Cement composition. Data on the effect of composition of cement on-heat evolved during hardening are given below. The variables collected were the amount of tricalcium aluminate (X I), the amount of tricalcium silicate (X₂), the amount of tetracalcium  alumino ferrite (X₃), the amount of dicalcium silicate (X₄), and the heat evolved in calories per gram of cement (Y).

a. Fit regression model (6.5) for four predictor variables to the data. State the estimated regression function.

b. Obtain the estimated ridge standardized regression coefficients, variance inflation factors, and R² for the following biasing constants: c = .000, .002, .004, .006, .008, .02, .04, .06, .08, .10.

c. Make a ridge trace plot for the biasing constants listed in part (b). Do the ridge regression coefficients exhibit substantial changes near c = O?

d. Suggest a reasonable value for the biasing constant c based on the ridge trace, VIF values, and R² values.

e. Transform the estimated standardized ridge regression coefficients selected in part (d) to the original variables and obtain the fitted values for the 13 cases. How similar are these fitted values to those obtained with the ordinary least squares fit ill part (a)?