C find the correlation matrix of the three independent

Question

Using the data of Exercise 99,

(a) Create a new variable, .

(b) Fit a surface of the form

(c) Find the correlation matrix of the three independent variables. Is there evidence of multi collinearity? (d) Standardize each of the independent variables, x₁ and x₂, and create a new variable that is the square of the standardized value of x₂

(e) Fit a surface of the same form as in part (b) to the standardized variables. Compare the goodness of fit of this surface to that of the linear surface fitted in Exercise 99.

(f) Plot the residuals of this regression analysis against the values of  and compare this plot to the one obtained in Exercise 99.

Exercise 99

(a) Fit a linear surface to the following data:

(b) How good a fit is obtained?

(c) Plot the residuals against  and determine whether the pattern is "random."

(d) Check for multi collinearity among the independent variables.