The following data come from an experiment to determine the relation between Y, the shear strength (psi) of a rubber compound, and X, the cure temperature (oF). (a) Draw the scatter plot to see if the simple linear regression model is appropriate. (b) Fit the quadratic polynomial Model (Y = shear strength |X1 = x, X2 = x2) to these data. (c) Draw the graph of the fitted polynomial on the same set of axes you used for the scatter plot. (d) Test the hypothesis that βˆ2 = 0. (e) Check the assumptions of the model by (1) graphing the studentized residual plot and (2) graphing the normal probability plot of the studentized residuals.

(Source: A.F. Dutka and F.J. Ewens (1971), A Method for Improving the Accuracy of Polynomial Regression Analysis, Journal of Quality Technology, pp. 149-155. Used with permission.)