Brand preference. In a small-scale experimental study of the relation between degree of brand liking (Y) and moisture content (X1) and sweetness (X2 ) of the product, the following results were obtained from the experiment based on a completely randomized design (data are coded): i: 1 2 3 ... 14 15 16
Xi1: 4 4 4 10 10 10
Xi2: 2 4 2 4 2 4
Yi: 64 73 63 95 94 100
a. Obtain the scatter plot matrix and the correlation 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 bt interpreted here? c. Obtain the residuals and prepare a box plot of the residuals. What information does this plot provide?
d. Plot the residuals against Y^, X1, X2, and X1, X2 on separate graphs. Also prepare a probability plot. Interpret the plots and summarize your findings.
e. Conduct the Breach-Pagan test for constancy of the error variance, assuming log sigma^2i = gama_0 + gama 1X_i1 + gama_2X_i2: use alpha = .01. State the alternatives, decision rule, and conclusion.
f. Conduct a formal test for lack of fit of the first-order regression function; use alpha = .01. State the alternatives, decision rule, and conclusion.