The following data are annual disposable income and total annual consumption for 12 families selected at a random from a large metropolitan area. Regard annual disposable income as the explanatory variable and total annual consumption as the dependent variable. From the regression of y on x, answer the questions that follow.

Annual Disposable Total Annual

Income ($) ( x) Consumption ($) ( y)

INC CONS

16,000 14,000

30,000 24,545

43,000 36,776

70,000 63,254

56,000 40,176

50,000 49,548

16,000 16,000

26,000 22,386

14,000 16,032

12,000 12,000

24,000 20,768

30,000 34,780

Calculate the following:

1. 1. Slope ( b₁)2.. Y-Intercept (b₀)3. SST, SSE SSR4. Mean Square Error (S² )5 Standard Error of Estimate ( S)5. Estimated Standard Deviation of b₁ (S_b1)6. Test Statistic (t)7. Margin of Error (MOE)

1. What is the estimated regression equation relating y to x
2. What percentage of the variation in y has been explained by the regression (r)

1. Construct a 90% confidence interval estimate of ₁

1. Use the t test to test the hypotheses of H₀: ₁ = 0 versus H_a: 0 at the 5% level of significance. State the decision rule, the test statistics, and your decision. What conclusion can be drawn from the result of the test?

1. Use the F test to test the hypotheses H₀: ₁ = 0 versus H_a: 0 at the 5% level of significance. State the decision rule, the test statistics, and your decision. What conclusion can be drawn from the result of the test? [BONUS]