## Attachment 1: Statgraphics Results of Analysis of Oil

- Firing MACT Floor Revised June 9 , 2011 Simple Regression

- Total Metals

- ERT vs. Total Metals_Fuel (Total Metals_Fuel>0&Total Metals_Fuel<0.04&Total Metals

- ERT<0.005)

– Figure 1

Dependent variable: Tot al Metals

- ERT Independent variable: Total Metals_Fuel
Selection variable: Total Metals_Fuel>0&Total Metals_Fuel<0.04&Total Metals

- ERT<0.005 Logarithmic

- Y square root

- X model: Y = exp(a + b*sqrt(X))

Coefficients Least Squares Standard T

Parameter Esti mate Error Statistic P

- Value
Intercept

- 9.96603 0.764876

- 13.0296 0.0000 Slope 46.9733 22.3174 2.10478 0.0411

NOTE: intercept = ln(a)

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 11.2703 1 11.2703 4.43 0.0411

Resid ual 111.937 44 2.54401
Total (Corr.) 123.207 45

Correlation Coefficient = 0.302447

R

- squared = 9.14744 percent

R

- squared (adjusted for d.f.) = 7.08261 percent

Standard Error of Est. = 1.595

Mean absolute error = 1.29514

Durbin

- Watson statistic = 0. 147332 (P= 0.0000 ) Lag 1 residual autocorrelation = 0.867689

The StatAdvisor The output shows the results of fitting a logarithmic

- Y square root

- X model to describe the relationship between Total Metals

- ERT and Total Metals_Fuel. The equation of the fitt ed model is

Total Metals

- ERT = exp(

- 9.96603 + 46.9733*sqrt(Total Metals_Fuel))

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Total Metals

- ERT and Total
Metals_Fuel at the 95.0% conf idence level.

The R

- Squared statistic indicates that the model as fitted explains 9.14744% of the variability in Total Metals

- ERT. The correlation coefficient equals 0.302447, indicating a relatively weak relationship between the variables. The standar d error of the estimate shows the standard deviation of the residuals to be 1.595. This value can be used to construct prediction limits for new observations by selecting the Forec asts option from the text

menu.

The mean absolute error (MAE) of 1.29514 i s the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an

ind ication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen. Analysis of Variance with Lack

- of

- Fit

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 11.2703 1 11.2703 4.43 0.0411

Residual 111.937 44 2.54401

Lack

- of

- Fit 110.844 40 2.7711 10.15 0.0177

Pure Error 1.0925 4 0.273125
Total (Corr.) 123.207 45

The StatAdvisor The lack of fit test is designed to determine whether the selected model is adequate to describe the observed data, or whether a more complicated model should be used. The test is performed by comparing the variability of the current model residuals to the variability b etween observations at replicate values of the inde pendent variable X. Since the P

- value for lack

- of

- fit in the ANOVA table is less than 0.05, there is statistically significant

lack

- of

- fit at the 95.0% confidence level. You might consider selecting a different model form from the Analysis Options dialog box.

## Description Test results are plotted and shown as blue boxes. The line of best fit or prediction equation (blue line) which is the equation that would be used to predict values of the dependent variable Stack concentration given valu es of the in dependent variable fuel concentration

. Confidence intervals (green lines) for the mean response at X. These describe how well the location of the line has been estimated given the
available data sample. Prediction limits (grey lines) for new observations. These describe how precisely one could predict where a single new

observation would lie

. Data quality is low

– most values outside of prediction intervals

Do these observations indicate achievability? If we were to establish a fuel standard for total me tals in the fuel would it give us confidence that we could meet

the proposed limit for total metals? For example, we could set the fuel limit as the maximum total metals fuel concentration observed for a test result that

meets the limit

- the brown right most vertical line on the graph. Or we could use the average of the tests that meet the proposed limit

– the green middle

vertical line on the graph. Or we could arbitrarily choose a value looking at the graph

– the magenta left most vertical line on the graph.

## Simple Regression

- Total Metals

- ERT vs. Total Metals_Fuel (Total Metals_Fuel>0&Total Metals_Fuel<0.04&Total Metals

- ERT<0.005&control_group_1<>"PM control") Figure 2
Dependent variable: Total Metals

- ERT Independent variable: Total Metals_Fue l
Selection variable: Total Metals_Fuel>0&Total Metals_Fuel<0.04&Total Metals

- ERT<0.005&control_group_1<>"PM control" Reciprocal

- Y square root

- X: Y = 1/(a + b*sqrt(X))

Coefficients Least Squares Standard T

Parameter Estimate Error Statistic P

- Value

I ntercept 65134.0 20646.5 3.15473 0.0043 Slope

- 1.39381E6 631577.

- 2.20687 0.0371

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 6.58952E9 1 6.58952E9 4.87 0.0371

Residual 3.24721E10 24 1.353E9
Total (Corr.) 3.90616E 10 25

Correlation Coefficient =

- 0.410725

R

- squared = 16.8695 percent

R

- squared (adjusted for d.f.) = 13.4058 percent

Standard Error of Est. = 36783.2

Mean absolute error = 26400.6

Durbin

- Watson statistic = 0.388059 (P= 0.0000 ) Lag 1 residual autocorre lation = 0.617885

The StatAdvisor The output shows the results of fitting a reciprocal

- Y square root

- X model to describe the relationship between Total Metals

- ERT and Total Metals_Fuel. The equation of the fitted model is

Total Metals

- ERT = 1/(6513 4

- 1.39381E6*sqrt(Total Metals_Fuel))

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Total Metals

- ERT and Total
Metals_Fuel at the 95.0% confidence level.

The R

- Squared statistic indica tes that the model as fitted explains 16.8695% of the variability in Total Metals

- ERT after transforming to a square root scale to linearize the model. The correlation coefficient equals

- 0.410725, indicating a relatively weak relationship between the va riables. The

standard error of the estimate shows the standard deviation of the residuals to be 36783.2. This value can be used to constr uct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute e rror (MAE) of 26400.6 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less tha n 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

Analysis of Variance with Lack

- of

- Fit

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 6.58952E9 1 6.58952E9 4.87 0.0371

Residual 3.24721E10 24 1.353E9

Lack

- of

- Fit 2.54758E10 20 1.27379E9 0.73 0.7213

Pure Error 6.99627E9 4 1.74907E9
Total (Corr.) 3.90616E10 25

The StatAdvisor

The lack of fit test is designed to determine whether the selected model is adequate to describe the observed data, or whether a more complicated model should be used. The test is performed by comparing the variability of the current model residuals to the variability b etween o bservations at replicate values of the independent variable X. Since the P

- value for lack

- of

- fit in the ANOVA table is greater or equal to 0.05, the model appears to be adequate for the observed data at the 95.0% confidence level.

# ICR Oil

- Fired Stack Te sts Plot at Stacks Without Pollution Controls

- Fuel vs. Stack with simple regression model and

confidence limits, MACT limit & Fuel Spec shown . Note that the Y scale on the graph is in powers of ten

## Simple Regression

- Total Metals

- ERT vs. Total Metal s_Fuel (Total Metals_Fuel>0&Total Metals_Fuel<0.04&Total Metals

- ERT<0.005&control_group_1="PM control") Figure 3
Dependent variable: Total Metals

- ERT Independent variable: Total Metals_Fuel
Selection variable: Total Metals_Fuel>0&Total Metals_Fuel<0.04&T otal Metals

- ERT<0.005&control_group_1="PM control" Square root

- Y reciprocal

- X model: Y = (a + b/X)^2

Coefficients Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.0218468 0.00301892 7.23662 0.0000 Slope

- 0.00000223634 0.00000166327

- 1.34455 0.1955

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 0.000191606 1 0.000191606 1.81 0.1955

Residual 0.00190778 18 0.000105988
Total (Corr.) 0.00209939 19

Correlation Coefficient =

- 0.3021 05

R

- squared = 9.12674 percent

R

- squared (adjusted for d.f.) = 4.07823 percent

Standard Error of Est. = 0.010295

Mean absolute error = 0.00825688

Durbin

- Watson statistic = 0.183465 (P= 0.0000 ) Lag 1 residual autocorrelation = 0.773634

The StatAdvisor

The o utput shows the results of fitting a square root

- Y reciprocal

- X model to describe the relationship between Total Metals

- ERT and Total Metals_Fuel. The equation of the fitted model is

Total Metals

- ERT = (0.0218468

- 0.00000223634/Total Metals_Fuel)^2

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Total Met als

- ERT and Total Metals_Fuel at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the m odel as fitted explains 9.12674% of the variability in Total Metals

- ERT. The correlation coefficient equals

- 0.302105, indicating a relatively weak relationship between the variables. The standard error of the estimate shows the stan dard deviation of

th e residuals to be 0.010295. This value can be used to construct prediction limits for new observations by selecting the Fore casts option from the

text menu.

The mean absolute error (MAE) of 0.00825688 is the average value of the residuals. The Durbin

- Wa tson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

Analysis of Variance with Lack

- of

- Fit

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 0.000191606 1 0.000191606 1.81 0.1955

Residual 0.0 0190778 18 0.000105988

Lack

- of

- Fit 0.00190778 18 0.000105988

Pure Error 0 0
Total (Corr.) 0.00209939 19

The StatAdvisor The lack of fit test is designed to determine whether the selected model is adequate to describe the observed data, or whether a more complicated model should be used. The test is performed by comparing the variability of the current model residuals to the variability b etween observations at replicate values of the independent variable X. Unfortunately, the test can not be run in this case because there are no replicate observations at the
same values of Total Metals_Fuel.

## Simple Regression

- Total Metals

- ERT vs. Sulfur Dioxide

- min (Total Metals

- ERT>0) Figure 4

Dependent variable: Total Metals

- ERT Independent variable: Sulfur Dioxide

- min

Selection variable: Total Metals

- ERT>0

S

- curve model: Y = exp(a + b/X)

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept

- 7.96231 0.239427

- 33.2556 0.0000 Slope

- 0.0482505 0.014 1626

- 3.40689 0.0013

NOTE: intercept = ln(a)

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 25.6656 1 25.6656 11.61 0.0013

Residual 110.562 50 2.21124
Total (Corr.) 136.227 51

Correlation Coefficient =

- 0.43405 4

R

- squared = 18.8403 percent

R

- squared (adjusted for d.f.) = 17.2171 percent

Standard Error of Est. = 1.48702

Mean absolute error = 1.22893

Durbin

- Watson statistic = 0.999216 (P= 0.0000 ) Lag 1 residual autocorrelation = 0.469783

Number of excluded rows: 1

The StatAdvisor The output shows the results of fitting a S

- curve model model to describe the relationship between Total Metals

- ERT and Sulfur Dioxide

- min. The equation of the fitted model is

Total Metals

- ERT = exp(

- 7.96231

- 0.0482505/Sulfur Dioxi de

- min)

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Total Metals

- ERT and Sulfur Dioxide

- min at the 95.0% confidence level.

The R

- Squared statistic indicates that the model as fitte d explains 18.8403% of the variability in Total Metals

- ERT. The correlation coefficient equals

- 0.434054, indicating a relatively weak relationship between the variables. The standard error of the estimate shows the stan dard deviation of

the residuals to be 1.48702. This value can be used to construct prediction limits for new observations by selecting the Forecasts option fro m the text

menu.

The mean absolute error (MAE) of 1.22893 is the average value of the residuals. The Durbin

- Watson (DW) statisti c tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

Analysis of Variance with Lack

- of

- Fit

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 25.6656 1 25.6656 11.61 0.0013

Residual 110.562 50 2.21124

Lac k

- of

- Fit 110.562 49 2.25636

Pure Error 0 1 0
Total (Corr.) 136.227 51

The StatAdvisor The lack of fit test is designed to determine whether the selected model is adequate to describe the observed data, or whethe r a more complicated

model shou ld be used. The test is performed by comparing the variability of the current model residuals to the variability between obs ervations at replicate values of the independent variable X. Since the P

- value for lack

- of

- fit in the ANOVA table is less than 0.0 5, there is statistically significant

lack

- of

- fit at the 95.0% confidence level. You might consider selecting a different model form from the Analysis Options dialog box.

## Simple Regression

- Total Metals

- ERT vs. Sulfur Dioxide

- min (Total Metals

ER T>0&control_group_1<>"PM control") Figure 5
Dependent variable: Total Metals

- ERT Independent variable: Sulfur Dioxide

- min

Selection variable: Total Metals

- ERT>0&control_group_1<>"PM control"

S

- curve model: Y = exp(a + b/X)

Coefficients Least Squares St andard T

Parameter Estimate Error Statistic P

- Value
Intercept

- 7.42587 0.282241

- 26.3103 0.0000 Slope

- 0.0614187 0.0131279

- 4.67848 0.0001

NOTE: intercept = ln(a)

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 35.63 6 1 35.636 21.89 0.0001

Residual 48.8427 30 1.62809
Total (Corr.) 84.4786 31

Correlation Coefficient =

- 0.649487

R

- squared = 42.1834 percent

R

- squared (adjusted for d.f.) = 40.2562 percent

Standard Error of Est. = 1.27597

Mean absolute error = 0.9 36371

Durbin

- Watson statistic = 1.12399 (P= 0.0031 ) Lag 1 residual autocorrelation = 0.390168

Number of excluded rows: 1

The StatAdvisor The output shows the results of fitting a S

- curve model model to describe the relationship between Total Metals

- ERT and Sulfur Dioxide

- min. The equation of the fitted model is

Total Metals

- ERT = exp(

- 7.42587

- 0.0614187/Sulfur Dioxide

- min)

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Total Metal s

- ERT and Sulfur Dioxide

- min at the 95.0% confidence level.

The R

- Squared statistic indicates that the model as fitted explains 42.1834% of the variability in Total Metals

- ERT. The correlation coefficient equals

- 0.649487, indicating a moderately stron g relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 1.27597. This value can be used to construct prediction limits for new observations by selecting the Forecasts option from the

te xt menu.

The mean absolute error (MAE) of 0.936371 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

Analysis of Variance with Lack

- of

- Fit

Sourc e Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 35.636 1 35.636 21.89 0.0001

Residual 48.8427 30 1.62809

Lack

- of

- Fit 48.8427 29 1.68423

Pure Error 0 1 0
Total (Corr.) 84.4786 31

The StatAdvisor The lack of fit test is designed t o determine whether the selected model is adequate to describe the observed data, or whether a more complicated model should be used. The test is performed by comparing the variability of the current model residuals to the variability b etween observations at replicate values of the independent variable X. Since the P

- value for lack

- of

- fit in the ANOVA table is less than 0.05, there is statistically significant

lack

- of

- fit at the 95.0% confidence level. You might consider selecting a different model form from the Analysis Options dialog box.

## Simple Regression

- Total Metals

- ERT vs. Filterable Particulate_Method 29 (Total Metals

- ERT>0&Filterable Particulate_Method 29>0&control_group_1<>"PM control") Figure 6
Dependent variable: Total Metals

- ERT Indepe ndent variable: Filterable Particulate_Method 29

Selection variable: Total Metals

- ERT>0&Filterable Particulate_Method 29>0&control_group_1<>"PM control" Double reciprocal model: Y = 1/(a + b/X)

Coefficients Least Squares Standard T

Parameter Estimate E rror Statistic P

- Value
Intercept

- 3948.35 3391.4

- 1.16422 0.2574 Slope 172.086 12.0956 14.2272 0.0000

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 3.40466E10 1 3.40466E10 202.41 0.0000

Residual 3.53225E9 21 1.68203E 8
Total (Corr.) 3.75788E10 22

Correlation Coefficient = 0.951843

R

- squared = 90.6004 percent

R

- squared (adjusted for d.f.) = 90.1528 percent

Standard Error of Est. = 12969.3

Mean absolute error = 8013.66

Durbin

- Watson statistic = 1.628 (P= 0.1680 )

L ag 1 residual autocorrelation = 0.177385

The StatAdvisor The output shows the results of fitting a double reciprocal model to describe the relationship between Total Metals

- ERT and Filterable Particulate_Method 29. The equation of the fitted model is

Total Metals

- ERT = 1/(

- 3948.35 + 172.086/Filterable Particulate_Method 29)

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Total Metals

- ERT and Filterable
Particulate_Method 29 at the 95.0 % confidence level.

The R

- Squared statistic indicates that the model as fitted explains 90.6004% of the variability in Total Metals

- ERT. The correlation coefficient equals 0.951843, indicating a relatively strong relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 12969.3. This value can be used to construct prediction limits for new observations by selecting the For ecasts option from the text

menu.

The mean absolute error (MAE) of 8013.66 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is greater than 0.05, the re is no

indication of serial autocorrelation in the residuals at the 95.0% confidence level.

Analysis of Variance with Lack

- of

- Fit

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 3.40466E10 1 3.40466E10 202.41 0.0000

Residual 3.53225E9 21 1.68203E8

Lack

- of

- Fit 3.53225E9 19 1.85908E8

Pure Error 0 2 0
Total (Corr.) 3.75788E10 22

The StatAdvisor The lack of fit test is designed to determine whether the selected model is adequate to describe the observed data, or whethe r a m ore complicated model should be used. The test is performed by comparing the variability of the current model residuals to the variability b etween observations at replicate values of the independent variable X. Since the P

- value for lack

- of

- fit in the AN OVA table is less than 0.05, there is statistically significant

lack

- of

- fit at the 95.0% confidence level. You might consider selecting a different model form from the Analysis Options dialog box.

## Simple Regression

- Antimony

- min vs. Antimony_Fuel _lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Antimony

- min Independent variable: Antimony_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Logarithmic

- Y squared

- X: Y = exp(a + b*X^2)

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept

- 11.094 0.59214

- 18.7354 0.0000 Slope

- 2.9955E6 1.83585E6

- 1.63166 0.1177

NOTE: intercept = ln(a)

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 18.9325 1 18.9325 2.66 0.1177

Residual 149.336 21 7.11126
Total (Corr.) 168.269 22

Correlation Coefficient =

- 0.33543

R

- squared = 11.2513 percent

R

- squared (adjusted for d.f.) = 7.02522 percent

Standard Error of Est. = 2.66669

Mean absolute error = 1.97289

Durbin

- Watson statistic = 1.13782 (P= 0.0140 ) Lag 1 residual autocorrelation = 0.299442

The StatAdvisor The output shows the results of fitting a logarithmic

- Y squared

- X model to describe the relationship between Antimony

- min and Antimony_Fuel_lb/MMBtu. The eq uation of the fitted model is

Antimony

- min = exp(

- 11.094

- 2.9955E6*Antimony_Fuel_lb/MMBtu^2)

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Antimony

- min and Antimony _Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 11.2513% of the variability in Antimony

- min. The correlation coefficient equals

- 0.33543, indicating a relatively weak relations hip between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 2.66669. This value can be used to construct prediction limits for new observations by selecting the Forecas ts option from the text

menu.

T he mean absolute error (MAE) of 1.97289 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Arsenic

- min vs. Arsenic_Fuel_lb /MMBtu (control_group_1<>"PM control")

Dependent variable: Arsenic

- min Independent variable: Arsenic_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Reciprocal

- Y logarithmic

- X model: Y = 1/(a + b*ln(X))

Coefficients
Least Squares Standa rd T

Parameter Estimate Error Statistic P

- Value
Intercept

- 3.36032E6 2.47051E6

- 1.36017 0.1870 Slope

- 448023. 249215.

- 1.79774 0.0854

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 4.13333E12 1 4.13333E12 3.23 0.0854

Residual 2.94154E13 23 1.27893E12
Total (Corr.) 3.35488E13 24

Correlation Coefficient =

- 0.351004

R

- squared = 12.3204 percent

R

- squared (adjusted for d.f.) = 8.50819 percent

Standard Error of Est. = 1.1309E6

Mean absolute error = 829746.

Durbin

- W atson statistic = 1.00004 (P= 0.0030 ) Lag 1 residual autocorrelation = 0.329762

The StatAdvisor The output shows the results of fitting a reciprocal

- Y logarithmic

- X model to describe the relationship between Arsenic

- min and Arsenic_Fuel_lb/MMBtu. The eq uation of the fitted model is

Arsenic

- min = 1/(

- 3.36032E6

- 448023*ln(Arsenic_Fuel_lb/MMBtu))

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Arsenic

- min and
Arsenic_F uel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 12.3204% of the variability in Arsenic

- min. The correlation coefficient equals

- 0.351004, indicating a relatively weak relationshi p between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 1.1309E6. This value can be used to construct prediction limits for new observations by selecting the Foreca sts option from the text

menu.

Th e mean absolute error (MAE) of 829746. is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Beryllium

- min vs. Beryllium_Fuel_ lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Beryllium

- min Independent variable: Beryllium_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Logarithmic

- Y squared

- X: Y = exp(a + b*X^2)

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept

- 16.3695 0.318308

- 51.4266 0.0000 Slope 4.55595E8 2.39643E8 1.90114 0.0699

NOTE: intercept = ln(a)

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 5.05757 1 5.057 57 3.61 0.0699

Residual 32.184 23 1.3993
Total (Corr.) 37.2416 24

Correlation Coefficient = 0.368517

R

- squared = 13.5805 percent

R

- squared (adjusted for d.f.) = 9.82308 percent

Standard Error of Est. = 1.18292

Mean absolute error = 0.931483

Durbin

- Watson statistic = 1.30724 (P= 0.0293 ) Lag 1 residual autocorrelation = 0.257879

The StatAdvisor The output shows the results of fitting a logarithmic

- Y squared

- X model to describe the relationship between Beryllium

- min and Beryllium_Fuel_lb/MMBtu. The equation of the fitted model is

Beryllium

- min = exp(

- 16.3695 + 4.55595E8*Beryllium_Fuel_lb/MMBtu^2)

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Beryllium

- min and Beryllium_Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 13.5805% of the variability in Beryllium

- min. The correlation coefficient equals 0.368517, indicating a relatively weak relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 1.18292. This value can be used to construct prediction limits for new observations by selecting the Forecas ts option from the tex t

menu.

The mean absolute error (MAE) of 0.931483 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Cadmium

- min vs. Cadmi um_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Cadmium

- min Independent variable: Cadmium_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Square root

- Y reciprocal

- X model: Y = (a + b/X)^2

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.000388897 0.0000762208 5.10224 0.0000 Slope 1.98069E

- 9 8.85044E

- 10 2.23796 0.0352

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 3.3698E

- 7 1 3.3698E

- 7 5.01 0.0352

Residual 0.00000154749 23 6.7282E

- 8
Total (Corr.) 0.00000188447 24

Correlation Coefficient = 0.422871

R

- squared = 17.882 percent

R

- squared (adjusted for d.f.) = 14.3116 percent

Standard Error of Est. = 0.000259388

Mean absolute error = 0.000193342

Durbin

- Watson statistic = 0.832674 (P= 0.0006 ) Lag 1 residual autocorrelation = 0.549682

The StatAdvisor The output shows the results of fitting a square root

- Y reciprocal

- X model to describe the relationship between Cadmium

- min and

Cadmium _Fuel_lb/MMBtu. The equation of the fitted model is

Cadmium

- min = (0.000388897 + 1.98069E

- 9/Cadmium_Fuel_lb/MMBtu)^2

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Cadmium

- min and
Cadmium_Fuel_lb/MMBtu at the 95.0% confidence level.

The R

- Squared statistic indicates that the model as fitted explains 17.882% of the variability in Cadmium

- min. The correlation coefficient equals 0.422871, indicating a relatively weak relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 0.000259388. This value can be used to construct prediction limits for new observations by selecting the For ecasts option from the

text menu.

T he mean absolute error (MAE) of 0.000193342 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since t he P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if th ere is any pattern that can be

seen.

## Simple Regression

- Chromium

- min vs. Chromium_Fu el_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Chromium

- min Independent variable: Chromium_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Square root

- X model: Y = a + b*sqrt(X)

Coefficients
Least Squares Standard T

P arameter Estimate Error Statistic P

- Value
Intercept 0.00000690311 0.00000212065 3.25518 0.0034 Slope

- 0.000289617 0.000289478

- 1.00048 0.3271

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 2.39151E

- 11 1 2.39151E

- 11 1.0 0 0.3271

Residual 5.7341E

- 10 24 2.38921E

- 11
Total (Corr.) 5.97326E

- 10 25

Correlation Coefficient =

- 0.200092

R

- squared = 4.0037 percent

R

- squared (adjusted for d.f.) = 0.00385365 percent

Standard Error of Est. = 0.00000488795

Mean absolute error = 0.00000379644

Durbin

- Watson statistic = 1.4608 (P= 0.0842 ) Lag 1 residual autocorrelation = 0.248151

The StatAdvisor The output shows the results of fitting a square root

- X model to describe the relationship between Chromium

- min and Chromium_Fuel_lb/MMB tu. The equation of the fitted model is

Chromium

- min = 0.00000690311

- 0.000289617*sqrt(Chromium_Fuel_lb/MMBtu)

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Chromium

- min and Chromium_Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 4.0037% of the variability in Chromium

- min. The correlation coefficient equals

- 0.200092, indicating a relati vely weak relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 0.00000488795. This value can be used to construct prediction limits for new observations by selecting the F orecasts opti on from the

text menu.

The mean absolute error (MAE) of 0.00000379644 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is greater than 0.05, there

is no indication of serial autocorrelation in the residuals at the 95.0% confidence level.

## Simple Regression

- Cobalt

- min vs. Cobalt_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dep endent variable: Cobalt

- min Independent variable: Cobalt_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Square root

- Y logarithmic

- X model: Y = (a + b*ln(X))^2

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.0093881 0.00317791 2.95418 0.0078 Slope 0.000551996 0.000298178 1.85123 0.0790

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 0.0000143308 1 0.0000143308 3.43 0.0790

Residual 0.0000836334 20 0.00000 418167
Total (Corr.) 0.0000979643 21

Correlation Coefficient = 0.382474

R

- squared = 14.6286 percent

R

- squared (adjusted for d.f.) = 10.3601 percent

Standard Error of Est. = 0.00204491

Mean absolute error = 0.00160795

Durbin

- Watson statistic = 1.146 03 (P= 0.0146 ) Lag 1 residual autocorrelation = 0.22293

The StatAdvisor The output shows the results of fitting a square root

- Y logarithmic

- X model to describe the relationship between Cobalt

- min and Cobalt_Fuel_lb/MMBtu. The equation of the fitted mode l is

Cobalt

- min = (0.0093881 + 0.000551996*ln(Cobalt_Fuel_lb/MMBtu))^2

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Cobalt

- min and
Cobalt_Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 14.6286% of the variability in Cobalt

- min after transforming to an inverse normal scale to linearize the model. The correlation coefficient equals 0.382474 , indicating a relatively weak relationship between the variables. The

standard error of the estimate shows the standard deviation of the residuals to be 0.00204491. This value can be used to con struct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 0.00160795 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in wh ich they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if th ere is any pattern that can be

seen.

## Simple Re gression

- Lead

- min vs. Lead_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Lead

- min Independent variable: Lead_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Square root

- Y logarithmic

- X model: Y = (a + b*ln(X))^2

C oefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.0150616 0.00691971 2.17663 0.0400 Slope 0.00120682 0.000724119 1.6666 0.1092

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 0.0000499711 1 0.0000499711 2.78 0.1092

Residual 0.000413793 23 0.000017991
Total (Corr.) 0.000463764 24

Correlation Coefficient = 0.328255

R

- squared = 10.7751 percent

R

- squared (adjusted for d.f.) = 6.89577 percent

Standard Error of Est. = 0.004 24158

Mean absolute error = 0.00226162

Durbin

- Watson statistic = 2.13547 (P= 0.6102 ) Lag 1 residual autocorrelation =

- 0.0683008

The StatAdvisor The output shows the results of fitting a square root

- Y logarithmic

- X model to describe the relationship betwee n Lead

- min and Lead_Fuel_lb/MMBtu. The equation of the fitted model is

Lead

- min = (0.0150616 + 0.00120682*ln(Lead_Fuel_lb/MMBtu))^2

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relatio nship between Lead

- min and Lead_Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 10.7751% of the variability in Lead

- min after transforming to an inverse normal

scale to lineari ze the model. The correlation coefficient equals 0.328255, indicating a relatively weak relationship between the variables. The

standard error of the estimate shows the standard deviation of the residuals to be 0.00424158. This value can be used to con s truct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 0.00226162 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to

determine if the re is any significant correlation based on the order in which they occur in your data file. Since the P

- value is greater than 0.05, there

is no indication of serial autocorrelation in the residuals at the 95.0% confidence level.

## Simple Regression

- M anganese

- min vs. Manganese_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Manganese

- min Independent variable: Manganese_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Exponential model: Y = exp(a + b*X)

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept

- 11.9072 0.521652

- 22.826 0.0000 Slope 12984.8 8612.12 1.50774 0.1458

NOTE: intercept = ln(a)

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 5.3657 1 5.3657 2.27 0.1458

Residual 51.9275 22 2.36034
Total (Corr.) 57.2932 23

Correlation Coefficient = 0.306028

R

- squared = 9.36533 percent

R

- squared (adjusted for d.f.) = 5.24557 percent

Standard Error of Est. = 1.53634

Mean absolute er ror = 1.20955

Durbin

- Watson statistic = 1.17857 (P= 0.0144 ) Lag 1 residual autocorrelation = 0.29887

The StatAdvisor The output shows the results of fitting an exponential model to describe the relationship between Manganese

- min and Manganese_Fuel_lb/MMB tu. The equation of the fitted model is

Manganese

- min = exp(

- 11.9072 + 12984.8*Manganese_Fuel_lb/MMBtu)

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant relationship between Manganese

- min and Manganese_Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 9.36533% of the variability in Manganese

- min after transforming to a reciprocal

scale to linearize the model. The c orrelation coefficient equals 0.306028, indicating a relatively weak relationship between the variables. The

standard error of the estimate shows the standard deviation of the residuals to be 1.53634. This value can be used to constr uct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 1.20955 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant corr elation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Nickel

- min vs. Nickel_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Nickel

- min Independent variable: Nickel_Fuel_lb/MMBtu Selection variable: control_group_1<>"PM control" Square root

- Y lo garithmic

- X model: Y = (a + b*ln(X))^2

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.0553471 0.0125613 4.40618 0.0002 Slope 0.00477889 0.00145121 3.29304 0.0032

Analysis of Variance

Source Sum of Squar es Df Mean Square F

- Ratio P

- Value

Model 0.00081577 1 0.00081577 10.84 0.0032

Residual 0.00173023 23 0.0000752272
Total (Corr.) 0.002546 24

Correlation Coefficient = 0.56605

R

- squared = 32.0413 percent

R

- squared (adjusted for d.f.) = 29.0866 perce nt
Standard Error of Est. = 0.00867336

Mean absolute error = 0.00673632

Durbin

- Watson statistic = 0.50558 (P= 0.0000 ) Lag 1 residual autocorrelation = 0.604332

The StatAdvisor The output shows the results of fitting a square root

- Y logarithmic

- X model to d escribe the relationship between Nickel

- min and Nickel_Fuel_lb/MMBtu. The equation of the fitted model is

Nickel

- min = (0.0553471 + 0.00477889*ln(Nickel_Fuel_lb/MMBtu))^2

Since the P

- value in the ANOVA table is less than 0.05, there is a statisti cally significant relationship between Nickel

- min and
Nickel_Fuel_lb/MMBtu at the 95.0% confidence level.

The R

- Squared statistic indicates that the model as fitted explains 32.0413% of the variability in Nickel

- min after transforming to an inverse no rmal scale to linearize the model. The correlation coefficient equals 0.56605, indicating a moderately strong relationship betwee n the variables. The

standard error of the estimate shows the standard deviation of the residuals to be 0.00867336. This val ue can be used to construct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 0.00673632 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residua ls to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Selenium

- min vs. Selenium_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Selenium

- min Independent variable: Selenium_Fuel_lb/MMBtu

Selection v ariable: control_group_1<>"PM control" Reciprocal

- Y square root

- X: Y = 1/(a + b*sqrt(X))

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 301636. 555551. 0.542949 0.5924 Slope 7.1141E7 5.66475E7 1.25586 0.221 8

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 1.7885E12 1 1.7885E12 1.58 0.2218

Residual 2.60818E13 23 1.13399E12
Total (Corr.) 2.78703E13 24

Correlation Coefficient = 0.253323

R

- squared = 6.41723 percent

R

- s quared (adjusted for d.f.) = 2.34841 percent

Standard Error of Est. = 1.06489E6

Mean absolute error = 607778.

Durbin

- Watson statistic = 0.842693 (P= 0.0006 ) Lag 1 residual autocorrelation = 0.190145

The StatAdvisor The output shows the results of fitting a reciprocal

- Y square root

- X model to describe the relationship between Selenium

- min and Selenium_Fuel_lb/MMBtu. The equation of the fitted model is

Selenium

- min = 1/(301636 + 7.1141E7*sqrt(Selenium_Fuel_lb/MMBtu))

Since the P

- value in the ANOVA t able is greater or equal to 0.05, there is not a statistically significant relationship between Selenium

- min and Selenium_Fuel_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 6.41723% of the variability in Selenium

- min after transforming to a square root scale to linearize the model. The correlation coefficient equals 0.253323, indicating a relatively weak relationship between the variables. The

standard error of the estimate shows the standard deviation of the residuals to be 1.06489E6. This value can be used to construct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 607778. is the average value of th e residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible seria l correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Hydrogen Fluoride

- ERT vs. Fuel_F_lb/MMBtu (control_group_1<>'PM control')

Dependent variable: Hydrog en Fluoride

- ERT Independent variable: Fuel_F_lb/MMBtu Selection variable: control_group_1<>'PM control' Reciprocal

- X model: Y = a + b/X

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.000447375 0.00007682 69 5.82315 0.0043 Slope

- 1.43779E

- 7 4.98762E

- 8

- 2.88273 0.0449

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 3.84272E

- 8 1 3.84272E

- 8 8.31 0.0449

Residual 1.84966E

- 8 4 4.62414E

- 9 Total (Corr.) 5.69237E

- 8 5

Corr elation Coefficient =

- 0.821623

R

- squared = 67.5064 percent

R

- squared (adjusted for d.f.) = 59.383 percent

Standard Error of Est. = 0.0000680011

Mean absolute error = 0.0000411972

Durbin

- Watson statistic = 1.52677 (P= 0.1259 ) Lag 1 residual autocorrelation =

- 0.112985

The StatAdvisor The output shows the results of fitting a reciprocal

- X model to describe the relationship between Hydrogen Fluoride

- ERT and Fuel_F_lb/MMBtu. The equation of the fitted model is

Hydrogen Fluoride

- ERT = 0.000447375

- 1.4 3779E

- 7/Fuel_F_lb/MMBtu

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Hydrogen Fluoride

- ERT and
Fuel_F_lb/MMBtu at the 95.0% confidence level.

The R

- Squared statistic indicates that th e model as fitted explains 67.5064% of the variability in Hydrogen Fluoride

- ERT. The correlation coefficient equals

- 0.821623, indicating a moderately strong relationship between the variables. The standard error of the estimate shows the

standard devi ation of the residuals to be 0.0000680011. This value can be used to construct prediction limits for new observations by sel ecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 0.0000411972 is the average value of the residual s. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is greater than 0.05, there

is no indication of serial autocorrelatio n in the residuals at the 95.0% confidence level.

## Simple Regression

- HCl emissions vs. Fuel_Cl_lb/MMBtu (control_group_1<>'PM control')

Dependent variable: HCl emissions Independent variable: Fuel_Cl_lb/MMBtu Selection variable: control_group_1<>'PM c ontrol' Double reciprocal model: Y = 1/(a + b/X)

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 1641.72 403.815 4.06552 0.0008 Slope 0.971213 0.725343 1.33897 0.1982

Analysis of Variance

Source Sum of Squ ares Df Mean Square F

- Ratio P

- Value

Model 3.39702E6 1 3.39702E6 1.79 0.1982

Residual 3.2211E7 17 1.89477E6
Total (Corr.) 3.56081E7 18

Correlation Coefficient = 0.308869

R

- squared = 9.54002 percent

R

- squared (adjusted for d.f.) = 4.21884 percent

S tandard Error of Est. = 1376.51

Mean absolute error = 986.153

Durbin

- Watson statistic = 0.331534 (P= 0.0000 ) Lag 1 residual autocorrelation = 0.63208

The StatAdvisor The output shows the results of fitting a double reciprocal model to describe the relation ship between HCl emissions and Fuel_Cl_lb/MMBtu. The equation of the fitted model is

HCl emissions = 1/(1641.72 + 0.971213/Fuel_Cl_lb/MMBtu)

Since the P

- value in the ANOVA table is greater or equal to 0.05, there is not a statistically significant re lationship between HCl emissions and Fuel_Cl_lb/MMBtu at the 95.0% or higher confidence level.

The R

- Squared statistic indicates that the model as fitted explains 9.54002% of the variability in HCl emissions. The correlation coefficient equals
0.308869, indicating a relatively weak relationship between the variables. The standard error of the estimate shows the standard devia tion of the residuals to be 1376.51. This value can be used to construct prediction limits for new observations by selecting the F orecasts option from the text

menu.

The mean absolute error (MAE) of 986.153 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be

seen.

## Simple Regression

- Hydrogen Chloride

- min vs. Fuel_Cl_lb/MMBtu

Dependent variable: Hydrogen Chloride

- min Independent variable: Fuel_Cl_lb/MMBtu

Double

- squared: Y = sqrt(a + b*X^2)

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value

Int ercept

- 0.0000207821 0.0000132059

- 1.57371 0.1224 Slope 0.626346 0.136682 4.58249 0.0000

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 1.17645E

- 7 1 1.17645E

- 7 21.00 0.0000

Residual 2.57708E

- 7 46 5.60236E

- 9
Total (C orr.) 3.75354E

- 7 47

Correlation Coefficient = 0.559844

R

- squared = 31.3425 percent

R

- squared (adjusted for d.f.) = 29.8499 percent

Standard Error of Est. = 0.0000748489

Mean absolute error = 0.0000348083

Durbin

- Watson statistic = 1.73737 (P= 0.1771 )

La g 1 residual autocorrelation = 0.130459

The StatAdvisor The output shows the results of fitting a double squared model to describe the relationship between Hydrogen Chloride

- min and Fuel_Cl_lb/MMBtu. The equation of the fitted model is

Hydrogen Chl oride

- min = sqrt(

- 0.0000207821 + 0.626346*Fuel_Cl_lb/MMBtu^2)

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Hydrogen Chloride

- min and
Fuel_Cl_lb/MMBtu at the 95.0% confidence level.

The R

- Squared statistic indicates that the model as fitted explains 31.3425% of the variability in Hydrogen Chloride

- min. The correlation coefficient equals 0.559844, indicating a moderately strong relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 0.0000748489. This value can be used to construct prediction limits for new observations by selecting the Forecasts option from the text menu.

The mean absolute error (MAE) of 0.0000348 083 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P

- value is greater than 0.05, there

i s no indication of serial autocorrelation in the residuals at the 95.0% confidence level.

## Simple Regression

- Hydrogen Fluoride

- min vs. Fuel_F_lb/MMBtu

Dependent variable: Hydrogen Fluoride

- min Independent variable: Fuel_F_lb/MMBtu

Linear model: Y = a + b*X

Coefficients
Least Squares Standard T

Parameter Estimate Error Statistic P

- Value
Intercept 0.0000908039 0.0000627728 1.44655 0.1562 Slope 0.101027 0.0187864 5.37765 0.0000

Analysis of Variance

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 0.00000292449 1 0.00000292449 28.92 0.0000

Residual 0.00000384281 38 1.01127E

- 7
Total (Corr.) 0.0000067673 39

Correlation Coefficient = 0.657381

R

- squared = 43.215 percent

R

- squared (adjusted for d.f.) = 41.7206 percent

Standard Err or of Est. = 0.000318004

Mean absolute error = 0.000193325

Durbin

- Watson statistic = 1.3531 (P= 0.0165 ) Lag 1 residual autocorrelation = 0.30473

The StatAdvisor The output shows the results of fitting a linear model to describe the relationship between Hyd rogen Fluoride

- min and Fuel_F_lb/MMBtu. The equation of the fitted model is

Hydrogen Fluoride

- min = 0.0000908039 + 0.101027*Fuel_F_lb/MMBtu

Since the P

- value in the ANOVA table is less than 0.05, there is a statistically significant relationship between Hydrogen Fluoride

- min and
Fuel_F_lb/MMBtu at the 95.0% confidence level.

The R

- Squared statistic indicates that the model as fitted explains 43.215% of the variability in Hydrogen Fluoride

- min. The correlation coefficient equals 0.657381, ind icating a moderately strong relationship between the variables. The standard error of the estimate shows the standard deviat ion of the residuals to be 0.000318004. This value can be used to construct prediction limits for new observations by selecting th e Forecasts option from

the text menu.

The mean absolute error (MAE) of 0.000193325 is the average value of the residuals. The Durbin

- Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in whi ch they occur in your data file. Since the P

- value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if th ere is any pattern that can be

seen.

Analysis o f Variance with Lack

- of

- Fit

Source Sum of Squares Df Mean Square F

- Ratio P

- Value

Model 0.00000292449 1 0.00000292449 28.92 0.0000

Residual 0.00000384281 38 1.01127E

- 7

Lack

- of

- Fit 0.00000378906 32 1.18408E

- 7 13.22 0.0019

Pure Error 5.37501E

- 8 6 8.95835E

- 9 Total (Corr.) 0.0000067673 39

The StatAdvisor The lack of fit test is designed to determine whether the selected model is adequate to describe the observed data, or whethe r a more complicated model should be used. The test is performed by comparing the variability of the current model residuals to the variability between observations at replicate values of the independent variable X. Since the P

- value for lack

- of

- fit in the ANOVA table is less than 0.05, there is statistically significa nt
lack

- of

- fit at the 95.0% confidence level. You might consider selecting a different model form from the Analysis Options dialog box.