The transient points of an electronic inverter are influenced by many factors. Table 12-20 gives data on the transient point (y, in volts) of PMOS-NMOS inverters and five candidate regressors:, x1 = width of the NMOS device, x2 = length of the NMOS device, x3 = width of the PMOS device, x4 = length of the PMOS device, and x5 = temperature (°C).
(a) Fit the multiple linear regression models to these data. Test for significance of regression using a = 0.01. Find the P-value for this test and use it to draw your conclusions.
(b) Test the contribution of each variable to the model using the t-test with a = 0.05. What are your conclusions?
(c) Delete x5 from the model. Test the new model for significance of regression. Also test the relative contribution of each regressor to the new model with the t-test. Using a = 0.05, what are your conclusions?
(d) Notice that the MSE for the model in part (c) is smaller than the MSE for the full model in part (a). Explain why this has occurred.
(e) Calculate the Studentized residuals. Do any of these seem unusually large?
(f) Suppose that you learn that the second observation was incorrectly recorded. Delete this observation and refit the model using x1, x2, x3, and x4 as the regressors. Notice that the R2 for this model is considerably higher than the R2 for either of the models fitted previously. Explain why the R2 for this model has increased.
(g) Test the model from part (f) for significance of regression using a = 0.05. Also investigate the contribution of each regressor to the model using the t-test with a = 0.05.
What conclusions can you draw?
(h) Plot the residuals from the model in part (f) versus and versus each of the regressors x1, x2, x3, and x4. Comment on the plots.