Use the Minitab output in the Exhibit for questions (1)-(8).

1. Calculate a 95% confidence interval for the coefficient of x 5. Use the t -table for the constant.
2. What is the conclusion from the hypothesis test that H0: β5= 0 versus H1: β5≠ 0 at α = 0.05 and why?
3. Calculate a 95% prediction interval for the observation in row 1.
4. To obtain at least 90% confidence that each of the10 slope coefficients β1, β2, …, β10 is simultaneously contained in its confidence interval, what significance level should be used for each interval?
5. What R-squared would result from the regression model of x 10 on x 1, x 2, x 3, …, x 9.
6. Use the Minitab output to calculate the F statistic for the test
   H0: β1 = β2 = β3 = 0 versus H1: at least one of these coefficients is not zero
7. Circle ALL of the following that are correct. Consider α = 0.05 in your conclusions. From this output you can conclude that
   1. No regressors are useful to predict y
   2. At least one regressor is useful to predict y
   3. There is a regressor useful to predict y , but it is not among this group of 10
   4. All 10 regressors together are needed to adequately predict y
   5. x 1 is not useful to a model that already contains x 2, x 3, …, x 9, x 10
8. Consider the model y = β0 + β1 x 1 + β2 x 2. On the following axes, provide a scatter plot of regressor variables x 1 and x 2 with one high leverage point.
   
9. Sketch an example of data for the simple regression model y on x with one point that has large influence as measured by DFFITS.
   Solution: We get
   
10. Residuals plots for a model are shown below.

1. List any failures of assumptions indicated by these plots.
2. Circle ALL of the following that are reasonable next steps after reviewing these residual plots.
   1. Evaluate adjusted R-squared
   2. Conduct tests of the coefficients
   3. Consider transformations
   4. Consider polynomial terms in the x ’s
   5. Consider weighted regression

11) Given the following data for a regression analysis calculate the mean squared error for pure error.

12) The following plot is a partial regression plot for x 1 in the model y = β0 + β1 x 1 + β2 x 2 + β3 x 3 + β4x4. Circle ALL of the following that can be correctly concluded.

1. The axes plot x 1 against the residuals from the model y = β0 + β1 x 1 + β2 x 2 + β3 x 3 + β4x4
2. The axes plot the residuals from the model x 1 = β0 + β2 x 2 + β3 x 3 + β4x4 against the residuals from the model y = β0 + β2 x 2 + β3 x 3 + β4x4
3. The axes plot the residuals from the model x 1 = β0 + β2 x 2 + β3 x 3 + β4x4 against the residuals from the model y = β0 + β1 x 1
4. A polynomial term for x 1 is expected to be useful for the model y = β0 + β1 x 1 + β2 x 2 + β3 x 3 + β4x4

13) Consider the following plot for a weighted simple linear regression between y and x . Approximate the weight that should be used at x = 7.

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