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, results were obtained from the experiment based on a completely randomized design. x1 and x2 are indices and have no units of measurements. Fit a regression model of the form y = β0 + β1x1 + β2x2 + e.

Here, e is the random error term which is assumed to be normally distributed with mean 0 and constant variance.

Data Set:
y x1 x2
64 4 2
73 4 4
61 4 2
76 4 4
72 6 2
80 6 4
71 6 2
83 6 4
83 8 2
89 8 4
86 8 2
93 8 4
88 10 2
95 10 4
94 10 2
100 10 4

Required:
a. Write your estimated regression equation. Round your answers to three decimal places.
b. Construct and interpret a 99% confidence interval for the mean brand liking score when the moisture content is 5 and the sweetness level is 4.
c. Construct and interpret a 99% prediction interval for the brand liking score when the moisture content is 5 and the sweetness level is 4.
d. Which interval (the mean response or the prediction interval) is wider? Why?
e. Conduct the global test of model significance. List out all the steps in detail.
f. What is the variance inflation factors associated with the two predictor variables? Is the multicollinearity assumption violated? Why or why not?