The data shown in Table E12-14 represent the thrust of a

Chapter 12, Problem 108SE

(choose chapter or problem)

 The data shown in Table E12-14 represent the thrust of a jet-turbine engine \(\text { (y) }\) and six candidate regressors: \(\mathrm{X}_{1}\) = primary speed of rotation, \(\mathrm{X}_{2}\) = secondary speed of rotation, \(\mathrm{X}_{3}\) = fuel flow rate, \(\mathrm{X}_{4}\) = pressure, \(\mathrm{X}_{5}\) = exhaust temperature, and \(\mathrm{X}_{6}\) = ambient temperature at time of test.

(a) Fit a multiple linear regression model using \(\mathrm{X}_{3}\) = fuel flow rate, \(\mathrm{X}_{4}\) = pressure, and \(\mathrm{X}_{5}\) = exhaust temperature as the regressors.

(b) Test for significance of regression using \(\alpha=0.01\). Find the P-value for this test. What are your conclusions?

(c) Find the t-test statistic for each regressor. Using \(\alpha=0.01\), explain carefully the conclusion you can draw from these statistics.

(d) Find \(\mathrm{R}^{2}\) and the adjusted statistic for this model.

(e) Construct a normal probability plot of the residuals and interpret this graph.

(f) Plot the residuals versus \(\hat{\mathrm{y}}\). Are there any indications of inequality of variance or nonlinearity?

(g) Plot the residuals versus \(\mathrm{X}_{3}\). Is there any indication of nonlinearity?

(h) Predict the thrust for an engine for which \(x_{2}=28900, x_{4}=170, \text { and } x_{5}=1589\)

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Text Transcription:

(y)

x1

x2  

x3  

x4

x5  

x6  

x3  

x4

x5

\alpha=0.01

\alpha=0.01

R^2

\hat y

x_2=28900, x_4=170, and  x_5=1589