Using the data of Exercise 14.100,
In exercise

(a) Create a new variable, x1x2.
(b) Fit a surface of the form

(c) Find the correlation matrix of the four independent variables. Is there evidence of multicollinearity?
(d) Standardize each of the three independent variables x1, x2, and x3, and create a new variable that is the product of the standardized values of x1 and x2.
(e) Fit a curved surface of the same form to the standardized variables. Compare the goodness of fit of this surface to that of the linear surface fitted in Exercise 14.100.
(f) Find the correlation matrix of the four standardized independent variables and compare with the results of part (c).

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