Refer to Brand preference Problem 6.5.
a. Fit first-order simple linear regression model (2.1) for relating brand liking (Y) to moisture content (X,). State the fitted regression function.
b. Compare the estimated regression coefficient for moisture content obtained in part (a) with the corresponding coefficient obtained in Problem 6.Sb. What do you find?
c. Does SSR(X1) equal SSR(XIIX2 ) here? If not, is the difference substantial?
d. Refer to the correlation matrix obtained in Problem 6.Sa. What bearing does this have on your findings in parts (b) and (c)?
Problem 6.5
Brand preference. In ,l small-scale experimental study of the relation between degree of brand liking (Y) and moisture content (XI) and sweetness (X2 ) of the product, the following results were obtained from the experiment based on a completely randomized design (date are coded):
a. Obtain the scatter plot matrix and the correction matrix,. What, information do these diagnostic aids provide here?
b. Fit regression model (6.1) to the data. State the estimated regression function. How is bi interpreted here?
c. Obtain the residuals and prepare ,l box plot of the residuals. What information does this plot provide?
d. Plot the residuals against Y, XI, X2 , and XI X2 on separate graphs. Also prepare a normal probability plot. Interpret the plots and summarize your findings.
e. Conduct the Breusch-Pagan test for constancy of the error variance, assuming log σ2i =
State the alternatives, decision rule and conclusion.
f. Conduct a formal test for lack of fit of the first-order regression function; use ex = .01. State the alternatives, decision rule, and conclusion.