Results: l12.sas

The REG Procedure

Model: MODEL1

Dependent Variable: logNO2

The Reg Procedure

MODEL1

Fit

logNO2

Number of Observations

Number of Observations Read 500
Number of Observations Used 500

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 7 145.09941 20.72849 74.97 <.0001
Error 492 136.03484 0.27649    
Corrected Total 499 281.13425      

Fit Statistics

Root MSE 0.52583 R-Square 0.5161
Dependent Mean 3.69837 Adj R-Sq 0.5092
Coeff Var 14.21780    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 0.57031 0.18836 3.03 0.0026
logCarsPrHr 1 0.50529 0.02832 17.84 <.0001
temp2m 1 -0.02389 0.00429 -5.57 <.0001
ws 1 -0.12535 0.01395 -8.99 <.0001
tempd 1 0.16701 0.02622 6.37 <.0001
windd 1 0.00078380 0.00029839 2.63 0.0089
hr 1 -0.01957 0.00437 -4.48 <.0001
day 1 0.00036329 0.00012331 2.95 0.0034

The REG Procedure

Model: MODEL1

Dependent Variable: logNO2

Observation-wise Statistics

logNO2

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for logNO2.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for logNO2.

Panel 2

Panel of scatterplots of residuals by regressors for logNO2.

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
dow 7 1 2 3 4 5 6 7

Number of Observations

Number of Observations Read 500
Number of Observations Used 500

The GLM Procedure

 

Dependent Variable: logNO2

Analysis of Variance

logNO2

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 15 175.6449906 11.7096660 53.73 <.0001
Error 484 105.4892555 0.2179530    
Corrected Total 499 281.1342461      

Fit Statistics

R-Square Coeff Var Root MSE logNO2 Mean
0.624773 12.62325 0.466854 3.698368

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
logCarsPrHr 1 73.71217123 73.71217123 338.20 <.0001
temp2m 1 21.60421361 21.60421361 99.12 <.0001
ws 1 33.04929047 33.04929047 151.63 <.0001
tempd 1 7.68306966 7.68306966 35.25 <.0001
sinwind 1 0.22474736 0.22474736 1.03 0.3104
coswind 1 2.94915497 2.94915497 13.53 0.0003
sinhr 1 3.37549492 3.37549492 15.49 <.0001
coshr 1 2.68688655 2.68688655 12.33 0.0005
day 1 2.20846008 2.20846008 10.13 0.0016
dow 6 28.15150179 4.69191696 21.53 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
logCarsPrHr 1 23.85620681 23.85620681 109.46 <.0001
temp2m 1 4.13767483 4.13767483 18.98 <.0001
ws 1 22.94848605 22.94848605 105.29 <.0001
tempd 1 14.70698699 14.70698699 67.48 <.0001
sinwind 1 0.77048449 0.77048449 3.54 0.0607
coswind 1 4.53144714 4.53144714 20.79 <.0001
sinhr 1 0.24945801 0.24945801 1.14 0.2852
coshr 1 5.90005934 5.90005934 27.07 <.0001
day 1 1.49290161 1.49290161 6.85 0.0091
dow 6 28.15150179 4.69191696 21.53 <.0001

The REG Procedure

Model: MODEL1

Dependent Variable: logNO2

 

C(p) Selection Method

The Reg Procedure

MODEL1

C(p) Selection Method

logNO2

Number of Observations

Number of Observations Read 500
Number of Observations Used 500

Results

Number in
Model		 C(p) R-Square Variables in Model
10 11.0000 0.5316 logCarsPrHr temp2m ws tempd sinwind coswind sinhr coshr day dow
9 11.2645 0.5294 logCarsPrHr temp2m ws tempd coswind sinhr coshr day dow
9 11.3373 0.5294 logCarsPrHr temp2m ws tempd sinwind coswind coshr day dow
8 12.1930 0.5266 logCarsPrHr temp2m ws tempd coswind coshr day dow
8 15.5773 0.5234 logCarsPrHr temp2m ws tempd coswind sinhr coshr day
9 16.2761 0.5246 logCarsPrHr temp2m ws tempd sinwind coswind sinhr coshr day
9 16.2946 0.5246 logCarsPrHr temp2m ws tempd sinwind coswind sinhr coshr dow
8 16.3238 0.5227 logCarsPrHr temp2m ws tempd sinwind coswind coshr dow
8 16.9447 0.5221 logCarsPrHr temp2m ws tempd coswind sinhr coshr dow
7 17.2876 0.5198 logCarsPrHr temp2m ws tempd coswind coshr day

The REG Procedure

Model: MODEL1

Dependent Variable: logNO2

Observation-wise Statistics

logNO2

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for logNO2.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for logNO2.

Panel 2

Panel of scatterplots of residuals by regressors for logNO2.

The GLMSELECT Procedure

The GLMSelect Procedure

Model Information

Data Set WORK.NO2
Dependent Variable logNO2
Selection Method Stepwise
Select Criterion AIC
Stop Criterion AIC
Choose Criterion AIC
Effect Hierarchy Enforced None

Number of Observations

Number of Observations Read 500
Number of Observations Used 500

Class Level Information

Class Level Information
Class Levels Values
dow 7 1 2 3 4 5 6 7

Dimensions

Dimensions
Number of Effects 11
Number of Parameters 17

The GLMSELECT Procedure

Model Building Summary

Stepwise Selection Summary

Stepwise Selection Summary
Step Effect
Entered		 Effect
Removed		 Number
Effects In		 Number
Parms In		 AIC
* Optimal Value of Criterion
0 Intercept   1 1 216.1121
1 logCarsPrHr   2 2 66.0738
2 ws   3 3 -41.2058
3 dow   4 9 -115.1555
4 tempd   5 10 -173.0209
5 coshr   6 11 -210.3101
6 temp2m   7 12 -223.6599
7 coswind   8 13 -237.6662
8 day   9 14 -242.7162
9 sinwind   10 15 -244.8185*

Stop Reason

Selection stopped at a local minimum of the AIC criterion.

Stop Details

Stop Details
Candidate
For		 Effect Candidate
AIC		   Compare
AIC
Entry sinhr -243.9995 > -244.8185
Removal sinwind -242.7162 > -244.8185

Selected Model

The GLMSELECT Procedure

Selected Model

The selected model, based on AIC, is the model at Step 9.

Selected Effects

Effects: Intercept logCarsPrHr temp2m ws tempd sinwind coswind coshr day dow

ANOVA

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value
Model 14 175.39553 12.52825 57.46
Error 485 105.73871 0.21802  
Corrected Total 499 281.13425    

Fit Statistics

Root MSE 0.46692
Dependent Mean 3.69837
R-Square 0.6239
Adj R-Sq 0.6130
AIC -244.81851
AICC -243.69221
SBC -683.59939

Parameter Estimates

Parameter Estimates
Parameter DF Estimate Standard
Error		 t Value
Intercept 1 1.463810 0.178008 8.22
logCarsPrHr 1 0.332323 0.024023 13.83
temp2m 1 -0.017311 0.003947 -4.39
ws 1 -0.128867 0.012415 -10.38
tempd 1 0.203765 0.024896 8.18
sinwind 1 0.067427 0.033732 2.00
coswind 1 -0.197002 0.042804 -4.60
coshr 1 -0.264785 0.041069 -6.45
day 1 0.000282 0.000110 2.57
dow 1 1 -0.354319 0.080585 -4.40
dow 2 1 0.275437 0.080874 3.41
dow 3 1 0.314854 0.077943 4.04
dow 4 1 0.378644 0.080436 4.71
dow 5 1 0.378441 0.081420 4.65
dow 6 1 0.204322 0.080995 2.52
dow 7 0 0 . .

The GLMSELECT Procedure

The GLMSelect Procedure

Model Information

Data Set WORK.NO2
Dependent Variable logNO2
Selection Method GROUP LASSO
Stop Criterion SBC
Effect Hierarchy Enforced None

Number of Observations

Number of Observations Read 500
Number of Observations Used 500

Class Level Information

Class Level Information
Class Levels Values
dow 7 1 2 3 4 5 6 7

Dimensions

Dimensions
Number of Effects 11
Number of Parameters 17

The GLMSELECT Procedure

Model Building Summary

Group LASSO Selection Summary

Group LASSO Selection Summary
Step Effect
Entered		 Effect
Removed		 Number
Effects In		 Number
Parms In		 SBC
* Optimal Value of Criterion
0 Intercept   1 1 -281.6733
1 logCarsPrHr   2 2 -301.0091
2     2 2 -322.7069
3     2 2 -340.9996
4 ws   3 3 -354.5888
5     3 3 -383.5988
6     3 3 -408.3973
7     3 3 -429.4266
8     3 3 -447.1334
9 temp2m tempd   5 5 -456.5994
10     5 5 -478.9855
11     5 5 -497.8826
12     5 5 -513.7308*

Stop Reason

Selection stopped at a local minimum of the SBC criterion.

Stop Details

Stop Details
Candidate
SBC		   Compare
SBC
-484.3582 > -513.7308

Selected Model

The GLMSELECT Procedure

Selected Model

The selected model is the model at the last step (Step 12).

Selected Effects

Effects: Intercept logCarsPrHr temp2m ws tempd

ANOVA

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value
Model 4 112.96002 28.24001 83.12
Error 495 168.17422 0.33975  
Corrected Total 499 281.13425    

Fit Statistics

Root MSE 0.58288
Dependent Mean 3.69837
R-Square 0.4018
Adj R-Sq 0.3970
AIC -32.80381
AICC -32.63343
SBC -513.73077

Parameter Estimates

Parameter Estimates
Parameter Estimate
Intercept 1.967286
logCarsPrHr 0.284979
temp2m -0.005539
ws -0.084514
tempd 0.045491

Quantile Regression for Arsenic Data

The QUANTREG Procedure

The Quantreg Procedure

Model Information

Model Information
Data Set WORK.ARSENIC
Dependent Variable nails
Number of Independent Variables 1
Number of Observations 21
Optimization Algorithm Simplex
Method for Confidence Limits Inv_Rank

Number of Observations

Number of Observations Read 21
Number of Observations Used 21

Summary Statistics

Summary Statistics
Variable Q1 Median Q3 Mean Standard
Deviation		 MAD
water 0 0.000690 0.0185 0.0163 0.0336 0.00102
nails 0.1180 0.1750 0.3955 0.3664 0.4868 0.1408

Quantile Level and Objective Function

Quantile Level and Objective Function
Quantile Level 0.5
Objective Function 1.1974
Predicted Value at Mean 0.3682

Parameter Estimates

Parameter Estimates
Parameter DF Estimate 95% Confidence Limits
Intercept 1 0.1142 0.0997 0.1457
water 1 15.6044 3.5833 34.8379

Quantile Fit Plot

Fitted values with QUANTILE= 0.5 for nails.

Regression for Median of Systolic After

The QUANTREG Procedure

The Quantreg Procedure

Model Information

Model Information
Data Set WORK.BP
Dependent Variable spa
Number of Independent Variables 1
Number of Observations 15
Optimization Algorithm Simplex
Method for Confidence Limits Inv_Rank

Number of Observations

Number of Observations Read 15
Number of Observations Used 15

Summary Statistics

Summary Statistics
Variable Q1 Median Q3 Mean Standard
Deviation		 MAD
spb 160.0 174.0 198.0 176.9 20.5651 20.7564
spa 145.0 157.0 168.0 158.0 20.0036 16.3086

Quantile Level and Objective Function

Quantile Level and Objective Function
Quantile Level 0.5
Objective Function 49.6026
Predicted Value at Mean 156.4496

Parameter Estimates

Parameter Estimates
Parameter DF Estimate 95% Confidence Limits
Intercept 1 -11.4103 -78.2234 59.2525
spb 1 0.9487 0.6112 1.2200

Quantile Fit Plot

Fitted values with QUANTILE= 0.5 for spa.

Regression for Median of Systolic After

The Print Procedure

Data Set WORK.ESTOUT

Obs Parameter DF Estimate LowerCL UpperCL
1 Intercept 1 -11.4103 -78.2234 59.2525
2 spb 1 0.9487 0.6112 1.2200

Regression for .2 Quantile of Systolic After

The QUANTREG Procedure

The Quantreg Procedure

Model Information

Model Information
Data Set WORK.BP
Dependent Variable spa
Number of Independent Variables 1
Number of Observations 15
Optimization Algorithm Simplex
Method for Confidence Limits Inv_Rank

Number of Observations

Number of Observations Read 15
Number of Observations Used 15

Summary Statistics

Summary Statistics
Variable Q1 Median Q3 Mean Standard
Deviation		 MAD
spb 160.0 174.0 198.0 176.9 20.5651 20.7564
spa 145.0 157.0 168.0 158.0 20.0036 16.3086

Quantile Level and Objective Function

Quantile Level and Objective Function
Quantile Level 0.2
Objective Function 30.1500
Predicted Value at Mean 149.9500

Parameter Estimates

Parameter Estimates
Parameter DF Estimate 95% Confidence Limits
Intercept 1 17.2500 -125.9079 78.2225
spb 1 0.7500 0.3584 1.4128

Quantile Fit Plot

Fitted values with QUANTILE= 0.2 for spa.

Regression for .2 Quantile of Systolic After

The Print Procedure

Data Set WORK.ESTOUT

Obs Parameter DF Estimate LowerCL UpperCL
1 Intercept 1 17.2500 -125.9079 78.2225
2 spb 1 0.7500 0.3584 1.4128