Results: arsenic1.sas

arsenic data

The Print Procedure

Data Set WORK.ARSENIC

Obs conc dist
1 3.19 2
2 3.26 4
3 1.82 8
4 1.02 10
5 1.85 12
6 2.05 15
7 1.34 21
8 0.79 23
9 0.66 30
10 0.30 36

The SGScatter Procedure

The SGScatter Procedure

The SGScatter Procedure

regression of conc on dist (1)

The GLM Procedure

The GLM Procedure

Data

Number of Observations

Number of Observations Read 10
Number of Observations Used 10

regression of conc on dist (1)

The GLM Procedure

Coefficients for estimate meanresp20

Coefficients for Estimate meanresp20
  Row 1
Intercept 1
dist 20

regression of conc on dist (1)

The GLM Procedure

 

Dependent Variable: conc

Analysis of Variance

conc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 6.88257399 6.88257399 23.53 0.0013
Error 8 2.34038601 0.29254825    
Corrected Total 9 9.22296000      

Fit Statistics

R-Square Coeff Var Root MSE conc Mean
0.746244 33.22342 0.540877 1.628000

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
dist 1 6.88257399 6.88257399 23.53 0.0013

Type II Model ANOVA

Source DF Type II SS Mean Square F Value Pr > F
dist 1 6.88257399 6.88257399 23.53 0.0013

Estimates

Parameter Estimate Standard
Error		 t Value Pr > |t| 95% Confidence Limits
intercept 2.88622593 0.31071996 9.29 <.0001 2.16970442 3.60274744
slope -0.07815068 0.01611225 -4.85 0.0013 -0.11530558 -0.04099577
mean 1.62800000 0.17104042 9.52 <.0001 1.23358008 2.02241992
meanresp20 1.32321235 0.18221803 7.26 <.0001 0.90301683 1.74340787

Solution

Parameter Estimate Standard
Error		 t Value Pr > |t| 95% Confidence Limits
Intercept 2.886225930 0.31071996 9.29 <.0001 2.169704415 3.602747444
dist -0.078150679 0.01611225 -4.85 0.0013 -0.115305583 -0.040995775

regression of conc on dist (1)

The GLM Procedure

Predictions

Values

Observation   Observed Predicted Residual 95% Confidence Limits for Mean Predicted Value
1   3.19000000 2.72992457 0.46007543 2.07416420 3.38568495
2   3.26000000 2.57362321 0.68637679 1.97555620 3.17169023
3   1.82000000 2.26102050 -0.44102050 1.76489469 2.75714630
4   1.02000000 2.10471914 -1.08471914 1.64981807 2.55962022
5   1.85000000 1.94841778 -0.09841778 1.52560216 2.37123341
6   2.05000000 1.71396575 0.33603425 1.31743396 2.11049753
7   1.34000000 1.24506167 0.09493833 0.81065108 1.67947226
8   0.79000000 1.08876032 -0.29876032 0.61834343 1.55917721
9   0.66000000 0.54170556 0.11829444 -0.10813360 1.19154473
10   0.30000000 0.07280149 0.22719851 -0.76520429 0.91080727

Information

Sum of Residuals 0.00000000
Sum of Squared Residuals 2.34038601
Sum of Squared Residuals - Error SS 0.00000000
PRESS Statistic 3.52155376
First Order Autocorrelation 0.23937056
Durbin-Watson D 1.40876096

Residual Plots

dist

Plot of Residual by dist for conc

Fit Plot

Fit Plot for conc by dist

regression of conc on dist (1)

The Print Procedure

Data Set WORK.NEW

Obs conc dist clml clmu clpl clpu yhat resid
1 3.19 2 2.07416 3.38568 1.32078 4.13907 2.72992 0.46008
2 3.26 4 1.97556 3.17169 1.19038 3.95686 2.57362 0.68638
3 1.82 8 1.76489 2.75715 0.91870 3.60334 2.26102 -0.44102
4 1.02 10 1.64982 2.55962 0.77709 3.43235 2.10472 -1.08472
5 1.85 12 1.52560 2.37123 0.63143 3.26540 1.94842 -0.09842
6 2.05 15 1.31743 2.11050 0.40518 3.02275 1.71397 0.33603
7 1.34 21 0.81065 1.67947 -0.07569 2.56581 1.24506 0.09494
8 0.79 23 0.61834 1.55918 -0.24427 2.42179 1.08876 -0.29876
9 0.66 30 -0.10813 1.19154 -0.86469 1.94811 0.54171 0.11829
10 0.30 36 -0.76520 0.91081 -1.42984 1.57544 0.07280 0.22720

descriptive statistics for residuals

The UNIVARIATE Procedure

Variable: resid

The Univariate Procedure

resid

Basic Measures of Location and Variability

Basic Statistical Measures
Location Variability
Mean 0.000000 Std Deviation 0.50994
Median 0.106616 Variance 0.26004
Mode . Range 1.77110
    Interquartile Range 0.63479

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.947998 Pr < W 0.6449
Kolmogorov-Smirnov D 0.173846 Pr > D >0.1500
Cramer-von Mises W-Sq 0.037821 Pr > W-Sq >0.2500
Anderson-Darling A-Sq 0.26181 Pr > A-Sq >0.2500

Quantiles

Quantiles (Definition 5)
Level Quantile
100% Max 0.686377
99% 0.686377
95% 0.686377
90% 0.573226
75% Q3 0.336034
50% Median 0.106616
25% Q1 -0.298760
10% -0.762870
5% -1.084719
1% -1.084719
0% Min -1.084719

Extreme Values

Extreme Values
Lowest Highest
Order Value Order Value
1 -1.0847191 6 0.118294
2 -0.4410205 7 0.227199
3 -0.2987603 8 0.336034
4 -0.0984178 9 0.460075
5 0.0949383 10 0.686377

regression of conc on dist (2) prediction interval for x=20

The GLM Procedure

The GLM Procedure

Data

Number of Observations

Number of Observations Read 11
Number of Observations Used 10

regression of conc on dist (2) prediction interval for x=20

The GLM Procedure

 

Dependent Variable: conc

Analysis of Variance

conc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 6.88257399 6.88257399 23.53 0.0013
Error 8 2.34038601 0.29254825    
Corrected Total 9 9.22296000      

Fit Statistics

R-Square Coeff Var Root MSE conc Mean
0.746244 33.22342 0.540877 1.628000

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
dist 1 6.88257399 6.88257399 23.53 0.0013

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
dist 1 6.88257399 6.88257399 23.53 0.0013

Solution

Parameter Estimate Standard
Error		 t Value Pr > |t|
Intercept 2.886225930 0.31071996 9.29 <.0001
dist -0.078150679 0.01611225 -4.85 0.0013

regression of conc on dist (2) prediction interval for x=20

The Print Procedure

Data Set WORK.NEW1A

Obs conc dist clml clmu clpl clpu yhat resid
1 3.19 2 2.07416 3.38568 1.32078 4.13907 2.72992 0.46008
2 3.26 4 1.97556 3.17169 1.19038 3.95686 2.57362 0.68638
3 1.82 8 1.76489 2.75715 0.91870 3.60334 2.26102 -0.44102
4 1.02 10 1.64982 2.55962 0.77709 3.43235 2.10472 -1.08472
5 1.85 12 1.52560 2.37123 0.63143 3.26540 1.94842 -0.09842
6 2.05 15 1.31743 2.11050 0.40518 3.02275 1.71397 0.33603
7 1.34 21 0.81065 1.67947 -0.07569 2.56581 1.24506 0.09494
8 0.79 23 0.61834 1.55918 -0.24427 2.42179 1.08876 -0.29876
9 0.66 30 -0.10813 1.19154 -0.86469 1.94811 0.54171 0.11829
10 0.30 36 -0.76520 0.91081 -1.42984 1.57544 0.07280 0.22720
11 . 20 0.90302 1.74341 0.00707 2.63936 1.32321 .

regression of conc on dist (3) ANOVA with uncorrected total SS

The GLM Procedure

The GLM Procedure

Data

Number of Observations

Number of Observations Read 10
Number of Observations Used 10

regression of conc on dist (3) ANOVA with uncorrected total SS

The GLM Procedure

 

Dependent Variable: conc

Analysis of Variance

conc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 33.38641399 16.69320699 57.06 <.0001
Error 8 2.34038601 0.29254825    
Uncorrected Total 10 35.72680000      

Fit Statistics

R-Square Coeff Var Root MSE conc Mean
0.746244 33.22342 0.540877 1.628000

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
Intercept 1 26.50384000 26.50384000 90.60 <.0001
dist 1 6.88257399 6.88257399 23.53 0.0013

Type II Model ANOVA

Source DF Type II SS Mean Square F Value Pr > F
Intercept 1 25.24177252 25.24177252 86.28 <.0001
dist 1 6.88257399 6.88257399 23.53 0.0013

Solution

Parameter Estimate Standard
Error		 t Value Pr > |t|
Intercept 2.886225930 0.31071996 9.29 <.0001
dist -0.078150679 0.01611225 -4.85 0.0013

regression of conc on dist (4) Standard output from proc glm

The GLM Procedure

The GLM Procedure

Data

Number of Observations

Number of Observations Read 10
Number of Observations Used 10

regression of conc on dist (4) Standard output from proc glm

The GLM Procedure

 

Dependent Variable: conc

Analysis of Variance

conc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 6.88257399 6.88257399 23.53 0.0013
Error 8 2.34038601 0.29254825    
Corrected Total 9 9.22296000      

Fit Statistics

R-Square Coeff Var Root MSE conc Mean
0.746244 33.22342 0.540877 1.628000

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
dist 1 6.88257399 6.88257399 23.53 0.0013

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
dist 1 6.88257399 6.88257399 23.53 0.0013

Solution

Parameter Estimate Standard
Error		 t Value Pr > |t|
Intercept 2.886225930 0.31071996 9.29 <.0001
dist -0.078150679 0.01611225 -4.85 0.0013

Fit Plot

Fit Plot for conc by dist

regression of conc on dist (5) Standard output from proc reg

The REG Procedure

Model: MODEL1

Dependent Variable: conc

The Reg Procedure

MODEL1

Fit

conc

Number of Observations

Number of Observations Read 10
Number of Observations Used 10

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 1 6.88257 6.88257 23.53 0.0013
Error 8 2.34039 0.29255    
Corrected Total 9 9.22296      

Fit Statistics

Root MSE 0.54088 R-Square 0.7462
Dependent Mean 1.62800 Adj R-Sq 0.7145
Coeff Var 33.22342    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 2.88623 0.31072 9.29 <.0001
dist 1 -0.07815 0.01611 -4.85 0.0013

regression of conc on dist (5) Standard output from proc reg

The REG Procedure

Model: MODEL1

Dependent Variable: conc

Observation-wise Statistics

conc

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for conc.

Residual Plots

dist

Scatter plot of residuals by dist for conc.

Fit Plot

Scatterplot of conc by dist overlaid with the fit line, a 95% confidence band and lower and upper 95% prediction limits.