The simple linear regression model provides a very good fit to a data set on rainfall and runoff volume. The equation of the least squares line is $\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24$
a. Use the fact that $s _ { y } = 1.44$
when rainfall volume is 40 m $3$
to predict runoff in a way that conveys information about reliability and precision. Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning.
b. Calculate a PI for runoff when rainfall is 50 using the same prediction level as in part (a). What can be said about the simultaneous prediction level for the two intervals you have calculated?

Question

The simple linear regression model provides a very good fit to a data set on rainfall and runoff volume. The equation of the least squares line is $\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24$ 
a. Use the fact that $s _ { y } = 1.44$ 
when rainfall volume is 40 m $3$ 
to predict runoff in a way that conveys information about reliability and precision. Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. 
b. Calculate a PI for runoff when rainfall is 50 using the same prediction level as in part (a). What can be said about the simultaneous prediction level for the two intervals you have calculated?

Quizplus · Accepted Answer

The Answer of The simple linear regression model provides a very good fit to a data set on rainfall and runoff volume. The equation of the least squares line is $\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24$ 
a. Use the fact that $s _ { y } = 1.44$ 
when rainfall volume is 40 m $3$ 
to predict runoff in a way that conveys information about reliability and precision. Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. 
b. Calculate a PI for runoff when rainfall is 50 using the same prediction level as in part (a). What can be said about the simultaneous prediction level for the two intervals you have calculated?

The Simple Linear Regression Model Provides a Very Good Fit y^=−1.128+.82697X,Y2=.975, and s=5.24\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24y^​=−1.128+.82697X,Y2=.975, and s=5.24

The Simple Linear Regression Model Provides a Very Good Fit $\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24$