The following data are annual disposable income and total annual consumption for

Question

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.Slope ( b1)

2..        Y-Intercept (b0)

3.         SST, SSE SSR

4.         Mean Square Error (S2 )

5          Standard Error of Estimate ( S)

5.         Estimated Standard Deviation of b1 (Sb1)

6.         Test Statistic (t)

7.         Margin of Error (MOE)

What is the estimated regression equation relating y to x

What percentage of the variation in y has been explained by the regression (r²)

Construct a 90% confidence interval estimate of1

Use the t test to test the hypotheses of H0: 1 = 0

Use the F test to test the hypotheses   H0: 1 = 0 versus Ha: 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

Explanation / Answer

We can solve the data by using excel, which give all the value related to question

the estimated regression equation relating y to x is

y=2521.379+0.8268x

93.11 percentage of the variation in y has been explained by the regression (r²)

We reject the null hypothesis because the F-critical value is greater than calculated value.

SUMMARY OUTPUT Regression Statistics Multiple R 0.964964 R Square 0.931155 Adjusted R Square 0.92427 Standard Error 4387.722 Observations 12 ANOVA df SS MS F Significance F Regression 1 2.6E+09 2.6E+09 135.2534 3.92E-07 Residual 10 1.93E+08 19252101 Total 11 2.8E+09 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2521.379 2619.588 0.96251 0.35849 -3315.43 8358.184 X Variable 1 0.826895 0.071101 11.62985 3.92E-07 0.668472 0.985318

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