, prestige).

X,,-S.P."s occupation (middle classness)
X,,-Meaningfulness of response on employment status

of head. .
X,y-Head’s occupation.
Xj4-S-P.'s completion of high schoo
Xje°5.P.'s education

X,«-Previous farm residence.
X,,-Response on health
XjHealth of S.P.
Xje-Physical impairments of S.P.
Xo—Per copita income in S.P. family linear
X,,-Ouadratic per capita income .
Xzx-Cubic per capita income ...
Xqy-Family income ....
X «Square fomily income.
Xqe-Cubic family income .
Xje-Morital status nonrespons:
Xqr~Education nonresponse
Xy—Income nonresponse .
Xje-Previous form residence nonresponse .
Xyo-Color .

Age of sample person (S.P.).
Square of age of S.P.

Cube of age of S.P.

Rural farm (=0), others (= 1).
Not in SMA (=0), in SMA (=1).
Reproduces col. 15, card 1.

From: Urbanized oreo 3 million or more (=1) to rural

S.P. is married (0), unmarried (= 1).

No. children in family (=0).

Youngest (child or sibling) is 12 or over (=1).
Youngest is 5 to 11 (=2).

Youngest is under 5 (= 3).

S.P. at work or looking (=0), other (=1).

Codes:
00 to 05 (=1).
06 to 09 (=2).
10 to 13 ).
14 to 27 (24).
28 to 36 (=5)-
37 up (=6).
Codes 06 to 27 (=1), others (=0).
See X,.
See Xyo-

High school incomplete (=0), others (=1).

From never ottended (11) through elementary (31-38),
high schoo! (41-44) and college (51-56).

Yes (-0), no (=1).

Response (=0), no response or don’t know (= 1).

Excellent (= 1) through poor (= 4).

None (=0), some (=1) to limits recreation activity (=2).

Col. 61 divided by col. 37.
Square of Xo.

Cube of Xzo-

Col. 61.

x3.

xi.

No response (=1), some (=O), zero st. dev.
No response (=0), some (~1).

Some (=0), none (=1).

Some (=0), none (= 1).

White (=0), nonwhite (= 1).

of evidence were used to judge the worth of the
resulting factor loadings. in the first place, the
measures of ‘‘variance explained,” the latent roots,
can be examined, These roots are helpful in deciding
how many factors to attempt to identify. Inthe second
place it was possible to compare the results with
hypotheses rather well formulated in advance of the
numerical work. The agreement here seems to be
quite close and argues in favor of the serious
acceptance of the factors. The third check consisted
of a comparison of the factor patterns independently
arrived at for the eight white region-by-sex sub-
populations, The similarities found here lend further
support to the above.

Figure 1 is a plot of the order of size of each of
the latent roots of the correlation matrix (lower

78

half of table 3) against its size. The only ‘‘rapid’’
drop as one moves from the first to the fifteenth
root is between the first and the second. If one were
to take exclusively a ‘rate of decrease’? criterion,
then he would have stopped trying to rotate or to
explain factors after noting that the first principal
axis one is a general factor.

However, armed with sufficient imagination and
bolstered by the sample size of 3,647, the drop
between the fourth and fifth roots and crossing the
unit variance was taken as evidence of four factors.

Nonetheless each integer number from 3 to 11 of
latent vectors were subjected to varimax rotation
and the patterns examined. All of the factor patterns
for five or more roots yielded at least one factor
which could be interpreted as only one original



Table 12. Standardized regression coefficients for cases of declared statistical significance

[Note: Coefficients of variables X, through X,, X,, through X,, ond X;, through Xy_ ore partial on one another, coefficients of
variables X, through X,, are partial on these previously removed and one another, while coefficients of Xzp through Xj, are
portial on all other variables}

Dependence pattern of Y,
Northeast North Central South West
Male | Female | Male | Female | Male | Female | Mole |Femole

Independent variable Group

Linear .. 1x, 1.326 1.944
Quadrati 1x, “3.115 -3.655
Age cubic... 1x, 1.551 1.709
Opposite of rurality. 1x,
SMSAY city 1x,
Urbanization. 1
1

Unmarriedness .
Child impedance .
S.P. other than at work.
S.P. occupation status .
S.P. occupation moderateness of status .
Head other than at work
Hecd's occupation status.
S.P. completed high school .
S.P. education status...
No previous farm residence
No response or DK on health
Poomess of health ..
Presence of impairments. .
Per capita income:

<> > K€ DC D6 EDC PE DEC DK DK EK DE DC

WX,
MH X,
HX,

A37
408

Hit
Ui
i

X, --531
x,
Xx,
Education no response 1x
x,
x
x

1.558)
985

104

Income no respons:
jence, no response

118

Dependence pattern of Y,
Northeast North Central South West

Independent voricble Group |Wole | Female | Male | Fenole | Male | Female | Mele | Female

tx, -2.145| 1.736
1X, 3.328| -3.978|

Age cubic... 1x, -1.585] 2.115}

Opposite of rurality xX

SMSA’ city 1x

Urbanization . fl
f

Unmarriedness .
Child impedane
S.P. other than at work.
S.P. occupation status .
S.P. occupation moderateness of stotus.
Head other than at work
Head’s occupation status.
S.P. completed high school ....
S.P. education stotus ..
No previous farm residence .
No response or DK on health.
Poomess of health ....
Presence of impairments .

+105)

122

+157

E> CHK DEH DEK DE DE PE CCK EEK

89



Portion of Predicted Y3Scores Derived from X: , X2,and X3

40+

A

Y, Scores

35 + Equation of the curve:
s X-40
¥g=-4.77 (25)

30 +

|

+8.56 (=)?

18.5
y

é

“4.21 (=

|

a

!
67.7 Agein
Years

-10 +4

APPENDIX A - FIGURE 3

92