Question: THE STARTING SALARY CASE

The MINITAB output of a simple linear regression analysis of the data set for this case (see Exercise 13.4 on page 501) is given in Figure 13.11. Recall that a labeled MINITAB regression output is on page 509.

Figure 13.11: MINITAB Output of a Simple Linear Regression Analysis of the Starting Salary Data

 a Find the least squares point estimates b ₀ and b ₁ of β ₀ and β ₁ on the output and report their values.

 b Find SSE and s on the computer output and report their values.

 c Find s _{b 1} and the t statistic for testing the significance of the slope on the output and report their values. Show (within rounding) how t has been calculated by using b ₁ and s _{b 1} from the computer output.

 d Using the t statistic and appropriate critical value, test H ₀ : β ₁ = 0 versus H _a : β ₁ + 0 by setting a equal to .05. Is the slope (regression relationship) significant at the .05 level?

 e Using the t statistic and appropriate critical value, test H ₀ : β ₁ = 0 versus H _a : β ₁ ≠ 0 by setting a equal to .01. Is the slope (regression relationship) significant at the .01 level?

 f Find the p -value for testing H ₀ : β ₀ = 0 versus H _a : β ₀ ≠ 0 on the output and report its value. Using the p -value, determine whether we can reject H ₀ by setting a equal to .10, .05, .01, and .001. How much evidence is there that the slope (regression relationship) is significant?

 g Calculate the 95 percent confidence interval for β ₁ using numbers on the output. Interpret the interval.

 h Calculate the 99 percent confidence interval for β ₁ using numbers on the output.

 i Find s _b0 and the t statistic for testing the significance of the y intercept on the output and report their values. Show (within rounding) how t has been calculated by using b ₀ and s _b0 from the computer output.

 j Find the p -value for testing H ₀ :β ₀ = 0 versus H _a : β ₀ ≠0 on the computer output and report its value. Using the p -value, determine whether we can reject H ₀ by setting a equal to .10, .05, .01, and .001. What do you conclude about the significance of the y intercept?

 k Using the data set and s from the computer output, hand calculate (within rounding) SS _xx , s _b0 , and s _b1 .

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