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: Total 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 Estimate 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

Residual 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 fitted 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% confidence 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 standard 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 Forecasts option from the text 

menu.

The mean absolute error (MAE) of 1.29514 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

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 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 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 values of the independent 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 metals 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_Fuel

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

Intercept 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.) 3.90616E10 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 autocorrelation = 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/(65134 - 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 indicates 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 variables. The 

standard error of the estimate shows the standard deviation of the residuals to be 36783.2. 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 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 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 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 between observations 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 Tests 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 Metals_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&Total 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 = -0.302105

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 output 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 Metals -ERT and 

Total Metals_Fuel at the 95.0% or higher confidence level.

The R-Squared statistic indicates that the model 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 standard deviation of 

the residuals to be 0.010295. 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 0.00825688 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

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

 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 between 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 0.0141626 -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 = -0.434054

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 Dioxide - 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 fitted 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 standard 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 from the text 

menu.

The mean absolute error (MAE) of 1.22893 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

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

 Lack-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 whether 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 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 MetalsERT>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 Standard 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 35.636 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 = 0.936371

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 Metals-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 strong 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 

text 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

Source 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 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 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 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

Independent 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 Error 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 1.68203E8

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)

Lag 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 Forecasts 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, there 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 whether 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 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 equation 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 relationship 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 Forecasts option from the text 

menu.

The 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 Standard 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-Watson 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 equation 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_Fuel_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 relationship 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 Forecasts option from the text 

menu.

The 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 5.05757 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 Forecasts option from the text 

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. Cadmium_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 Forecasts option from the 

text menu.

The 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 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 - Chromium - min vs. Chromium_Fuel_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

Parameter 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 1.00 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/MMBtu. 

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 relatively 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 Forecasts option 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")

Dependent 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 0.00000418167

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 = 1.14603 (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 model 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 construct 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 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 - 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

Coefficients

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. = 0.00424158

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 between 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 relationship 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 linearize 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 construct 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 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 - Manganese - 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 error = 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/MMBtu. 

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 correlation 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 construct 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 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 - 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 logarithmic-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 Squares 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 percent

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 describe 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 statistically 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 normal 

scale to linearize the model. The correlation coefficient equals 0.56605, indicating a moderately strong relationship between the variables. The 

standard error of the estimate shows the standard deviation of the residuals to be 0.00867336. 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 0.00673632 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 - Selenium - min vs. Selenium_Fuel_lb/MMBtu (control_group_1<>"PM control")

Dependent variable: Selenium - min

Independent variable: Selenium_Fuel_lb/MMBtu

Selection variable: 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 0.2218

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

Dependent variable: Hydrogen 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 0.0000768269 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

Correlation 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 - 1.43779E-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 the 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 deviation of the residuals to be 0.0000680011. 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 0.0000411972 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 - 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 control'

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 Squares 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

Standard 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 relationship 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 relationship 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 deviation of the 

residuals to be 1376.51. 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 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

Intercept -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 (Corr.) 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)

Lag 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 Chloride - 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 0.0000348083 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 - 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 Error 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 Hydrogen 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, indicating a moderately strong relationship between the variables. The standard error of the estimate shows the standard deviation 

of the residuals to be 0.000318004. 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 0.000193325 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 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 0.00000292449 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 whether 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 significant 

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