Consider the engine thrust data in Exercise 12-108. Refit

Chapter 12, Problem 109SE

(choose chapter or problem)

Consider the engine thrust data in Exercise 12-108. Refit the model using \(y^{*}=\ln y\) as the response variable and \(x_{3}^{*}=\ln _{3}\) as the regressor (along with \(x_{4} and x_{5}\)).

(a) Test for significance of regression using \(\alpha=0.01\). Find the \(P \text {-value }\) for this test and state your conclusions.

(b) Use the \(t \text {-statistic }\) to test \(H_{0}=\beta_{j}=0\) versus \(H_{1}: \beta_{j} \neq 0\) for each variable in the model. If \(\alpha=0.01\), what conclusions can you draw?

(c) Plot the residuals versus \(\hat{\mathrm{y}}^{4}\) and versus \(x_{3}^{*}\). Comment on these plots. How do they compare with their counterparts obtained in Exercise 12-108 parts (f) and (g)?

Equation Transcription:

value

statistic

Text Transcription:

y*=ln y

x_2 ^*=ln_3

x_4

x_5

alpha=0.01

P-value

t-statistic

H_0=beta_j=0

H_i:beta_j neq 0

alpha=0.01

Hat y*

X_3 ^*