The accompanying data on x1 = card cylinder speed (rpm), card production rate (kg/h), x3 = number

Question:

The accompanying data on x1 = card cylinder speed (rpm), card production rate (kg/h), x3 = number of draw frame doubling, and y = tenacity (RKM) appeared in the article "Impact of Carding Parameters and Draw Frame Doubling on the Properties of Ring Spun Yarn" (J. of Engineered Fibers and Fabrics, 2013: 72-78).

a. Minitab's Best Subsets Regression option gave the following output when applied to the complete second order model. Notice that adjusted R2 for the model containing all predictors is much smaller than R2 itself, indicating that the model contains too many predictors relative to the sample size. Which model(s) would you recommend, and why?

b. When the model with predictors x3, x23, and x1 was fit, the t ratio corresponding to the coefficient on x1 was 21.32. If the first two predictors remain in the model, is inclusion of x1 justified? Explain your reasoning.
c. Here is output from relating y to x3 via the quadratic regression model. A normal probability plot of the standardized residuals is quite straight, and the plot of e* versus y^ shows no discernible pattern. Does this model specify a useful relationship, and should the quadratic predictor be retained in the model?

d. For the model of part (c), the standard deviation of a predicted Y value when x3 = 6 is .164. Predict tenacity in this situation in a way that conveys information about precision and reliability.