Ch 12.6 - 110SE

Chapter 12, Problem 110SE

(choose chapter or problem)

Transient points of an electronic inverter are influenced by many factors. Table E12-15 gives data on the transient point , in volts) of PMOS-NMOS inverters and five candidate regressors: \(x_{1}=\) width of the NMOS device, \(x_{2}=\)  length of the NMOS device, \(x_{3}=\)  width of the PMOS device, \(x_{4}=\)  length of the PMOS device, and \(x_{5}=\)  temperature

\(\left({ }^{\circ} \mathrm{C}\right)\)
(a) Fit a multiple linear regression model that uses all regressors to these data. Test for significance of regression using \(\alpha=0.01\). Find the \(P \text {-value }\) for this test and use it to draw your conclusions.
(b) Test the contribution of each variable to the model using the  -test with \(\alpha=0.05\) What are your conclusions?
(c) Delete \(x_{5}\) 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  -test. Using \(\alpha=0.05\) what are your conclusions?
(d) Notice that the \(M S_{E}\) for the model in part (c) is smaller than the \(M S_{E}\)  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 recorded incorrectly. Delete this observation and refit the model using \(x_{1}, x_{2}, x_{3}\), and \(x_{4}\) as the regressors. Notice that the \(R^{2}\) for this model is considerably higher than the \(R^{2}\) for either of the models fitted previously. Explain why the \(R^{2}\) for this model has increased.
(g) Test the model from part (f) for significance of regression using \(\alpha=0.05\) Also investigate the contribution of each regressor to the model using the  -test with \(\alpha=0.05\) What conclusions can you draw?

(h) Plot the residuals from the model in part (f) versus \(\hat{y}\) and versus each of the regressors

\(\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{X}_{3} \text { and } \mathrm{x}_{4}\) Comment on the plots.

Equation Transcription:

 

 

 

 

 

 

 

 

 

 

   

Text Transcription:

x1=

x2=  

x3=  

x4=

x5=

(°^C)

\alpha=0.01

P-value

\alpha=0.05

x5

\alpha=0.05

 

MSE

 

MSE

 

x1,x2,x3

 

x4

 

R2

 

R2

 

R2

 

\alpha=0.05

 

\alpha=0.05

\hat y  

x1,x2,x3 and x4