The data in the accompanying table represent the rate of return of a certain com

Question

The data in the accompanying table represent the rate of return of a certain company stock for 11 months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts (a) through (d) below. (a) Treating the rate of return of the index as the explanatory variable, x, use technology to determine the estimates of beta_0 and beta_1. The estimate of beta_0 is (Round to four decimal places as needed.) The estimate of beta_1 is (Round to four decimal places as needed.) (b) Assuming the residuals are normally distributed, test whether a linear relation exists between the rate of return of the index, x, and the rate of return for the company stock, y, at the alpha = 0.10 level of significance. Choose the correct answer below. State the null and alternative hypotheses. A. H_0: beta_1 = 0 H_1: beta_1 > 0 B. H_0: beta_1 = 0 H_1: beta_1 notequalto 0 C. H_0: beta_0 = 0 H_1: beta_0 notequalto 0 D. H_0: beta_0 = 0 H_1: beta_0 > 0 Determine the P-value for this hypothesis test. P-value = (Round to three decimal places as needed.) State the appropriate conclusion at the alpha = 0.10 level of significance. Choose the correct answer below. A. Do not reject H_0. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate the company stock. B. Reject H_0. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of company stock. C. Reject H_0. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

Explanation / Answer

a) B0 = 1.2286

B1 = 0.7622

Null and Alternate Hypothesis

Option B is Correct

P value = 0.027

Conclusion:

Option C is Correct

SUMMARY OUTPUT Regression Statistics Multiple R 0.661586 R Square 0.437696 Adjusted R Square 0.375218 Standard Error 3.230852 Observations 11 ANOVA df SS MS F Significance F Regression 1 73.12704 73.12704 7.005575 0.026615 Residual 9 93.94565 10.43841 Total 10 167.0727 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.228593 0.986348 1.245597 0.244363 -1.00268 3.459867 -1.00268 3.459867 X Variable 1 0.762186 0.287965 2.646805 0.026615 0.110765 1.413607 0.110765 1.413607

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