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.