EXST7034 : Regression Techniques Geaghan Logistic regression Page 1 1 ***********************************************************************; 2 *** EXST7034 Homework Example ***; 3 *** Problem from Neter, Kutner, Nachtsheim, Wasserman 1996,14.9 ***; 4 ***********************************************************************; 5 6 dm'log;clear;output;clear'; 7 options nodate nocenter nonumber ps=512 ls=132 nolabel; 8 ODS HTML style=minimal rs=none body='C:\Geaghan\Current\EXST7034\Fall2005\SAS\Toxicity01.html' ; NOTE: Writing HTML Body file: C:\Geaghan\Current\EXST7034\Fall2005\SAS\Toxicity01.html 9 10 DATA Toxicity indicator; INFILE CARDS MISSOVER; 11 TITLE1 'Logistic regression : Toxicity experiment'; 12 LABEL X = 'Dose level (log scale)'; 13 LABEL R = 'No of insects which died'; 14 LABEL N = 'No of insects exposed'; 15 LABEL P = 'Mortality proportion'; 16 INPUT X R N; 17 P = R / N; 18 LOGIT = LOG(P/(1-P)); 19 WT = N*P*(1-P); 20 output toxicity; 21 indicator = 1; output indicator; 22 R = N - R; indicator = 0; output indicator; 23 *** NOTE: expected variance of P is 1/(n*p*(1-p)) ***; 24 CARDS; NOTE: The data set WORK.TOXICITY has 6 observations and 7 variables. NOTE: The data set WORK.INDICATOR has 12 observations and 7 variables. NOTE: DATA statement used (Total process time): real time 0.03 seconds cpu time 0.03 seconds 24 ! RUN; 31 ; 32 PROC PRINT DATA=toxicity; VAR X R N P; 33 TITLE2 'Sorted Raw Data Listing : original data'; RUN; NOTE: There were 6 observations read from the data set WORK.TOXICITY. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used (Total process time): real time 0.11 seconds cpu time 0.00 seconds 34 PROC PRINT DATA=indicator; VAR X R N P indicator; 35 TITLE2 'Sorted Raw Data Listing : with indicator variable'; RUN; NOTE: There were 12 observations read from the data set WORK.INDICATOR. NOTE: The PROCEDURE PRINT printed page 2. NOTE: PROCEDURE PRINT used (Total process time): real time 0.05 seconds cpu time 0.01 seconds Logistic regression : Toxicity experiment Sorted Raw Data Listing : original data Obs X R N P 1 1 28 250 0.112 2 2 53 250 0.212 3 3 93 250 0.372 4 4 126 250 0.504 5 5 172 250 0.688 6 6 197 250 0.788 Logistic regression : Toxicity experiment Sorted Raw Data Listing : with indicator Obs X R N P indicator 1 1 28 250 0.112 1 2 1 222 250 0.112 0 3 2 53 250 0.212 1 4 2 197 250 0.212 0 5 3 93 250 0.372 1 6 3 157 250 0.372 0 7 4 126 250 0.504 1 8 4 124 250 0.504 0 9 5 172 250 0.688 1 10 5 78 250 0.688 0 11 6 197 250 0.788 1 12 6 53 250 0.788 0EXST7034 : Regression Techniques Geaghan Logistic regression Page 2 37 PROC REG DATA=toxicity; 38 TITLE2 'Using PROC REG'; 39 TITLE3 'As a Simple linear regression with proportion'; 40 MODEL P = X; 41 output out=next1 p=pred1 r=resid1; 42 RUN; 42 ! QUIT; NOTE: The data set WORK.NEXT1 has 6 observations and 9 variables. NOTE: The PROCEDURE REG printed page 3. NOTE: PROCEDURE REG used (Total process time): real time 0.11 seconds cpu time 0.05 seconds Logistic regression : Toxicity experiment Using PROC REG As a Simple linear regression with proportion The REG Procedure Model: MODEL1 Dependent Variable: P Number of Observations Read 6 Number of Observations Used 6 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.34862 0.34862 677.88 <.0001 Error 4 0.00206 0.00051429 Corrected Total 5 0.35068 Root MSE 0.02268 R-Square 0.9941 Dependent Mean 0.44600 Adj R-Sq 0.9927 Coeff Var 5.08472 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 -0.04800 0.02111 -2.27 0.0854 X 1 0.14114 0.00542 26.04 <.0001 44 PROC REG DATA=indicator; freq R; 45 TITLE3 'As a Simple linear regression with indicator variable'; 46 MODEL indicator = X; 47 output out=next2 p=pred2 r=resid2; 48 RUN; 48 ! QUIT; NOTE: The data set WORK.NEXT2 has 12 observations and 9 variables. NOTE: The PROCEDURE REG printed page 4. NOTE: PROCEDURE REG used (Total process time): real time 0.13 seconds cpu time 0.05 seconds Logistic regression : Toxicity experiment Using PROC REG As a Simple linear regression with indicator variable The REG Procedure Model: MODEL1 Dependent Variable: indicator Number of Observations Read 12 Number of Observations Used 12 Sum of Frequencies Read 1500 Sum of Frequencies Used 1500EXST7034 : Regression Techniques Geaghan Logistic regression Page 3 Frequency: R Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 87.15571 87.15571 460.57 <.0001 Error 1498 283.47029 0.18923 Corrected Total 1499 370.62600 Root MSE 0.43501 R-Square 0.2352 Dependent Mean 0.44600 Adj R-Sq 0.2346 Coeff Var 97.53557 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1