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.

Month Rates of return Rates of return of the index-x the company stock-y

Apr-07 4.33 3.38

May-07 3.25 5.09

Jun-07 -1.78 0.54

Jul-07 -3.20 2.88

Aug-07 1.29 2.69

Sept-07 3.58 7.41

Oct-07 1.48 -4.83

Nov-07 -4.40 -2.38

Dec-07 -0.86 2.37

Jan-08 -6.12 -4.27

Feb-08 -3.48 -3.77

​(a) Treating the rate of return of the index as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

The estimate of β0 is:

           ​(Round to four decimal places as​ needed.)

The estimate of β1.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 α =0.10 level of significance.

What is the null and alternative hypotheses?

What is the P-Value for this hypothesis?

(Round to three decimal places as​ needed.)

What is the conclusion from α =0.10 level of significance? Reject or Accept H0? There is or sufficient evidence to conclude linear relation?

​(c) Assuming the residuals are normally​ distributed, construct a​ 90% confidence interval for the slope of the true​ least-squares regression line.

           Lower Bound:

           (Round to four decimal places as​ needed.)

            Upper Bound:

            (Round to four decimal places as​ needed.)

​(d) What is the mean rate of return for the company stock if the rate of return of the index is 3.15​%?

            (Round to three decimal places as​ needed.)

Answer 1

(a) The step-by-step instructions to obtain a simple linear regression output using Excel2010 * Store the variable Rates of the retun of the index (X)and Company stock (Y) in the columns of the Excel 2010 worksheet. Choose the Data ->Data Analysis ->Regression * Select the range of the variable Company stock (Y) and then select the range of variable Rates of the return of the index (X) * Choose the confidence level is 90%. * Tick the labels. * Click ok. The simple linear regression output using Excel2010

SUMMARY OUTPUT Rearession Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.663946888 0.44082547 0.378694967 3.226678587 ANOVA Significance F MS Regression Residual Total 173.87087131 73.87087 7.095154 0.02588949 9 93.70309232 10.41145 10 167.5739636 Coefficients Standard Error tstat P-value Lower 95% U er95% Lower 95.0% Uper 95.0% 1.239760956 0.985074091 1.258546 0.239861 -0.988631456 3.4681533680.988631456 3.468153368 Rates of the retun of the index(X) 0.766052541 0.287592565 2.663673 0.0258890.115472961 1.416632121 0.115472961 1.416632121 Intercept

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The values of the estim ate of the coefficient of slope is £ is of the Excel2010 output is given below A-076605] The values of the estim ate of the coefficient of slope is £ is A 1.2397 (b) Step1: To, test whether there is linear relati onship between the variables Rate of return of the index (X) and Company stock (Y) The null and alternative hypotheses are as follows Ho A0 (There is no linear relati onship) Hl. A#0 (There is a linear relationship) Step2: The l evel of significance is α = 0·10 Step3: The values of h and s* are A 0.766052541s,0.287592565 of the coefficients output of the Excel2010 is The formula for calculating the t-test statistic is 6-A 0.766052541-0 0.287592565 0.766052541 0.287592565 - 2.663673 t2.6636 Step4: The P - value approach P-value 2P(o) 2(1P<2.6636) 2 (1-0.987055) 2 (0.012945) 0.025889 P - valu0.025889< 0.10. We reject the null hypothesis H Step5: If t11.383028738. Reject the null hypothesis Ho. Otherwise, we do not reject Ho Step6: Conclusion Since, the P- value -0.0259< a 0.10. We reject the null hypothesis Ho Since, the t-value is t 2.6636>t00.92.7764. We reject the null hypothesis Ho Hence, we conclude that the data provide sufficient evidence to conclude that the independent variable Rates of the retun of the index (X) and the dependent variable Company stock (Y) are positively linearly related

The 90% confidence interval for the slope of the model. al2,-2 The coefficients of the param eters of the simple linear regression output of the Exce12010 is given below The values of b, S are 0.766052541 and S 0.287592565 of the Excel2010 0.766052541t/-2 (0.287592565) 0.766052541t 0059 (0.287592565) 0.7660525411.833112933(0.287592565) 0.76605241+0.527189649 (0.238862891,1.29324219) The interpretation of the confi dence interval of the slope coefficient Rates of the retun of the index(X) we can be 90% confident that the population slope coefficient Company stock (X), Ais in the interval [0.2389,1.2932] Lower bound0 2389 Upper bound 12932

d) The value of the mean rate of return for the company stock if the rate of return of the index is X-3 15% is -1239760956+0.766052541X Company stock-1.239760956+0.766052541 (Rate of return of the index) Company stock 1.239760956 +0.766052541(3.15) Company stock 1.239760956+2.413065503 Company stock 3.652826459 Comany ock B or he cok herae of return Therefore, the mean rate of return for the company stock if the rate of return of the index is X-3, 15% is approximately Company stocks 3553