Question: Problem 6.5:

In a small-scale experimental study of the relation between degree of brand liking \((Y)\) and moisture content \(({{X}_{1}})\) and sweetness \(({{X}_{2}})\) of the product, the following results were obtained from the experiment based on a completely randomized design (data are coded): [Note X_n in 1^st column and 2^nd row should read X_i1 AND X_n in 1^st column and 3^rd row should read X_i2]

a. Obtain the studentized deleted residuals and identify any outlying Y observations at the .01 level.

State the decision rule and conclusion.

b. Obtain the diagonal elements of the hat matrix, and provide an explanation for the pattern in these elements.

Hint: Since SPSS lists “centered leverage values,” you need to add 1/n to all values obtained in SPSS to get “leverage values.” Compare HO#37, numbers on the last page (.151, .009, etc.) to those in Table 10.3. You need to add 1/20 (.050) to the former to get the latter.

HO#37

Table 10.3:

c. Are any of the observations outlying with regard to their X values according to the rule of thumb stated in the chapter?

d. Obtain the DFFITS, DFBETAS, and Cook’s D for all cases. Identify possibly influential cases and assess the influence of them. What do you conclude?