Refer to KNN Exercise 6.5 Brand Preference. We will be examining models with more than one explanatory variable next week. For now, consider what investigations can be done with just the single variable ideas studied thus far. a. Fit each of the following one variable models, and assess model fit: 1. Y = 0+ X1 + 2. Y = Bo + B1X2 + 3. Y Bo+B1X1X2 + = b. From your results in (a), which of the variables do you think might be helpful in a single model? 6.5. Brand preference. In a small-scale experimental study of the relation between degree of brand liking (Y) and moisture content () and sweetness (X2) of the product, the following results were obtained from the experiment based on a completely randomized design (data are coded): 1: 1 2 3 14 15 16 Xi: 4 4 4 10 10 10 Xiz 2 4 2 4 2 4 Y;: 64 73 61 95 94 100 a. Obtain the scatter plot matrix and the correlation matrix. What information do these diag- nostic aids provide here? b. Fit regression model (6.1) to the data. State the estimated regression function. How is by 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 , X1, X2, and XX2 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 o Yo+YXi1 + Y2X;2; use = .01. State the alternatives, decision rule, and conclusion. = f. Conduct a formal test for lack of fit of the first-order regression function; use = .01. State the alternatives, decision rule, and conclusion.