1 ************************************************************************; 2 *** EXST7034 Example 1 using PC-SAS - Toluca Company Example ***; 3 *** Problem from Neter, Kutner, Nachtsheim & Wasserman 1996, #1.21 ***; 4 ************************************************************************; 5 ODS HTML style=minimal rs=none 6 body='C:\Geaghan\EXST\EXST7034New\Fall2002\SAS\03b-Toluca-Nknw1-Ex.html' ; NOTE: Writing HTML Body file: C:\Geaghan\EXST\EXST7034New\Fall2002\SAS\03b-Toluca-Nknw1-Ex.html 9 OPTIONS LS=155 PS=256 NOCENTER NODATE NONUMBER; 10 DATA ONE; INFILE CARDS MISSOVER; 11 TITLE1 'EXST7034 - Chapter 3 examples : Toluca example'; 12 * LABEL X = 'Lot size'; 13 * LABEL Y = 'work hours'; 14 INPUT X Y; 15 group = 'Upper'; If X lt 80 then group = 'Lower'; 16 anotherX = X; 17 CARDS; NOTE: The data set WORK.ONE has 25 observations and 4 variables. NOTE: DATA statement used: real time 0.10 seconds 43 ; 44 PROC SORT; BY group X Y; run; NOTE: There were 25 observations read from the data set WORK.ONE. NOTE: The data set WORK.ONE has 25 observations and 4 variables. NOTE: PROCEDURE SORT used: real time 0.05 seconds 45 PROC REG DATA=ONE lineprinter; id x; 46 TITLE2 'Regression Models done with SAS REG procedure'; 47 MODEL Y = X / XPX I P CLM CLI R CLB alpha=0.01; 48 TEST X = 5; 49 OUTPUT OUT=Next2 PREDICTED=YHat RESIDUAL=E; RUN; NOTE: 25 observations read. NOTE: 25 observations used in computations. 50 OPTIONS PS=35 ls=80; PLOT Y*X='O' PREDICTED.*X='P'/ OVERLAY; 51 PLOT RESIDUAL.*X='e'; RUN; NOTE: The data set WORK.NEXT2 has 25 observations and 6 variables. NOTE: The PROCEDURE REG printed pages 1-6. NOTE: PROCEDURE REG used: real time 0.17 seconds EXST7034 - Chapter 3 examples : Toluca example Regression Models done with SAS REG procedure The REG Procedure Model: MODEL1 Model Crossproducts X'X X'Y Y'Y Variable Intercept X Y Intercept 25 1750 7807 X 1750 142300 617180 Y 7807 617180 2745173 X'X Inverse, Parameter Estimates, and SSE Variable Intercept X Y Intercept 0.2874747475 -0.003535354 62.365858586 X -0.003535354 0.0000505051 3.5702020202 Y 62.365858586 3.5702020202 54825.459192 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 252378 252378 105.88 <.0001 Error 23 54825 2383.71562 Corrected Total 24 307203 Root MSE 48.82331 R-Square 0.8215 Dependent Mean 312.28000 Adj R-Sq 0.8138 Coeff Var 15.63447 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| 99% Confidence Limits Intercept 1 62.36586 26.17743 2.38 0.0259 -11.12299 135.85470 X 1 3.57020 0.34697 10.29 <.0001 2.59613 4.54427EXST7034 - Chapter 3 examples : Toluca example Regression Models done with SAS REG procedure The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Dep Var Predicted Std Error Std Error Student Cook's Obs X Y Value Mean Predict 99% CL Mean 99% CL Predict Residual Residual Residual -2-1 0 1 2 D 1 20 113.0000 133.7699 19.9079 77.8819 189.6579 -14.2499 281.7897 -20.7699 44.580 -0.466 | | | 0.022 2 30 121.0000 169.4719 16.9697 121.8322 217.1117 24.3653 314.5785 -48.4719 45.779 -1.059 | **| | 0.077 3 30 212.0000 169.4719 16.9697 121.8322 217.1117 24.3653 314.5785 42.5281 45.779 0.929 | |* | 0.059 4 30 273.0000 169.4719 16.9697 121.8322 217.1117 24.3653 314.5785 103.5281 45.779 2.261 | |**** | 0.351 5 40 160.0000 205.1739 14.2723 165.1067 245.2412 62.3742 347.9737 -45.1739 46.691 -0.968 | *| | 0.044 6 40 244.0000 205.1739 14.2723 165.1067 245.2412 62.3742 347.9737 38.8261 46.691 0.832 | |* | 0.032 7 50 157.0000 240.8760 11.9793 207.2459 274.5060 99.7471 382.0048 -83.8760 47.331 -1.772 | ***| | 0.101 8 50 221.0000 240.8760 11.9793 207.2459 274.5060 99.7471 382.0048 -19.8760 47.331 -0.420 | | | 0.006 9 50 268.0000 240.8760 11.9793 207.2459 274.5060 99.7471 382.0048 27.1240 47.331 0.573 | |* | 0.011 10 60 224.0000 276.5780 10.3628 247.4861 305.6698 136.4612 416.6948 -52.5780 47.711 -1.102 | **| | 0.029 11 70 252.0000 312.2800 9.7647 284.8673 339.6927 172.5022 452.0578 -60.2800 47.837 -1.260 | **| | 0.033 12 70 323.0000 312.2800 9.7647 284.8673 339.6927 172.5022 452.0578 10.7200 47.837 0.224 | | | 0.001 13 70 361.0000 312.2800 9.7647 284.8673 339.6927 172.5022 452.0578 48.7200 47.837 1.018 | |** | 0.022 14 80 342.0000 347.9820 10.3628 318.8902 377.0739 207.8652 488.0988 -5.9820 47.711 -0.125 | | | 0.000 15 80 352.0000 347.9820 10.3628 318.8902 377.0739 207.8652 488.0988 4.0180 47.711 0.0842 | | | 0.000 16 80 399.0000 347.9820 10.3628 318.8902 377.0739 207.8652 488.0988 51.0180 47.711 1.069 | |** | 0.027 17 90 376.0000 383.6840 11.9793 350.0540 417.3141 242.5552 524.8129 -7.6840 47.331 -0.162 | | | 0.001 18 90 377.0000 383.6840 11.9793 350.0540 417.3141 242.5552 524.8129 -6.6840 47.331 -0.141 | | | 0.001 19 90 389.0000 383.6840 11.9793 350.0540 417.3141 242.5552 524.8129 5.3160 47.331 0.112 | | | 0.000 20 90 468.0000 383.6840 11.9793 350.0540 417.3141 242.5552 524.8129 84.3160 47.331 1.781 | |*** | 0.102 21 100 353.0000 419.3861 14.2723 379.3188 459.4533 276.5863 562.1858 -66.3861 46.691 -1.422 | **| | 0.094 22 100 420.0000 419.3861 14.2723 379.3188 459.4533 276.5863 562.1858 0.6139 46.691 0.0131 | | | 0.000 23 110 421.0000 455.0881 16.9697 407.4483 502.7278 309.9815 600.1947 -34.0881 45.779 -0.745 | *| | 0.038 24 110 435.0000 455.0881 16.9697 407.4483 502.7278 309.9815 600.1947 -20.0881 45.779 -0.439 | | | 0.013 25 120 546.0000 490.7901 19.9079 434.9021 546.6781 342.7703 638.8099 55.2099 44.580 1.238 | |** | 0.153 Sum of Residuals 0 Sum of Squared Residuals 54825 Predicted Residual SS (PRESS) 65818 Test 1 Results for Dependent Variable Y Mean Source DF Square F Value Pr > F Numerator 1 40478 16.98 0.0004 Denominator 23 2383.71562 EXST7034 - Chapter 3 examples : Toluca example Regression Models done with SAS REG procedure The REG Procedure Model: MODEL1 Dependent Variable: Y --+------+------+------+------+------+------+------+------+------+------+--- Y | | 600 + + | | | O | | P | | O P | | ? O | 400 + O ? + | O O O O | | O ? | | P | | O O P O | | O ? O | 200 + O P + | P O O | | P O | | O | | | | | 0 + + | | --+------+------+------+------+------+------+------+------+------+------+--- 20 30 40 50 60 70 80 90 100 110 120 X ----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---- 100 + e + | | | e | | | | e | 50 + e e + R | e e | e RESIDUAL | e | s | | i | e e | d 0 + e e + u | e e | a | e e e | l | e | | | -50 + e e e + | e | | e | | e | | | -100 + + ----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---- 20 30 40 50 60 70 80 90 100 110 120 X 52 PROC PLOT DATA=Next2; PLOT E*X='x' / VREF=0; RUN; 53 OPTIONS PS=256 ls=88; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE PLOT printed page 7. NOTE: PROCEDURE PLOT used: real time 0.00 seconds EXST7034 - Chapter 3 examples : Toluca example Regression Models done with SAS REG procedure Plot of E*X. Symbol used is 'x'. | | 100 + x | | x | | x 50 + x x R | x x e | x s | i | x x d 0 +------------------------------------------x-------------x--------------- u | x x a |x x x l | x | -50 + x x x | x | x | x | -100 + | -+------+------+------+------+------+------+------+------+------+------+- 20 30 40 50 60 70 80 90 100 110 120 X NOTE: 1 obs hidden. 55 PROC UNIVARIATE DATA=Next2 PLOT NORMAL; VAR E; RUN; NOTE: The PROCEDURE UNIVARIATE printed page 8. NOTE: PROCEDURE UNIVARIATE used: real time 0.00 seconds EXST7034 - Chapter 3 examples : Toluca example Regression Models done with SAS REG procedure The UNIVARIATE Procedure Variable: E (Residual) Moments N 25 Sum Weights 25 Mean 0 Sum Observations 0 Std Deviation 47.7953359 Variance 2284.39413 Skewness 0.31691262 Kurtosis -0.3941493 Uncorrected SS 54825.4592 Corrected SS 54825.4592 Coeff Variation . Std Error Mean 9.55906718 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 47.79534 Median -5.98202 Variance 2284 Mode . Range 187.40404 Interquartile Range 72.91414 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -0.5 Pr >= |M| 1.0000 Signed Rank S -7.5 Pr >= |S| 0.8448 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.978904 Pr < W 0.8626 Kolmogorov-Smirnov D 0.09572 Pr > D >0.1500 Cramer-von Mises W-Sq 0.033263 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.207142 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 103.52808 99% 103.52808 95% 84.31596 90% 55.20990 75% Q3 38.82606 50% Median -5.98202 25% Q1 -34.08808 10% -60.28000 5% -66.38606 1% -83.87596 0% Min -83.87596 Extreme Observations ------Lowest----- ------Highest----- Value Obs Value Obs -83.8760 7 48.7200 13 -66.3861 21 51.0180 16 -60.2800 11 55.2099 25 -52.5780 10 84.3160 20 -48.4719 2 103.5281 4 Stem Leaf # Boxplot 10 4 1 | 8 4 1 | 6 | 4 3915 4 | 2 79 2 +-----+ 0 1451 4 | + | -0 876 3 *-----* -2 4100 4 +-----+ -4 385 3 | -6 60 2 | -8 4 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**+1 Normal Probability Plot 110+ *+++++ | * ++++ | ++++ | **+*+* | **++ 10+ +**** | +**** | ++*** | +*+** | +*+* -90+ *+++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 57 PROC SORT; BY group X Y; run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The data set WORK.NEXT2 has 25 observations and 6 variables. NOTE: PROCEDURE SORT used: real time 0.04 seconds 58 PROC means data=next2 noprint; BY group; var e; 59 OUTPUT OUT=NEXT3 median=med; 60 run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The data set WORK.NEXT3 has 2 observations and 4 variables. NOTE: PROCEDURE MEANS used: real time 0.06 seconds 61 data next2; merge next2 next3; by group; 62 absE = abs(e); 63 esquared = e*e; 64 logesq = log(esquared); 65 logX = Log(X); 66 leveneTest = abs(e - med); 67 drop _TYPE_ _FREQ_; 68 run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: There were 2 observations read from the data set WORK.NEXT3. NOTE: The data set WORK.NEXT2 has 25 observations and 12 variables. NOTE: DATA statement used: real time 0.00 seconds 69 proc print data=next2; run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE PRINT printed page 9. NOTE: PROCEDURE PRINT used: real time 0.04 seconds EXST7034 - Chapter 3 examples : Toluca example Regression Models done with SAS REG procedure l e a e v n s e o q l n g t u o e r h Y a a g l T O o e H m b r e o e b u r a e s e s g s s X Y p X t E d E d q X t 1 20 113 Lower 20 133.770 -20.770 -19.8760 20.770 431.39 6.06701 2.99573 0.894 2 30 121 Lower 30 169.472 -48.472 -19.8760 48.472 2349.53 7.76197 3.40120 28.596 3 30 212 Lower 30 169.472 42.528 -19.8760 42.528 1808.64 7.50033 3.40120 62.404 4 30 273 Lower 30 169.472 103.528 -19.8760 103.528 10718.06 9.27969 3.40120 123.404 5 40 160 Lower 40 205.174 -45.174 -19.8760 45.174 2040.68 7.62104 3.68888 25.298 6 40 244 Lower 40 205.174 38.826 -19.8760 38.826 1507.46 7.31818 3.68888 58.702 7 50 157 Lower 50 240.876 -83.876 -19.8760 83.876 7035.18 8.85868 3.91202 64.000 8 50 221 Lower 50 240.876 -19.876 -19.8760 19.876 395.05 5.97902 3.91202 0.000 9 50 268 Lower 50 240.876 27.124 -19.8760 27.124 735.71 6.60084 3.91202 47.000 10 60 224 Lower 60 276.578 -52.578 -19.8760 52.578 2764.44 7.92459 4.09434 32.702 11 70 252 Lower 70 312.280 -60.280 -19.8760 60.280 3633.68 8.19800 4.24850 40.404 12 70 323 Lower 70 312.280 10.720 -19.8760 10.720 114.92 4.74422 4.24850 30.596 13 70 361 Lower 70 312.280 48.720 -19.8760 48.720 2373.64 7.77218 4.24850 68.596 14 80 342 Upper 80 347.982 -5.982 -2.6840 5.982 35.78 3.57752 4.38203 3.298 15 80 352 Upper 80 347.982 4.018 -2.6840 4.018 16.14 2.78156 4.38203 6.702 16 80 399 Upper 80 347.982 51.018 -2.6840 51.018 2602.83 7.86436 4.38203 53.702 17 90 376 Upper 90 383.684 -7.684 -2.6840 7.684 59.04 4.07829 4.49981 5.000 18 90 377 Upper 90 383.684 -6.684 -2.6840 6.684 44.68 3.79945 4.49981 4.000 19 90 389 Upper 90 383.684 5.316 -2.6840 5.316 28.26 3.34143 4.49981 8.000 20 90 468 Upper 90 383.684 84.316 -2.6840 84.316 7109.18 8.86914 4.49981 87.000 21 100 353 Upper 100 419.386 -66.386 -2.6840 66.386 4407.11 8.39097 4.60517 63.702 22 100 420 Upper 100 419.386 0.614 -2.6840 0.614 0.38 -0.97572 4.60517 3.298 23 110 421 Upper 110 455.088 -34.088 -2.6840 34.088 1162.00 7.05790 4.70048 31.404 24 110 435 Upper 110 455.088 -20.088 -2.6840 20.088 403.53 6.00025 4.70048 17.404 25 120 546 Upper 120 490.790 55.210 -2.6840 55.210 3048.13 8.02228 4.78749 57.894 70 proc ttest data=next2; 71 TITLE2 'TTest for the Modified Levene test'; 72 class group; var leveneTest; 73 run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE TTEST printed page 10. NOTE: PROCEDURE TTEST used: real time 0.00 seconds EXST7034 - Chapter 3 examples : Toluca example TTest for the Modified Levene test The TTEST Procedure Statistics Lower CL Upper CL Lower CL Upper CL Variable group N Mean Mean Mean Std Dev Std Dev Std Dev leveneTest Lower 13 25.26 44.815 64.37 23.205 32.361 53.419 leveneTest Upper 12 9.6702 28.45 47.23 20.939 29.558 50.186 leveneTest Diff (1-2) -9.35 16.365 42.08 24.134 31.052 43.558 Statistics Variable group Std Err Minimum Maximum leveneTest Lower 8.9753 0 123.4 leveneTest Upper 8.5326 3.298 87 leveneTest Diff (1-2) 12.431 T-Tests Variable Method Variances DF t Value Pr > |t| leveneTest Pooled Equal 23 1.32 0.2010 leveneTest Satterthwaite Unequal 23 1.32 0.1993 Equality of Variances Variable Method Num DF Den DF F Value Pr > F leveneTest Folded F 12 11 1.20 0.7710 75 proc npar1way data=next2; 76 TITLE2 'Nonparametric analysis of abs(residuals)'; 77 TITLE3 'Other tests of residuals for homogeneity'; 78 class group; var abse; 79 run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE NPAR1WAY printed pages 11-16. NOTE: PROCEDURE NPAR1WAY used: real time 0.00 seconds 80 proc npar1way data=next2; 81 TITLE2 'Nonparametric analysis of abs(residuals)'; 82 TITLE3 'Other tests of residuals for homogeneity'; 83 class group; var e; 84 run; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE NPAR1WAY printed pages 17-22. NOTE: PROCEDURE NPAR1WAY used: real time 0.04 seconds EXST7034 - Chapter 3 examples : Toluca example Nonparametric analysis of abs(residuals) Other tests of residuals for homogeneity The NPAR1WAY Procedure Analysis of Variance for Variable absE Classified by Variable group group N Mean Lower 13 46.343994 Upper 12 28.450337 Source DF Sum of Squares Mean Square F Value Pr > F Among 1 1997.941694 1997.941694 2.6730 0.1157 Within 23 17191.444414 747.454105 Wilcoxon Scores (Rank Sums) for Variable absE Classified by Variable group Sum of Expected Std Dev Mean group N Scores Under H0 Under H0 Score Lower 13 199.0 169.0 18.384776 15.307692 Upper 12 126.0 156.0 18.384776 10.500000 Wilcoxon Two-Sample Test Statistic 126.0000 Normal Approximation Z -1.6046 One-Sided Pr < Z 0.0543 Two-Sided Pr > |Z| 0.1086 t Approximation One-Sided Pr < Z 0.0608 Two-Sided Pr > |Z| 0.1217 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square 2.6627 DF 1 Pr > Chi-Square 0.1027 Median Scores (Number of Points Above Median) for Variable absE Classified by Variable group Sum of Expected Std Dev Mean group N Scores Under H0 Under H0 Score Lower 13 8.0 6.240 1.273735 0.615385 Upper 12 4.0 5.760 1.273735 0.333333 Median Two-Sample Test Statistic 4.0000 Z -1.3818 One-Sided Pr < Z 0.0835 Two-Sided Pr > |Z| 0.1670 Median One-Way Analysis Chi-Square 1.9093 DF 1 Pr > Chi-Square 0.1670 Van der Waerden Scores (Normal) for Variable absE Classified by Variable group Sum of Expected Std Dev Mean group N Scores Under H0 Under H0 Score Lower 13 3.826510 0.0 2.264058 0.294347 Upper 12 -3.826510 0.0 2.264058 -0.318876 Van der Waerden Two-Sample Test Statistic -3.8265 Z -1.6901 One-Sided Pr < Z 0.0455 Two-Sided Pr > |Z| 0.0910 Van der Waerden One-Way Analysis Chi-Square 2.8565 DF 1 Pr > Chi-Square 0.0910 Savage Scores (Exponential) for Variable absE Classified by Variable group Sum of Expected Std Dev Mean group N Scores Under H0 Under H0 Score Lower 13 2.470789 0.0 2.346881 0.190061 Upper 12 -2.470789 0.0 2.346881 -0.205899 Savage Two-Sample Test Statistic -2.4708 Z -1.0528 One-Sided Pr < Z 0.1462 Two-Sided Pr > |Z| 0.2924 Savage One-Way Analysis Chi-Square 1.1084 DF 1 Pr > Chi-Square 0.2924 Kolmogorov-Smirnov Test for Variable absE Classified by Variable group EDF at Deviation from Mean group N Maximum at Maximum Lower 13 0.000 -0.865332 Upper 12 0.500 0.900666 Total 25 0.240 Maximum Deviation Occurred at Observation 17 Value of absE at Maximum = 7.684040 Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS 0.249800 D 0.500000 KSa 1.249000 Pr > KSa 0.0883 Cramer-von Mises Test for Variable absE Classified by Variable group Summed Deviation group N from Mean Lower 13 0.192246 Upper 12 0.208267 Cramer-von Mises Statistics (Asymptotic) CM 0.016021 CMa 0.400513 Kuiper Test for Variable absE Classified by Variable group Deviation group N from Mean Lower 13 0.025641 Upper 12 0.500000 Kuiper Two-Sample Test (Asymptotic) K 0.525641 Ka 1.313051 Pr > Ka 0.3751 86 TITLE2 'Other tests for homogeneity of residuals'; 87 proc reg data=next2; TITLE3 'SLR'; model Y = x; run; NOTE: 25 observations read. NOTE: 25 observations used in computations. NOTE: The PROCEDURE REG printed page 23. NOTE: PROCEDURE REG used: real time 0.05 seconds 88 proc reg data=next2; TITLE3 'e*e on X'; model esquared = x; run; NOTE: 25 observations read. NOTE: 25 observations used in computations. NOTE: The PROCEDURE REG printed page 24. NOTE: PROCEDURE REG used: real time 0.00 seconds EXST7034 - Chapter 3 examples : Toluca example Other tests for homogeneity of residuals SLR The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 252378 252378 105.88 <.0001 Error 23 54825 2383.71562 Corrected Total 24 307203 Root MSE 48.82331 R-Square 0.8215 Dependent Mean 312.28000 Adj R-Sq 0.8138 Coeff Var 15.63447 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 62.36586 26.17743 2.38 0.0259 X 1 3.57020 0.34697 10.29 <.0001 Other tests for homogeneity of residuals e*e on X Dependent Variable: esquared Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 7896142 7896142 1.09 0.3070 Error 23 166395896 7234604 Corrected Total 24 174292038 Root MSE 2689.72195 R-Square 0.0453 Dependent Mean 2193.01837 Adj R-Sq 0.0038 Coeff Var 122.64931 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 3590.90811 1442.13939 2.49 0.0204 X 1 -19.96985 19.11502 -1.04 0.3070 Breusch-Pagan Test - P(>Chi square with 1 d.f.) = 0.364907535493054 89 proc reg data=next2; TITLE3 'log(e*e) on X'; model logesq = x; run; NOTE: 25 observations read. NOTE: 25 observations used in computations. NOTE: The PROCEDURE REG printed page 25. NOTE: PROCEDURE REG used: real time 0.05 seconds 90 proc reg data=next2; TITLE3 'Log(e*e) on log(X)'; model logesq = logx; NOTE: 25 observations read. NOTE: 25 observations used in computations. 91 options ps=55; NOTE: The PROCEDURE REG printed page 26. NOTE: PROCEDURE REG used: real time 0.05 seconds EXST7034 - Chapter 3 examples : Toluca example Other tests for homogeneity of residuals log(e*e) on X The REG Procedure Model: MODEL1 Dependent Variable: logesq Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 15.35148 15.35148 2.78 0.1093 Error 23 127.19606 5.53026 Corrected Total 24 142.54754 Root MSE 2.35165 R-Square 0.1077 Dependent Mean 6.33733 Adj R-Sq 0.0689 Coeff Var 37.10793 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 8.28646 1.26088 6.57 <.0001 X 1 -0.02784 0.01671 -1.67 0.1093 Log(e*e) on log(X) Dependent Variable: logesq Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 15.55203 15.55203 2.82 0.1068 Error 23 126.99551 5.52154 Corrected Total 24 142.54754 Root MSE 2.34980 R-Square 0.1091 Dependent Mean 6.33733 Adj R-Sq 0.0704 Coeff Var 37.07867 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 13.17710 4.10248 3.21 0.0039 logX 1 -1.64898 0.98254 -1.68 0.1068 91 PROC PLOT DATA=next2; PLOT e*x / href=75 vref=0; RUN; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE PLOT printed page 27. NOTE: PROCEDURE PLOT used: real time 0.00 seconds 92 PROC PLOT DATA=next2; PLOT logesq*logx / href=4.32; RUN; NOTE: There were 25 observations read from the data set WORK.NEXT2. NOTE: The PROCEDURE PLOT printed page 28. NOTE: PROCEDURE PLOT used: real time 0.00 seconds EXST7034 - Chapter 3 examples : Toluca example Other tests for homogeneity of residuals Log(e*e) on log(X) Plot of E*X. Legend: A = 1 obs, B = 2 obs, etc. | | 125 + | | | | | | A | 100 + | | | | | | | A 75 + | | | | | | | A 50 + A | A | A | R | A | e | | s 25 + A | i | | d | A | u | | A A a 0 +-----------------------------------------+----------------A---------------- l | | A B | | | A A | A -25 + | | | A | | | A | -50 + A A | | | | A | | | A -75 + | | A | | | | | -100 + | ---+------+------+------+------+------+------+------+------+------+------+-- 20 30 40 50 60 70 80 90 100 110 120 X Log(e*e) on log(X) Plot of logesq*logX. Legend: A = 1 obs, B = 2 obs, etc. 10 + | | | | | | A | | A | A | | | A | A 8 + A | A A | A A A | | A A | | | A | | | A | | | 6 + A A | A | | | | logesq | | | A | | | | | 4 + | A | | A A | | A | | | | A | | | | 2 + | | | | | | | | | | | | | 0 + | | | | | | | A | | ---+---------------+---------------+---------------+---------------+-- 3.0 3.5 4.0 4.5 5.0 logX 94 proc freq data=one; table x / NOROW NOCOL NOPERCENT; run; NOTE: There were 25 observations read from the data set WORK.ONE. NOTE: The PROCEDURE FREQ printed page 29. NOTE: PROCEDURE FREQ used: real time 0.04 seconds EXST7034 - Chapter 3 examples : Toluca example Other tests for homogeneity of residuals Log(e*e) on log(X) The FREQ Procedure Cumulative X Frequency Frequency ------------------------------ 20 1 1 30 3 4 40 2 6 50 3 9 60 1 10 70 3 13 80 3 16 90 4 20 100 2 22 110 2 24 120 1 25 95 proc mixed DATA=ONE; CLASSES AnotherX; 96 title2 'Analysis of Lack of Fit using PROC MIXED - Full Model'; 97 model Y = AnotherX / htype=1 3 DDFM=Satterthwaite solution; 98 run; NOTE: The PROCEDURE MIXED printed pages 30-31. NOTE: PROCEDURE MIXED used: real time 0.05 seconds EXST7034 - Chapter 3 examples : Toluca example Analysis of Lack of Fit using PROC MIXED - Full Model The Mixed Procedure Model Information Data Set WORK.ONE Dependent Variable Y Covariance Structure Diagonal Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Residual Class Level Information Class Levels Values anotherX 11 20 30 40 50 60 70 80 90 100 110 120 Dimensions Covariance Parameters 1 Columns in X 12 Columns in Z 0 Subjects 1 Max Obs Per Subject 25 Observations Used 25 Observations Not Used 0 Total Observations 25 EXST7034 - Chapter 3 examples : Toluca example Analysis of Lack of Fit using PROC MIXED - Full Model The Mixed Procedure Covariance Parameter Estimates Cov Parm Estimate Residual 2684.35 Fit Statistics -2 Res Log Likelihood 158.1 AIC (smaller is better)&