GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 171

Weather and Individual HappinessYoshiro Tsutsui

January 2011; revised March 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Weather and Individual HappinessYoshiro Tsutsui
Osaka University
Abstract
This paper investigates the influence of weather on happiness. While previous studies
have examined climatic influence by comparing the well-being of people living indifferent regions, this paper focuses on how daily changes in weather affect individuals
living in a single location. Our data set consists of 516 days of data on 75 students from
Osaka University. Daily information on outside events, as well as the daily physicalcondition and individual characteristics of the respondents, are used as controls.
Subjective happiness is negatively related to temperature and humidity. In a quadraticmodel, happiness is maximized at 13.9 degrees Celsius. The effects of othermeteorological variables—wind speed and precipitation—are not significant. The
sensitivity of happiness to temperature also depends on attributes such as sex, age, andacademic department. Happiness is more strongly affected by current weather
conditions than average weather over the day. While sadness and depression (negative
affect) are affected by weather in a similar way to happiness, enjoyment (positive affect)
behaves somewhat differently.
JEL Classification Number: I31, Q51, Q54
Keywords: happiness, weather, daily web survey, Osaka region
Correspondence to:
Graduate School of Economics, Osaka University
1-7 Machikane-yama, Toyonaka, 560-0043 Japan
Phone: +81-6-6850-5223
Fax:+81-6-6850-5274
E-mail: tsutsui@econ.osaka-u.ac.jp
Running title : Weather and Individual HappinesI am grateful for the insightful comments by two anonymous reviewers of this journal, which
triggered a revision and extension of the earlier version. Financial support from the 21st Century
Center of Excellence (COE) and Global Center of Excellence (GCOE) programs of Osaka
University is gratefully acknowledged.

1.

Introduction

This paper seeks to identify the effect of weather on happiness. Although economists areinterested in the material factors shaping happiness, such as income (Frey and Stutzer 2002),
happiness is known to depend on a broader range of variables, including education, health, andpersonal characteristics such as age, gender, ethnicity, and personality (Dolan et al. 2008).
Climate and the natural environment also affect happiness.1 There have been manystudies arguing that climate is an important element of quality of life (e.g. see Moro et al. 2008,
Oswald and Wu 2010).2 In spite of the importance of climate, a relatively limited number ofstudies have analyzed its influence on happiness (Dolan et al. 2008).3
A survey of earlier studies on the impact of climate on happiness indicates the current
state of this field of inquiry. Rehdanz and Maddison (2005) analyzed a panel of 67 countries andfound that temperature and precipitation have a significant effect on happiness. Specifically,
people prefer higher mean temperatures in the coldest month and lower temperatures in the

1
2

Recall the famous lyric by the Carpenters: “Rainy days and Mondays always get me down.”
Additional direct evidence for the fact that people regard a pleasant climate as essential for agood life and for personal satisfaction is obtained from a large-scale survey conducted by Osaka
University in 2007 and 2008. In that survey, respondents were asked to select a prefecture inwhich they wished to live and to select the reasons for their choices. Of the 16 possible reasons,"Nice climate and rich natural environment” was tied for the most common.
3
Several articles analyze the effect of climate on life patterns. For example, Maddison (2003)
demonstrated that climate is a significant determinant of expenditure patterns. Hoch and Drake(1974) investigated the relation between climate and wages, under the hypothesis that higher
money wages compensate for a lower quality of life. Maddison and Bigano (2003) studied therelationship between climate and wage and home price differentials in Italy. Van Praag (1988)
researched the dependence of household costs on climatic conditions, and estimated a climate
index and climate equivalence scales for European cities. Bigano et al. (2008) analyzed theeffect of climate on sea levels and tourism flows.
-1-hottest month. Those living in regions with many dry months prefer more precipitation.
Examining the data on Ireland, Brereton et al. (2008) found that wind speed has a significant
negative influence on happiness, while the effects of increases in both January minimum andJuly maximum temperatures are positive and significant. Using the first two waves of theRussian National Panel data set on 3,727 households in 1993 and 1994, Frijters and van Praag(1998) revealed that while temperature and precipitation exert a measurable influence on
self-reported happiness and on the cost of living in Russia, the effects of climate in that nation
are different from those in the rest of Europe, an incongruity that “is probably due to the greater
range of climate in Russia.”
Psychologists have studied the relationship between mood and weather. Recently, using
three large-scale German surveys, Kämpfer and Mutz (2011) found that respondents surveyed
on days with exceptionally sunny weather reported higher life satisfaction compared withrespondents interviewed on days with “ordinary” weather. Using data from a large-scale
depression-screening program in the south of the Netherlands, Huibers et al. (2010) reported
that the prevalence of major depression and sad mood showed seasonal variation, with peaks inthe summer and fall. Eisinga et al. (2011) found that television viewing time in the Netherlands
is related to weather.
Most of these previous studies have examined the effect of climate by comparing the-2-happiness of the residents of different regions or countries. Although the studies conclude thathappiness is affected by regional differences in climate, they are unable to assess whether thehappiness of an individual responds to daily weather variations. Answering the latter question
requires time series data on individual happiness rather than cross-sectional data. Thus, thecentral question in this study - whether the happiness of individuals varies with daily weatherchanges – has not yet been definitively answered.
One notable exception is Schwarz and Clore (1983), who telephoned 84 German subjects
on sunny and rainy days to ask about their immediate mood (momentary happiness) andwell-being (general life happiness). On sunny days subjects reported higher levels of
momentary happiness, while on rainy days mood was lower. This study suggests thatmomentary happiness depends on current weather. Barnston (1988), using six-week
mood/productivity diaries from 62 students in 1974, report that the weather appears to influencemood and productivity, but only to a small extent.
Recently, three more relevant studies have been published. Denissen et al. (2008)
collected mood data for 1,233 people over 14 days, and found that temperature, wind power,
and sunlight influence negative affect. However, the size of the effect of weather on mood wassmall. Kööt et al. (2011), sampling subjects’ affect for 14 days on 7 occasions per day, foundthat positive and negative affect were weakly related to temperature, and that positive affect was-3-also related to sunlight. Klimstra et al. (2011) identified weather reactivity types by linking
self-reported daily mood across 30 days to objective weather data. They found large individual
differences in how people’s moods were affected by weather, which may hide the effect ofweather on mood as a whole.
A limitation of these studies is the limited number of sampling days: even the longest
study covers only six weeks. In order to investigate the effect of weather on happiness or mood,
it is desirable to analyze data covering the whole year.
To this end, I conducted a daily web survey to collect data on the levels of happiness of
75 college students over 17 months, resulting in 32,125 observations. Additionally, I collecteddaily data on important individual-level control variables. Though many studies have concluded
that the effect of weather is weak (if it exists at all), controlling for individual factors that arelikely to affect happiness (or mood) may increase weather’s effect size. In this paper, daily
information on events that occurred on the same day, and on the physical conditions of the
respondents, are used as control variables (in addition to fixed individual characteristics, or“attributes”).
The rest of this paper is organized as follows: In Section 2, I explain the data and methods.
The subsequent section presents the basic estimation results. In Section 4, I check the robustnessof the results, and extend the basic equation to incorporate individual attributes. Section 5-4-

concludes.

2.

Data and Methods

2.1

The daily web survey

Survey participants consisted of 70 undergraduate and graduate students of Osaka University.
We asked these respondents to report their daily happiness and their evaluation of the day’s
personal events and news. The survey was conducted from November 1, 2006 to March 31,
2008. Since five subjects did not finish the survey, I added five more subjects in the middle ofthe survey period, increasing the total number of respondents to 75. At the outset of the web
survey, detailed data on the attributes (fixed individual characteristics) of each subject werecollected.
Subjects were paid 160 yen per daily survey response. Additionally, those who responded
more than 22 days in a month were paid 1300 yen as a bonus, while those who answered morethan 27 days received 2600 yen.4 The overall daily response rate was about 89%.
The first question in the daily web survey was: “(Q1) How happy are you now?” The
respondents answered this question on a scale of 0 to 10, where 0 was “very unhappy” and 10

4

Respondents were also asked to report their happiness every hour over one day of their choice
per month. Answering this hourly survey was a necessary condition for the monthly bonus.
-5-was “very happy.” I named this variable HAPPINESS.5
Other questions also attempted to assess subjects’ emotional state. Question 5 asked:“What was the most important piece of personal news that you received since responding to thequestionnaire yesterday? How do you evaluate this news?” The answer, labeled P_NEWS,
could range between -5 and 5, where 5 was “very good” and -5 was “very bad.” Question 7
asked about news received via public news media: “What was the most important piece ofnews from television or newspapers that you received since responding to the questionnaire
yesterday? How do you evaluate this news?” This answer, labeled M_NEWS (for “macro
news”), could also range between -5 and 5.
Some questions asked respondents about their physical condition, which I named SLEEP,HEALTH, and STRESS. SLEEP was defined as the answer to the following question: “(Q9) Did
you sleep well last night?” An answer of 1 indicated poor sleep; 2, somewhat poor sleep; 3,
good sleep; and 4, very good sleep. HEALTH was assessed with the following question: “(Q10)
How is your health now?” The answers ranged from 1 (good), 2 (generally good), 3 (generally
not good), to 4 (bad); the variable HEALTH was defined by subtracting the answer to thisquestion from 5. STRESS was defined by the answer to the following question: “(Q11) Do you
feel any stress now?” Answers ranged from 1 (a lot), 2 (a little), 3 (not much), and 4 (none).

5

In section 4.6, I investigate the effect of weather on affect measures other than self-reported
happiness.
-6-

Variables were defined so a higher value corresponded to a physical condition presumably more
conducive to happiness (better health, less stress, etc.).

2.2

Meteorological data

Weather data was obtained from the website of the Meteorological Agency of Japan. Hourly anddaily data on temperature (TEMPERATURE), humidity (HUMIDITY), wind speed(WINDSPEED), precipitation (PRECIPITATION), and hours of sunshine (SUNSHINE) areavailable for Osaka city. The hourly data of TEMPERATURE, HUMIDITY, and WINDSPEED
are the values taken at the beginning of the hour, PRECIPITATION is the total precipitation overthe hour, and SUNSHINE is the fraction of sunshine time over the hour. Since the exact time ofeach subject’s survey responses was recorded automatically, I matched each individual responsewith hourly weather data at the time of the response. However, in order to consider the
possibility that happiness was influenced by the average weather over the entire day rather than
the weather at the time of the survey response, I also included daily averages in the analysis(subsection 4.5).
Although the exact location of respondents at the time they answered the survey is notknown, they were almost certainly in the Osaka region for most of the time, because all subjects
were students of Osaka University when the survey was conducted. Osaka University has two-7-

campuses, one in Toyonaka and one in Suita, which are suburbs of Osaka (see Figure 1).6 The
distance between the two campuses is only about five kilometers, so that the difference inweather between the two is not considerable. Weather data for Suita are not available, while
only limited data are available for Toyonaka. One reason to use Toyonaka’s weather data would
be that it is the location of one of the campuses. On the other hand, the Osaka weather data isricher. Furthermore, the distance between Toyonaka campus and the Osaka City Hall is only 13
kilometers, so that the weather of these two cities does not differ very much. For these reasons I
use the Osaka weather data in my baseline analyses, but I check the robustness of the resultswith the Toyonaka data when applicable. I conclude that using the meteorological data of Osaka
city does not produce large biases in any of my estimates (see subsections 4.1 and 4.3).
Osaka city is located in the middle of Japan, facing Osaka Bay. The daily averagetemperatures for the observation period, which ranged between 5 and 30 degrees Celsius, areshown in Figure 2. The climate of Osaka is mild and characterized by four seasons, of which
spring and autumn are most loved by residents.7 Winter is not severe: the average temperature
in February, the coldest month, was around 5 degrees Celsius, with almost no snow in theobservation years. However, it is hot and humid in summer; the average temperature in August
was around 30 degrees during the observation period. Osaka residents often complain about the67

Out of 75 total subjects, 38 belong to Suita campus, 32 to Toyonaka, and five unknown.
Sei Shonagon described beautiful scenes set in both of these seasons in her famous book
Makurano Soshi (The Pillow Book), written in the 10th and 11th centuries.
-8-high temperature and high humidity of the city in summer. Indeed, the discomfort index (DI)rises to a high value (80) in August.8 The correlation coefficient between DI and temperature
for the observation period is over 0.99, suggesting that high temperatures made people in Osaka
uncomfortable.

2.3

Descriptive analysis of the data

Table 1 presents the means, standard deviations, and maximum and minimum values of thevariables used in this paper, along with the correlation coefficients between HAPPINESS andthe other variables. The observation period is from November 1, 2006 to March 31, 2008, andthe number of observations is 32,125. The means displayed in the table indicate that personal
news is, on average, good (positive), while macro news is generally bad (negative). Averagetemperature is about 15 degrees Celsius; average humidity, about 60%; average wind speed, 2.4m/s; average time of sunshine per hour, about 0.2 hours; and average precipitation per hour,0.12 mm.
The correlations of P_NEWS, HEALTH, and STRESS with HAPPINESS are quite high.
Among the meteorological variables, TEMPERATURE shows the highest correlation withhappiness, followed by SUNSHINE; however, the size of these correlations is much less than8

For an explanation of the discomfort index, see Tselepidaki et al. (1992).
-9-

that of P_NEWS, suggesting that the effect of weather is relatively limited, if it exists at all.

2.4

Statistical methods

I regress HAPPINESS on the variables representing the conditions of the subjects, themeteorological variables, and the day-of-the-week dummies.9 Thus, the basic equation to be
estimated is:

,

,

∑

,

,

where

,

,

,

,

,

,

is an individual-level fixed effect and

,

,

,

, ,

(1)

is a disturbance term.

I estimate all the equations with three models: ordinary least squares (OLS), a fixed
effects model, and a random effects model, and then for each regression select a model using a
Hausman test (random effects model vs. fixed effects model) and an F-test of the same constant(OLS vs. fixed effects model). 10 Section 4 contains several modifications of the basic
regression equation, included as robustness checks.

9

In subsection 4.4, I check whether the results are robust to inclusion of respondent attributes
in the regression.
10
Since happiness is an ordered variable, it should be estimated with an ordered probit (logit).
However, because it is difficult to interpret the effect sizes in such models, and because
controlling for individual-level effects is important, I use the fixed and random effects models.
- 10 -

3.

Estimation results of the basic equation

The estimation results are shown in Table 2. In the first column, I show the results for the basic
equation (1).11 All control variables associated with the conditions of the subjects are highly
significant, with reasonable signs. The coefficients on P_NEWS, HEALTH, and STRESS areespecially large, while M_NEWS and SLEEP also have some impact. Estimates forday-of-the-week dummies reveal that the subjects are significantly happier on Sunday andSaturday than on Monday. The magnitude of the weekend effect is comparable to that of macro
news.
Among the meteorological variables, temperature, humidity, and sunshine are significant
at the 5% level. The estimated coefficients of temperature and humidity take a negative sign,
implying that the students of Osaka University are happier when the temperature and humidity
are lower. The coefficient on sunshine also takes a negative sign.
In the second column of the table, I present the results when all control variables areomitted.12 The adjusted R-squared falls from 0.628 to 0.0024, confirming the importance of thecontrol variables. However, the sign and significance of the estimates of the meteorologicalvariables does not change much, suggesting that the meteorological variables are not correlatedwith the control variables; temperature, humidity, and sunshine are negative and significant at

11
12

In this case, the fixed effects model was selected.
In this case, the random effects model was selected.
- 11 -

the 1% level, while the other variables are not significant.
The finding that subjects liked lower temperatures is consistent with our intuition, sincesummer in Osaka is generally perceived to be too hot. However, it does not seem reasonable toassert that temperature has a linear negative influence, because the temperature in winter israther low in the Osaka region. Thus, it is reasonable to assume that there is a temperature
within the observed range that maximizes happiness. To assess this, I add squared temperature(TEMP_SQ) to the basic specification; the estimation results are shown in the third column ofTable 2. The linear term and the squared term are significantly positive and negative,
respectively, at the 1% level. This result implies that the subjects are the happiest at 13.9
degrees Celsius, which is the average temperature in April and November.
The result that longer sunshine time lowers happiness contradicts our intuition. The
reason of this result may be that SUNSHINE takes a zero value during nighttime, during whichpeople tend to be happier (Kahneman et al., 2004). To assess this effect, I added hour dummies
for each hour of the day to the basic equation. Subjects were significantly happier from 19:00 to
23:00 than during the daytime. The coefficients on SUNSHINE and HUMIDITY became
insignificant when hour dummies were included, while that on TEMPERATURE remained
significantly negative at the 1% level (results not shown). When hour dummies were added tothe model with no control variables, the coefficient on SUNSHINE became significantly- 12 -

positive.
In addition, I re-estimated the basic equation while excluding all data reported at night.
Estimates using data from 7:00 to 17:00 are presented in the fourth column of Table 2. The
number of observations was reduced to 12,187. While temperature remained significant at the
5% level, SUNSHINE became insignificant. Given these results, I conclude that the negative
coefficient on SUNSHINE is spurious, and merely reflects the fact that people are happier atnight.
Since some meteorological variables are more correlated with each other than with
HAPPINESS, a multicollinearity problem is suspected. Thus, I re-estimated the model including
only one meteorological variable at a time. The coefficient on humidity became insignificant,while the other coefficients did not change much (results not shown).
Overall, temperature has the most noteworthy effect among the meteorological variables.
Still, the magnitude of the estimate is not large: the change in happiness brought about by analteration of 20 degrees Celsius is equivalent in size to a change in one point of macro news on
a ten-point-scale. This result is consistent with previous studies (Denissen et al. 2008, Barnston
1988).

4.

Robustness checks and extensions- 13 -

In this section, I check the robustness of the results obtained in the previous section and extend
the basic equation in several ways. First, I assess whether the results are valid when I use datafrom Toyonaka city instead of Osaka city for some of the meteorological variables. Second, I
separate the total period into “summer” and “winter” seasons and check if the result in theprevious section on temperature is confirmed. Third, since the exact location of respondents is
not known, I examine if lack of this information brings about large biases. Specifically, I utilize
the information on days when the respondents travel and on days when they attend classes toinfer whether subjects stayed near the Toyonaka-Osaka region during the bulk of theobservation period. Fourth, I extend the model to incorporate variables representing theattributes (fixed individual characteristics) of respondents - sex, age, living standard, body massindex, etc. I examine not only the effect of these variables on happiness, but also their effects on
the sensitivity of happiness to weather. Fifth, I estimate the basic equation with daily
meteorological data instead of hourly data. Finally, I determine if the meteorological variables
have the same effect on alternative positive and negative affect variables (such as sadness,pleasure, and depression) that they have on happiness.

4.1

Examination of possible bias due to the use of Osaka city data instead of Toyonaka citydata

- 14 -

Let me begin with the analysis using the Toyonaka city data. Since one of the two campuses ofOsaka University is in Toyonaka city, it might be the case that subjects spent more time in
Toyonaka city than in Osaka city. Thus, it is interesting to check the size of the biases arisingfrom the use of Osaka city weather data instead of Toyonaka city data. In a re-estimation of thebasic model, I use Toyonaka data for temperature (T_TEMPRETURE), wind speed(T_WINDSPEED), and precipitation (T_PRECIPITATION), and Osaka city data for humidity
and sunshine (as these latter two are not available for Toyonaka city). The estimation results arepresented in the left-hand columns of Table 3. The estimates are quite similar to those in Table 2,
implying that using the alternative city data does not affect the results. The right-hand columnsof Table 3 show the results when the data from Osaka city, HUMIDITY and SUNSHINE, aredeleted; the estimates are again quite similar. This is not surprising, since the two cities are quitenear, so that the correlation between the Osaka and Toyonaka data is 0.992 for temperature,
0.495 for wind speed, and 0.389 for precipitation. These results support, at least partially, theuse of the meteorological data of Osaka city, even though respondents’ exact locations are notknown.

4.2

Effect of temperature is opposite in summer and winterIn section 3, it was demonstrated that happiness increases with temperature up to about 14- 15 -

degrees Celsius, and then decreases. This result leads to the prediction that in summer people
like lower temperatures, while in winter they prefer higher temperatures. To see if this is reallythe case I divide the total observation period into two seasons, warm (“summer”) and cold(“winter”), and re-estimate the basic equation; the former period is from May 16 to November
15, while the latter includes the remainder of the sample period.13
The estimation results are presented in Table 4. In the first columns, the results for“summer” are shown. Most of the estimates are similar to those in Table 2, confirming the basic
results. However, although the key coefficient of TEMPERATURE takes a negative sign, it isinsignificant at the 10% level. In the second column, I show the estimates when meteorologicalvariables other than TEMPERATURE are omitted. The coefficient on TEMPERATURE becomessignificantly negative at the 5% level, supporting the prediction. In the table’s third column, theresults for “winter” are presented. The coefficient on TEMPERATURE is significantly positiveat the 5% level, again confirming the prediction. When meteorological variables other than
TEMPERATURE are omitted, the result is unchanged. These results indicate that people in the
Osaka region do not like higher temperatures in summer, but do like them in winter, as one
would expect.14

Note that the total period started in “winter” time and ended in “winter” time sixteen months
later; thus, the “winter” sample consists of two separated periods, while the “summer” time
consists of one consecutive period.
14 I also re-did the estimation dividing the total period into three subperiods: “winter” definedas January to March, “summer” defined as July to September, and “other seasons” (spring and13- 16 -

4.3

Analysis using data on travel and class attendance

One potential problem with the survey data is that the location of respondents at the time of
response is not recorded. However, the respondents are all students of Osaka University, so thatthey live within a relatively small region, near the Toyonaka-Suita area, over which hourly
weather is almost uniform. Indeed, in subsection 4.1, I confirmed that the use of Toyonaka or
Osaka city data does not change the results at all. Thus, the use of Osaka data is acceptable anddoes not lead to large biases, except on days when respondents traveled away from the area. In
this subsection, I will further examine the robustness of the results, utilizing two additional
location variables that give some indication of respondents’ locations.
In the questionnaire, I asked the respondents to rank the importance of their mostimportant personal event on that day, and to identify the event. One hundred and forty sevenanswers listed travel as the most important event. This is a small number out of the total of
32,125 answers (0.5%). This does not mean that these are all the trips the subjects made overthe sample period, since in most cases they stopped responding to the survey while they weretraveling for a long time, especially when they went abroad. On the other hand, subjects
probably reported their trips when they could, because traveling represents an important
autumn). The coefficient for winter was positive and that for summer was negative, but they
were insignificant at the 10% level. The reason for these insignificant results is probably thatvariation of temperature is small within each season.
- 17 -

personal event. Therefore, it is reasonable to suppose that subjects’ responses were made near
the Osaka region, unless they explicitly noticed that they were traveling.
When I add a cross term between TEMPERATURE and a travel dummy (equal to unity if
a respondent was traveling and zero otherwise) to the basic equation, the coefficient of the crossdummy is positive (p-value of 23%). Although the significance level is low, the result suggeststhat the effect of TEMPERATURE became smaller when subjects made a trip, suggesting that
deleting the traveling samples strengthens the sensitivity of happiness to temperature. In
addition, estimation results when deleting traveling samples produces almost identical results to
those shown in Table 2, suggesting that the results in the previous section are robust (results notshown). Estimation results for the basic equation using only traveling samples (N=147) are
shown in the left-hand columns of Table 5. While P_NEWS and STRESS are significant andpositive, all meteorological variables, including TEMPERATURE and SUNSHINE, areinsignificant; this is exactly what one would expect, although it may also arise from the small
sample.
From December 1, 2007 to March 31, 2008, I collected data on whether respondents
attended class on the day of the response. The total number of responses during this period is7,459, while the number during which students attended class is 2,342. It is essentially certainthat students were in the Osaka area when the “attended class” responses were made.

- 18 -

To measure the effect of attending class on happiness and on its sensitivity to temperature,
I added a dummy variable CLASS that takes a value of unity if a subject attended class on the
day of response and zero otherwise, as well as a cross term between TEMPERATURE and the
CLASS dummy (CLASS*TEMP), to the basic equation; the estimation results are presented in
the middle columns of Table 5. The coefficients on the variables of news and physicalconditions are quite similar to those in Table 2. The coefficient on CLASS is negative, but notsignificant at the 10% level, suggesting that attending a class might have lowered happiness. As
for the meteorological variables, one notable result is that the coefficient on TEMPERATURE is
positive and significant at the 10% level, suggesting that higher temperature relates to higher
happiness. This is reasonable because the sample period is in the winter season.
Day-of-the-week dummies are not significant here. This is also reasonable, because the period
includes a two-week New Year vacation and term examinations in early February, followed by
one and a half months of spring vacation, so that the distinction between weekdays andweekends was not very important during the period. The cross term is positive but insignificant,suggesting that attending class does not affect the sensitivity of happiness to temperature. This
last result has an important implication for the current paper. Reports on days on which subjects
attended a class were definitely sent from Toyonaka-Osaka region. The result that classattendance does not affect my estimates suggests that subjects also stayed in the- 19 -

Toyonaka-Osaka region on most of the days when they had no classes. This result is consistent
with the report that subjects made only 147 responses while traveling.
Weekdays and weekends might see different effects on the sensitivity of happiness tometeorological variables. To assess this, I added a cross term between TEMPERATURE and a
weekend dummy to the basic equation; the estimation results are presented in the right-handcolumns of Table 5. The cross term is not significant at all, indicating that the sensitivity ofhappiness to temperature does not differ between weekdays and weekends.
To reiterate, the effect of temperature in Osaka city on happiness when respondents weretraveling is smaller than when they were not. In addition, the sensitivity to temperature does notdiffer based whether or not subjects attended class on the day or whether it was a weekday orweekend. These results suggest that the subjects made most of their answers while in the
Toyonaka-Osaka region, so that biases from day-to-day location changes is very small.

4.4

Effects of attributes on the sensitivity of happiness to temperature

At the start of the web survey in 2006, I sent a paper questionnaire to the respondents toinvestigate their attributes (fixed individual characteristics). Thus, it is possible to examine
whether the inclusion of these attributes as regressors changes the estimates of the basic modelfrom section 3. The variables that I add to the basic model are a dummy variable for male sex- 20 -

(DMAN), age (AGE), current living standard ranked from 0 to 10 (LIVING), living standard
when subjects were 15 years old (LIVING15), a variable coding the highest education level that
subjects’ fathers finished (F_ACADEMIC, which takes larger values for higher education levels),
an equivalent variable for subjects’ mothers (M_ACADEMIC), smoking habit (SMOKING)ranging from 1 (do not smoke) to 6 (more than two boxes per day), body mass index (BMI),
strength of religious belief on a five-point scale (RELIGION), and a dummy variable for area ofacademic study that takes a value of unity when respondents belong to science departments and0 when they are affiliated with humanities or social science departments (SCIENCE).
Descriptive statistics for these variables are presented in Table 6. Out of 55 respondents
who answered all the questions, the number of males is 38 (69%). Age ranges from 18 to 28
years old, with an average of 21.5. Only three subjects smoke, and these are all light smokers.
BMI ranges between 15 and 33, with an average of 20.8. Most of the subjects are not deeply
religious.
Estimation results for the model when these attributes are included are presented in Table
7. The number of observations decreases to 20,131. The left-hand columns show the results of
OLS estimation.15 The coefficients on all the variables of the basic equation are qualitatively
the same as those in Table 2, except that the coefficient on HUMIDITY becomes insignificant

15

Since the attributive variables have only one observation per subject, fixed effects models
that include these variables cannot be estimated.
- 21 -

and that no coefficients on day-of-the-week dummies are significant.
Most of the attributes are significant, and the signs of their coefficients are consistent withintuition and with previous studies (e.g. Frey and Stutzer 2002). Females are happier than males,
and younger students are happier than older students. Higher current and past standards of living
are positively correlated with happiness. Those whose mothers have more education are happier,while for fathers the result is the opposite.16 The coefficient on SMOKING is negative but
insignificant (possibly due to the fact that there were no heavy smokers). Higher BMI iscorrelated with higher happiness. Religious people are happier. Those who belong to science
departments are unhappier than those affiliated with humanities and social science departments.
It is interesting to ask whether the sensitivity of happiness to weather conditions differs
depending on a respondent’s attributes. To check this, I constructed cross terms between theattributes and TEMPERATURE and added these to the extended equation shown in Table 7. The
estimation results are presented in Table 8. Estimates for variables of physical condition andday-of-the-week dummies are omitted to save space, since they are almost the same as those in
Table 7. In the first column, cross terms between female and male dummies and
TEMPERATURE (DWOMAN*TEMP and DMAN*TEMP) are added. Interestingly, only males
prefer low temperatures, while females are not affected by temperature, which is consistent with

16

This result is not easy to interpret.
- 22 -

the result of Barston (1988).
In the second column, cross terms between TEMPERATRE and academic department
dummies (SCIENCE*TEMP and HUMANITY*TEMP) are added. Science majors are negatively
affected by higher temperatures, while humanities majors show insignificant sensitivity. This
may simply be due to the fact that science majors contain a much higher percentage of males
than humanities departments.
In the third column, a cross term between AGE and TEMPERATURE is added. The crossterm is significantly negative at the 5% level, indicating that older students dislike hightemperatures more. In the fourth column, a cross term between living standard and
TEMPERATURE is added; however, living standard does not affect sensitivity to temperature.
In sum, the sensitivity of happiness to temperature does depend on certain individual
attributes.

4.5

Hourly weather data vs. daily average weather data

Various specifications, including the basic equation, have so far been estimated with hourly
weather data on the right-hand side. However, it might be the case that happiness is influenced
more by overall weather over the course of a day than by weather at the exact time of the survey.
To investigate this possibility, I re-estimated the basic equation with daily weather data.

- 23 -

Estimation results using daily data for Osaka city are presented in the left-hand columns ofTable 9. In the table, a daily average weather variable is identified with a “D_” at the beginningof the variable name. D_TEMPERATURE, D_HUMIDITY, and D_WINDSPEED are daily
averages, while D_SUNSHINE and D_PRECIPITATION are total daily amounts.
The estimates for the control variables, including day-of-the-week dummies, are almost
identical to the estimates in the specifications using hourly weather data. However, the estimatesfor meteorological variables are somewhat different. Among them, D_TEMPERATURE is only
noteworthy at the 1% significance level (Table 9); the other four variables are not significant at
all. Comparing these results with those obtained with hourly data suggests that hourly data havea stronger effect on HAPPINESS than do daily average data, and that the effect of temperature is
the most robust.
To further examine the former suggestion, I estimated a regression incorporating bothhourly and daily meteorological variables, shown in the right-hand columns of Table 9. Hourly
data are significant for humidity and sunshine, while daily data are not, suggesting that theformer has more explanatory power. For temperature, both hourly and daily data are
insignificant; however, the hourly data have a negative coefficient (p-value of 15%), while thedaily data take a positive sign. These results support the notion that hourly data have more
explanatory power, suggesting that happiness depends on current weather rather than on average- 24 -

weather over a day.

4.6

Impact of weather on other affect variables

In the questionnaire, I solicited additional measures of positive and negative affect. The first ofthese is “(Q2) Are you sad now?” Possible responses to this question are 1 (sad), 2 (somewhatsad), 3 (somewhat not sad), and 4 (not sad). I define the variable SADNESS as the answer to thisquestion. The second is “(Q3) Are you enjoying life now?” Possible responses are 1 (enjoyinglife), 2 (somewhat enjoying life), 3 (somewhat not enjoying life), and 4 (not enjoying life). I
define the variable ENJOYMENT as 5 minus the answer to this question. Finally, respondents
were asked “(Q4) Are you depressed now?” They had four possible responses: 1 (verydepressed), 2 (somewhat depressed), 3 (somewhat not depressed), and 4 (not depressed). I
define the variable DEPRESSION as the answer to this question. Note that all of these variables
are defined so that a higher value indicates a more positive affect. It is interesting to ask how
these variables are affected by the weather.
In Table 1, descriptive statistics for SADNESS, PLEASURE, and DEPRESSION are
shown. The correlation coefficients between HAPPINESS and these three variables range from
0.4 to 0.6. The correlations between these affect variables and the various conditions of thesubjects are quite similar to those of HAPPINESS. However, the correlations of these affect- 25 -

measures with the meteorological variables are slightly different from those of HAPPINESS.
For example, the correlation with humidity is positive for ENJOYMENT and DEPRESSION,
while it is negative for other measures of affect.
In Table 10, I present regression results for the basic model using these three measures as
the dependent variable. Results for negative affect variables, SADNESS and DEPRESSION, areconsistent with the results for HAPPINESS, in that temperature has a negative effect onhappiness. However, SUNSHINE has positive effects on SADNESS and DEPRESSION. On theother hand, positive affect, PLEASURE, behaves somewhat differently. Higher temperaturecorrelates with higher PLEASURE, which is the opposite of the outcome for HAPPINESS. Thus,
the effects of meteorological variables on well-being depend on how well-being is measured.

5.

Conclusions

This paper investigates the time-series dependence of happiness on weather for individuals
living in a single location, while most earlier studies examine the effects of differing climates on
geographically dispersed populations. Although there are some studies that focus on how daily
weather affects mood, the present study is unique in that the data covers 17 months, which ismuch longer than the six weeks or less covered in previous studies. Additionally, this study
includes detailed data on the individual attributes, physical conditions, and daily experiences of- 26 -

the respondents, which allow more robust controls than in past studies.
Empirical analysis reveals that happiness is negatively related to temperature in a linear
model, and is maximized at 13.9 degrees Celsius in a quadratic model. Humidity and sunshine
also have a negative effect on happiness; however, the result for sunshine is found to be
spurious: the effect is entirely due to the fact that sunshine is zero at night and people arehappier at night. The other meteorological variables, wind speed, and precipitation, do notsignificantly affect happiness.
I check the robustness of my results in various ways. The survey I use does not identify
the exact locations of respondents; however, all of the respondents were students of Osaka
University, so that they stayed near campus for most of the sample period. Using subjects’
reports on travel and class attendance, I showed that the use of Osaka city weather data does notproduce large biases. In addition, using detailed data on subjects’ attributes, I found that thesensitivity of happiness to temperature depends on attributes such as sex, age and academic
major. It is also the case that happiness is more strongly affected by current hourly weather thanby averaged weather over the entire day. Finally, while negative affect is affected by weather ina similar way to happiness, positive affect behaves in a somewhat different manner.

- 27 -

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- 29 -

Table 1.

Descriptive statistics
CORRELATION withMean

Std Dev

Minimum

Maximum

HAPPINESSHAPPINESS

5.867

1.972

0

10

1

SADNESS

3.172

0.853

1

4

0.501

1

ENJOYMENT

2.450

0.907

1

4

0.597

0.357

1

DEPRESSION

3.075

0.949

1

4

0.448

0.728

0.362

1

P_NEWS

0.522

2.355

-5

5

0.644

0.415

0.542

0.439

M_NEWS-0.415

2.043

-5

5

0.183

0.112

0.117

0.137

SLEEP

2.616

0.976

1

4

0.172

0.190

0.080

0.161

HEALTH

2.270

0.787

1

4

-0.308-0.289-0.233-0.307

STRESS

2.005

0.911

1

4

0.403

0.392

0.298

0.427

TEMPERATURE

15.103

8.126

-0.1

36.9

-0.044-0.030-0.021-0.038HUMIDITY61.24514.34415

94-0.001-0.006

0.009

0.001

WINDSPEED

2.385

1.306

0

9.9

-0.008-0.0001-0.007-0.009SUNSHINE

0.201

0.366

0

1

-0.031-0.004-0.053-0.015PRECIPITATION

0.117

0.807

0

26

0.0002-0.003-0.0002-0.004

Note: The number of observations is 32125.

30

SADNESSENJOYMENT

DEPRESSION

Table 2.

Estimation results for the basic equation

Variable
P_NEWS
M_NEWSSLEEPHEALTHSTRESSSUNDAYTUESDAYWEDNESDAY
THURSDAYFRIDAY
SATURDAYTEMPERATURE
TEMP_SQHUMIDITY
WINDSPEEDSUNSHINE
PRECIPITATION
Constant
Adjusted R2
Number of observations
Hausman test
Estimation method

Coefficient P-value
Coefficient P-value
Coefficient P-value
Coefficient P-value
0.397[.000]
0.397[.000]
0.374[.000]
0.065[.000]
0.065[.000]
0.063[.000]
0.029[.001]
0.028[.001]
0.038[.007]-0.227[.000]-0.227[.000]-0.302[.000]
0.322[.000]
0.322[.000]
0.406[.000]
0.051[.044]
0.053[.036]
0.066[.130]
0.046[.066]
0.046[.066]-0.010[.811]
0.030[.228]
0.029[.245]
0.037[.363]
0.005[.833]
0.006[.818]-0.009[.831]
0.048[.056]
0.048[.056]
0.016[.702]
0.064[.010]
0.065[.010]
0.066[.120]-0.003[.003]-0.009[.000]
0.012[.002]-0.003[.035]-0.00042[.000]-0.001[.039]-0.002[.004]-0.001[.058]-0.002[.100]-0.003[.620]
0.007[.331]-0.001[.837]
0.003[.701]-0.080[.000]-0.144[.000]-0.076[.001]
0.002[.951]
0.001[.929]
0.000[.969]-0.002[.831]-0.014[.466]
6.158[.000]
0.628
0.002
0.628
0.651
32123

32123
[.0006]

FIXED

32123
[.2046]RANDOM

12187[.0011]

FIXED[.0044]
FIXED

Note: On the basis of the results of the Hausman test and the F-test of the same constant, estimates of the random effects models are presented
in the second columns and estimates of the fixed effects model in the other columns.
31

Table 3. Estimation results using Toyonaka city data for temperature, wind speed, and precipitation
Independent Variable
Coefficient
P-value
Coefficient
P-value
P_NEWS

0.397[.000]

0.397[.000]

M_NEWS

0.065[.000]

0.065[.000]

SLEEP

0.029

[.001]

0.028[.001]HEALTH-0.227[.000]-0.227[.000]STRESS

0.322[.000]

0.321[.000]SUNDAY

0.052[.040]

0.056[.027]TUESDAY

0.047[.062]

0.047[.059]

WEDNESDAY

0.030[.223]

0.030[.228]THURSDAY

0.006[.799]

0.009[.726]FRIDAY

0.049[.051]

0.050[.045]SATURDAY

0.065[.009]

0.067[.007]

T_TEMPERATURE-0.002[.006]-0.003[.000]HUMIDITY-0.001[.048]

T_WINDSPEED-0.004[.368]-0.003[.413]SUNSHINE-0.079[.000]

T_ PRECIPITATION-0.003[.653]-0.004[.536]

2

Adjusted R

0.628

0.628

Number of observations

32111

32111
[.0015]

Hausman test
Estimation method

FIXED[.0008]
FIXED

Note: T_TEMPERATURE, T_WINDSPEED, and T_PRECIPITATION indicate that the data are those of Toyonaka city.
On the basis of the results of the Hausman test and the F-test of the same constant, estimates of the fixed effects model are presented.
32

Table 4.

Estimates for summer and winter samples
SummerIndependent Variable
Coefficient
P-value Coefficient
P_NEWS
0.383[.000]
0.383
M_NEWS
0.076[.000]
0.077
SLEEP
0.016
[.234]
0.016
HEALTH-0.168[.000]-0.167
STRESS
0.261[.000]
0.260
SUNDAY
0.046[.256]
0.052
TUESDAY
0.046[.256]
0.045
WEDNESDAY
0.040[.321]
0.038
THURSDAY
0.010[.803]
0.011
FRIDAY
0.045[.271]
0.049
SATURDAY
0.093[.022]
0.096
TEMPERATURE-0.003[.153]-0.005
HUMIDITY-0.0004[.685]WINDSPEED-0.0003[.977]SUNSHINE-0.074[.053]PRECIPITATION
0.001[.938]
2
Adjusted R
0.647
0.672
Number of observations
11187
11187
Hausman test[.0012]Estimation method
FIXED
FIXED

P-value[.000][.000][.256][.000][.000][.203][.262][.335][.784][.222][.017][.031]

WinterCoefficient
0.416
0.059
0.026
-0.222
0.330
0.051
0.054
0.037
0.006
0.045
0.049
0.005
-0.001-0.004-0.074
0.008
0.647
17745

[.0006]
FIXED

33

P-value Coefficient[.000]
0.417[.000]
0.059[.020]
0.025[.000]-0.222[.000]
0.330[.125]
0.052[.103]
0.054[.261]
0.035[.857]
0.010[.170]
0.046[.131]
0.049[.024]
0.004[.069][.537][.010][.727]
0.647
17745

P-value[.000][.000][.024][.000][.000][.115][.097][.291][.772][.163][.133][.036][.0024][.0012]
FIXEDTable 5.

Effect of class attendance and weekend on the sensitivity to temperature

Independent Variable
P_NEWS
M_NEWSSLEEPHEALTHSTRESSCLASSSUNDAYTUESDAYWEDNESDAY
THURSDAYFRIDAY
SATURDAYTEMPERATURE
CLASS*TEMPWEEKEND*TEMPHUMIDITY
WINDSPEEDSUNSHINE
PRECIPITATION
Constant
Adjusted R2
Number ofobservations
Hausman test
Estimation method

Coefficient P-value Coefficient P-value Coefficient P-value
0.521[.000]
0.431[.000]
0.397[.000]-0.010[.872]
0.060[.000]
0.065[.000]-0.099[.451]
0.014[.362]
0.029[.001]-0.198[.217]-0.158[.000]-0.227[.000]
0.505[.000]
0.187[.000]
0.322[.000]-0.101[.123]
0.520[.191]
0.017[.702]
0.053[.157]
0.560[.187]-0.035[.423]
0.046[.066]
0.077[.871]
0.031[.474]
0.030[.228]
0.095[.812]-0.006[.897]
0.005[.833]
0.581[.127]
0.025[.558]
0.048[.056]
0.452[.231]
0.046[.284]
0.066[.076]
0.004[.771]
0.007[.072]-0.002[.014]
0.003[.670]-0.0001[.950]-0.006[.512]-0.001[.244]-0.001[.039]
0.099[.260]
0.006[.487]-0.003[.618]
0.247[.634]-0.159[.000]-0.080[.000]-0.154[.592]-0.030[.282]
0.001[.929]
4.969[.000]
0.398
0.761
0.628
147
7459
32123
[.3275][.0003]RANDOM

FIXED[.0010]FIXED

Note: In the left-hand columns, estimation results are presented where only traveling days areused.
The observation period for the results shown in the middle columns is from December 1, 2007
to March 31, 2008. The coefficient on TEMPERATURE is positive, since the estimation period
is “winter”.

34

Table 6.

Descriptive statistics of attribute variables

DMAN
AGE
LIVING
LIVING15
F_ACADEMIC
M_ACADEMICSMOKINGBMIRELIGIONSCIENCEMean
0.691
21.545
5.236
5.400
5.745
4.618
1.055
20.8411.473
0.600

Std Dev Minimum Maximum
0.466
0
1
2.026
18
28
1.563
1
8
1.461
2
8
2.382
2
11
1.769
1
9
0.229
1
2
2.883
15.39733.412
1.052
1
5
0.494
0
1

Note: The number of observations is 55.

35

Table 7. Estimates of the model incorporating attribute variables
Independent Variable
P_NEWS
M_NEWSSLEEPHEALTHSTRESSSUNDAYTUESDAYWEDNESDAY
THURSDAYFRIDAY
SATURDAYTEMPERATURE
HUMIDITY
WINDSPEEDSUNSHINE
PRECIPITATION
DMAN
AGE
LIVING
LIVING15
F_ACADEMIC
M_ACADEMICSMOKINGBMIRELIGIONSCIENCE
Constant
Adjusted R2
Number of observations
Estimation method

Coefficient
0.426
0.084
0.075
-0.312
0.263
0.013
0.035
0.021
-0.0050.031
0.056-0.0040.001
0.000-0.0540.002-0.734-0.0130.095
0.016-0.0170.089-0.0730.044
0.194-0.130
4.610
0.526
20131
OLS

36

P-value[.000][.000][.000][.000][.000][.703][.313][.540][.883][.378][.108][.001][.434][.960][.061][.881][.000][.014][.000][.092][.004][.000][.124][.000][.000][.000][.000]

Coefficient
0.398
0.092
0.062
-0.248
0.268
0.023
0.025
0.017
-0.0150.030
0.062-0.003-0.001
0.005-0.0970.007-0.771-0.0290.126
0.031-0.0230.058-0.2660.044
0.215-0.056
5.012
0.523
20131
RANDOMP-value[.000][.000][.000][.000][.000][.478][.435][.591][.650][.359][.058][.006][.382][.434][.001][.540][.000][.479][.045][.671][.621][.300][.421][.119][.010][.779][.000]

Table 8. Interaction between weather and attributes
Independent Variable
Coefficient
P-value Coefficient
P-value Coefficient
P-value Coefficient
P-value
DWOMA*TEMP
0.002[.352]DMAN*TEMP-0.005[.000]SCIENCE*TEMP-0.006[.000]
HUMANITY*TEMP
0.002[.212]
TEMP
0.021[.061]
AGE*TEMP-0.001[.031]
TEMP
0.000[.953]LIVING*TEMP-0.001[.334]HUMIDITY-0.001[.362]-0.001[.367]-0.001[.382]-0.001[.376]WINDSPEED
0.005[.434]
0.005[.447]
0.005[.457]
0.005[.438]SUNSHINE-0.098[.000]-0.094[.001]-0.097[.001]-0.097[.001]PRECIPITATION
0.007[.534]
0.007[.530]
0.007[.540]
0.007[.530]
DMAN-0.668[.001]-0.773[.000]-0.772[.000]-0.770[.000]
AGE-0.029[.480]-0.029[.474]-0.012[.767]-0.029[.479]LIVING
0.125[.047]
0.126[.045]
0.126[.045]
0.135[.034]LIVING15
0.032[.660]
0.032[.661]
0.031[.671]
0.031[.670]
F_ACADEMIC-0.023[.618]-0.023[.615]-0.023[.614]-0.023[.623]
M_ACADEMIC
0.059[.296]
0.058[.301]
0.058[.298]
0.058[.300]SMOKING-0.266[.421]-0.271[.413]-0.269[.416]-0.263[.426]
BMI
0.044[.120]
0.044[.117]
0.044[.118]
0.044[.120]RELIGION
0.214[.011]
0.214[.011]
0.215[.011]
0.215[.010]SCIENCE-0.059[.771]
0.069[.735]-0.057[.779]-0.056[.781]
Constant
4.946[.000]
4.933[.000]
4.656[.000]
4.962[.000]
2
Adjusted R
0.524
0.524
0.523
0.524
Number of observations
20131
20131
20131
20131
Estimation method
RANDOMRANDOMRANDOMRANDOM
Note: The results for the control variables representing physical conditions and weekday dummies are omitted here to save space. They are almost
identical to those of the random effects model in Table 7.
37

Table 9.

Estimation results using daily average weather data

Variable
P_NEWS
M_NEWSSLEEPHEALTHSTRESSSUNDAYTUESDAYWEDNESDAY
THURSDAYFRIDAY
SATURDAYTEMPERATURE
D_TEMPERATURE
HUMIDITY
D_HUMIDITY
WINDSPEED
D_WINDSPEEDSUNSHINE

Coefficient P-value
Coefficient P-value
0.397[.000]
0.396[.000]
0.066[.000]
0.065[.000]
0.027[.002]
0.028[.001]-0.228[.000]-0.227[.000]
0.323[.000]
0.324[.000]
0.055[.032]
0.053[.040]
0.051[.046]
0.051[.044]
0.030
0.007
0.046
0.068

[.225][.770][.072][.007]

0.030
0.007
0.047
0.066

[.225][.790][.067][.009]-0.0070.004-0.0020.001-0.001-0.003-0.080[.158][.410][.041][.468][.909][.765][.001]-0.003[.005]-0.001[.427]-0.003[.754]

D_SUNSHINE-0.001[.662]

0.002[.513]PRECIPITATION
D_ PRECIPITATION
Adjusted R2

0.001
0.627

[.476]

0.000
0.001
0.627

[.977][.432]

Number of observations
Hausman test
Estimation method

31632

31632
[.0004]

FIXED[.0021]FIXED

Note: Daily data are indicated with a “D_” at the beginning of a variable name.

38

Table 10.

Estimation results for alternative affect variables

Dependent Variable
Independent Variable
P_NEWS
M_NEWSSLEEPHEALTHSTRESSSUNDAYTUESDAYWEDNESDAY
THURSDAYFRIDAY
SATURDAYTEMPERATURE
HUMIDITY
WINDSPEEDSUNSHINE
PRECIPITATION
Constant
Adjusted R2
Number of observations
Hausman test
Estimation method

SADNESS
PLEASURE
DEPRESSION
Coefficient P-value
Coefficient P-value
Coefficient P-value
0.115[.000]
0.157[.000]
0.132[.000]
0.004[.038]
0.016[.000]
0.003[.204]
0.029[.000]-0.007[.101]
0.029[.000]-0.025[.000]-0.136[.000]-0.063[.000]
0.190[.000]
0.175[.000]
0.286[.000]
0.003[.821]
0.033[.011]
0.006[.688]
0.007[.567]-0.025[.050]
0.029[.036]
0.016[.186]
0.004[.782]
0.008[.539]
0.028[.026]-0.012[.327]
0.018[.192]
0.008[.527]
0.022[.082]
0.026[.057]
0.0003[.982]
0.049[.000]
0.008[.544]-0.001[.032]
0.001[.079]-0.001[.024]-0.0003[.231]-0.0005[.104]-0.0002[.590]-0.00002[.995]-0.00001[.998]-0.003[.289]
0.019[.091]-0.052[.000]
0.042[.001]
0.001[.908]-0.004[.356]-0.003[.561]
2.721[.000]
2.489[.000]
0.254
0.544
0.296
32123

32123
[.2016]RANDOM

32123[.0135]

FIXED[.2874]RANDOM

39

Figure 1.

Map of three locations: two campuses of Osaka University and Osaka city

Osaka University
Toyonaka Campus

Osaka University
Suita Campus

Osaka City

40

Figure 2.

Average temperature of Osaka city

35

30

25

20

15

10

5

0

41