The reduced regression models for testing for interaction

Reference no: EM131096209

Refer to Cash offers Problems 19.10 and 22.15. Assume that covariance model (22.26) is applicable.

a. State the regression model equivalent to covariance model (22.26) for this case; use 1, -1,

o indicator variables. Fit this full model.

b. State the reduced regression models for testing for interaction and factor A and factor B main effects, respectively. Fit these reduced regression models.

c. Test for interaction effects; use α = .05. State the alternatives, decision rule, and conclusion. What is the P-value of thy test?

d. Test for factor A main effects; use α = .05. State the alternatives, decision rule, and conclusion. What is the P-value of the test?

e. Test for factor B main effects; use α = .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.

Problems 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 (X_ij) 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 α = .01. State the alternatives, decision rule, and conclusion. What is the P-value of the test?

Problem 19.10

Refer to Cash offers Problem 16.10. Six male and six female volunteers were used in each age group. The observations (in hundred dollars), classified by age (factor A) and gender of owner (factor B), follow.

a. Obtain the fitted values for ANOYA model (19.23).

b. Obtain the residuals. Do they sum to zero for each treatment?

c. Prepare aligned residual dot plots for the treatments. What departures from ANOYA model (19.23) can be studied from these plots? What are your findings?

d. Prepare a normal probability plot of the residuals. Also obtain the coefficient of correlation between the ordered residuals and their expected values under normality. Does the normality assumption appear to be reasonable here?

e. The observations for each treatment were obtained in the order shown. Prepare residual, sequence plots and interpret them. What are your findings?

Problem 16.10

Cash offers. A consumer organization studied the effect of age of automobile owner on size of cash offer for a used car by utilizing 12 persons in each of three age groups (young, middle, elderly) who acted as the owner of a used car. A medium price, six-year-old car was selected for the experiment, and the "owners" solicited cash offers for this car from 36 dealers selected at random from the dealers in the region. Randomization was used in assigning the dealers to the "owners." The offers (in hundred dollars) follow. Assume that ANOVA model (16.2) is applicable

a. Prepare aligned dot plots of the data. Do the factor level means appear to differ? Does the variability of the observations within each factor level appear to be approximately the same for all factor levels?

b. Obtain the fitted values.

c. Obtain the residuals.

d. Obtain the analysis of variance table.

e. Conduct the F test for equality off actor level means; use α= .01. State the alternatives. decision rule, and conclusion. What is the P-value of the test?

f. What appears to be the nature of the relationship between age of owner and mean cash offer?

Reference no: EM131096209

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