Question

A random sample of 42 firms was chosen from the S&P 500 firms listed in the Spring 2003 Special Issue of Business Week (The Business Week Fifty Best Performers). The indicated dividend yield (DIVYIELD), the earnings per share (EPS), and the stock price (PRICE) were recorded for these 42 firms.† These data are available in the worksheet entitled DIV4. Run a regression using DIVYIELD as the dependent variable and EPS and PRICE as the independent variables. Use the output to answer the following questions.

(a) What is the sample regression equation relating DIVYIELD to PRICE and EPS? (Round your answers to three decimal places.)

DIVYIELD =  +  PRICE +  EPS

(b) What percentage of the variation of DIVYIELD has been explained by the regression? (Round your answer to two decimal places.)

%

(c) Test the overall fit of the regression. Use a 10% level of significance.
State the hypotheses to be tested.

H₀: β₁ = β₂ = 0
H_a: At least one of the coefficients is not equal to 0.H₀: At least one of the coefficients is not equal to 0.
H_a: β₁ = β₂ = 0    H₀: None of the coefficients are equal to zero.
H_a: β₁ = β₂ = 0H₀: β₁ = β₂ = 0
H_a: None of the coefficients are equal to zero.

State the decision rule.

Reject H₀ if p < 0.10.
Do not reject H₀ if p ≥ 0.10.Reject H₀ if p > 0.05.
Do not reject H₀ if p ≤ 0.05.    Reject H₀ if p > 0.10.
Do not reject H₀ if p ≤ 0.10.Reject H₀ if p < 0.05.
Do not reject H₀ if p ≥ 0.05.

State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter the degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places).

---Select--- μ z G F t (  ,  ) = , p ---Select--- ≤ ≥ < > =  

(d) What conclusion can be drawn from the test result?

Do not reject H₀. Neither variable appears to be useful in explaining the variation in dividend yield.Do not reject H₀. At least one of the coefficients is equal to zero. The model is not useful in explaining the variation in dividend yield.    Reject H₀. At least one of the coefficients is equal to zero. The model is not useful in explaining the variation in dividend yield.Reject H₀. Neither variable appears to be useful in explaining the variation in dividend yield.

(e) Is it necessary to test each coefficient individually to see if either PRICE or EPS is related to DIVYIELD? Why or why not?

Yes. Since we tested them together, we can only confirm that at least one coefficient is equal to zero.Yes. Since we tested them together, we can only confirm that at least one coefficient is related to DIVYIELD.    No. From the overall fit test we know that both coefficients are related to DIVYIELD.No. From the overall fit we know that neither coefficient is significant.

Company Name	DIVYIELD	PRICE	EPS
Delphi	3.62	8	0.61
Liz Claiborne	0.8	28	2.16
Snap-On	4	14	1.76
Darden Restaurants	0.45	18	1.37
Tribune	0.98	45	1.8
Interpublic Group	3.94	10	0.77
TJX	0.75	16	1.08
Dollar General	1.23	10	0.76
Circuit City Stores	1.58	4	0.57
Winn-Dixie Stores	1.64	12	1.65
Kellogg	3.42	30	1.75
Campbell Soup	3.04	21	1.39
Exxon Mobil	2.7	34	1.61
EOG Resources	0.39	41	0.65
Washington Mutual	3.36	35	4.05
North Fork Bancorporation	3.35	32	2.58
Union Planters	4.85	28	2.59
Bank of New York	3.34	23	1.24
Household International	3.58	28	3.22
Charles Schwab	0.56	8	0.52
American International Group	0.38	49	2.1
Loews	1.37	44	4.65
Simon Property Group	6.93	35	1.93
Stryker	0.18	65	1.7
Baxter International	2.05	28	1.67
Eli Lilly	2.37	57	2.5
Bristol-Myers Squibb	4.81	23	0.12
General Electric	3.16	24	1.51
Rockwell Collins	1.83	20	1.29
Cummins	5.01	24	1.82
First Data	0.23	35	1.62
Deluxe	3.67	40	3.36
Union Pacific	1.67	55	5.05
Autodesk	0.83	14	0.28
Scientific-Atlanta	0.31	13	0.35
International Flavors & Fragrances	1.91	31	1.84
Eastman Chemical	5.47	32	1.02
Alltel	3.22	43	2.96
Dominion Resources	4.79	54	4.82
Cinergy	5.71	32	2.34
Peoples Energy	5.92	36	2.51
Nicor	6.12	30	2.94

Answer 1

Here we are using regression function of excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.295464
R Square	0.087299
Adjusted R Square	0.040494
Standard Error	1.843435
Observations	42
ANOVA
	df	SS	MS	F	Significance F
Regression	2	12.67655	6.338276	1.865158	0.168425
Residual	39	132.5318	3.398252
Total	41	145.2084
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.450218	0.652922	3.752694	0.000569	1.129558	3.770878	1.129558	3.770878
PRICE	-0.02931	0.025961	-1.12902	0.265786	-0.08182	0.023201	-0.08182	0.023201
EPS	0.604067	0.313829	1.92483	0.061567	-0.03071	1.238846	-0.03071	1.238846

Here the equation is

DIVYIELD = 2.45022 - 0.02931 * Price + 0.6041 * EPS

(b) Here

R²= 0.0873

so here8.73 percentage of the variation of DIVYIELD has been explained by the regression.

(c)

H0: β1 = β2 = 0
Ha: At least one of the coefficients is not equal to 0

Do not reject H0 if p ≥ 0.10.

associted p - value = 0.16 which is greater than 0.10 so p > 0.10

State the appropriate test statistic name is F test

degrees of freedom

Regression = 2

Residual = 39

Test statistic value = F = 1.865

Associated p-value = 0.1684

(d)

Do not reject H0. Neither variable appears to be useful in explaining the variation in dividend yield.

(e) No. From the overall fit we know that neither coefficient is significant.