22.16 Only!: There is some SAS code for reference
You only need to conduct the estimation and test. Does not have to be regression approach where
i is the main effect of factor A at the i th level, j is the main effect of factor B at the j th level, and
()ij is the interaction effect when factor A is at the i th level and factor B is at the j th level. The
covariance model for a two-factor study with a single concomitant variable, assuming the
relation between Y and the concomitant variable X is linear, is:
Yijk=..+i+i+()ij+(XijkX)+ijki=1,,a;j=1.,b;k=1,,n
proc glm data=CH22PR15; class A B; model Y=ABBABX/ clparam alpha=0.025; estimate 'D 1'
A 110; estimate 'D 2' A 101 estimate 'D 3' A 011 estimate 'D 4' B 11 run;
*22.15. Refer to Cash offers Problem 19.10. An analyst wishes to use each dealer's sales volume
as a concomitant variable. The sales data ( Xijk, in hundred thousand dollars) follow. a. Obtain
the residuals for covariance model (22.26). b. For each treatment, plot the residuals against the
fitted values. Also prepare a normal probability plot of the residuals and calculate the coefficient
of correlation between the ordered residuals and their expected values under normality. What do
you conclude from your analysis? c. State the generalized regression model to be employed for
testing whether or not the treatment regression lines have the same slope. Conduct this test using
=.01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? 22.16.
Refer to Cash offers Problems 19.10 and 22.15. Assume that covariance model (22.26) is
applicable. c. Test for interaction effects; use =.05. State the alternatives, decision rule, and
conclusion. What is the P-value of the test? d. Test for factor A main effects; use =.05. State the
alternatives, decision rule, and conclusion. What is the P-value of the test? e. Test for factor B
main effects; use =.05. State the alternatives, decision rule, and conclusion. What is the P-value
of the test? f. For each factor, make all pairwise comparisons between the factor level main
effects. Use the Bonferroni procedure with a 90 percent family confidence coefficient. State your
findings..
22.16 Only! There is some SAS code for referenceYou only need to .pdf
1. 22.16 Only!: There is some SAS code for reference
You only need to conduct the estimation and test. Does not have to be regression approach where
i is the main effect of factor A at the i th level, j is the main effect of factor B at the j th level, and
()ij is the interaction effect when factor A is at the i th level and factor B is at the j th level. The
covariance model for a two-factor study with a single concomitant variable, assuming the
relation between Y and the concomitant variable X is linear, is:
Yijk=..+i+i+()ij+(XijkX)+ijki=1,,a;j=1.,b;k=1,,n
proc glm data=CH22PR15; class A B; model Y=ABBABX/ clparam alpha=0.025; estimate 'D 1'
A 110; estimate 'D 2' A 101 estimate 'D 3' A 011 estimate 'D 4' B 11 run;
*22.15. Refer to Cash offers Problem 19.10. An analyst wishes to use each dealer's sales volume
as a concomitant variable. The sales data ( Xijk, in hundred thousand dollars) follow. a. Obtain
the residuals for covariance model (22.26). b. For each treatment, plot the residuals against the
fitted values. Also prepare a normal probability plot of the residuals and calculate the coefficient
of correlation between the ordered residuals and their expected values under normality. What do
you conclude from your analysis? c. State the generalized regression model to be employed for
testing whether or not the treatment regression lines have the same slope. Conduct this test using
=.01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? 22.16.
Refer to Cash offers Problems 19.10 and 22.15. Assume that covariance model (22.26) is
applicable. c. Test for interaction effects; use =.05. State the alternatives, decision rule, and
conclusion. What is the P-value of the test? d. Test for factor A main effects; use =.05. State the
alternatives, decision rule, and conclusion. What is the P-value of the test? e. Test for factor B
main effects; use =.05. State the alternatives, decision rule, and conclusion. What is the P-value
of the test? f. For each factor, make all pairwise comparisons between the factor level main
effects. Use the Bonferroni procedure with a 90 percent family confidence coefficient. State your
findings.
