Question

Following is information on the price per share and the dividend for a sample of 30 companies.

Obs	Price	Dividend
1	20.21	3.14
2	22.22	3.36
3	31.60	0.46
4	33.78	7.99
5	36.07	0.77
6	36.33	8.46
7	36.37	7.62
8	38.20	8.03
9	39.06	6.33
10	39.86	7.96
11	43.65	8.95
12	49.29	9.61
13	53.94	11.11
14	54.62	13.28
15	55.31	10.22
16	57.27	9.53
17	57.61	12.60
18	58.51	10.43
19	59.72	7.97
20	60.81	9.19
21	64.22	16.50
22	64.87	16.10
23	64.95	13.76
24	65.16	10.54
25	66.64	21.15
26	68.39	14.30
27	69.77	24.42
28	75.11	11.54
29	78.12	17.65
30	80.21	17.36

a. Calculate the regression equation that predicts price per share based on the annual dividend (round answer to 4 decimal places)

Price = ____ + _____ dividend

b1. State the null and alternate hypotheses

a. H₀: β = 0 and H₁: β ≠ 0

b. H₀: β = 0 and H₁: β = 0

c. H₀: β ≠ 0 and H₁: β ≠ 0

d. H₀: β ≤ 0 and H₁: β > 0

b2. State the decision rule. Use the 0.05 significance level (round answer to 3 decimal places)

Reject H₀ if t is not between ± ______

b3. Compute the value of the test statistic (round answer to 4 decimal places)

The test statistic is ______

b4. What is your decision regarding H_0?

a. do not reject

b. reject

b5. Can we conclude the slope is not equal to zero?

a. yes

b. no

c. Determine the coefficient of determination? (round answer 4 decimal places)

R_{2 ______}

d1. Determine the correlation coefficient (round answer 4 decimal places)

Correlation coefficient ______

d2. Can you conclude that it is greater than 0 using the 0.05 significance level?

______ H_0. We _____ (a. can, b. cannot) conclude that the correlation in the population is _____ (a. greater than, b. less than) Zero.

e. If the dividend is $10, what is the predicted price per share? (round 4 decimal places)

Price ______

f. What is the 95% prediction interval of price per share if the dividend is $10? (round 4 decimal places)

[ _____ , ____ ]

Answer 1

Answer:

Here we use Excel to fit a regression line. We use regression option in data analysis from Excel.

Here the response variable y is Price the explanatory variable x is Dividend.

The output of the regression can be given as

D E F G H L M N SUMMARY OUTPUT Regression Statistics Multiple R 0.811358445 R Square 0.658302526 Adjusted R Square 0.646099045 Standard Error 9.682764843 Observations 30 ANOVA df Significance F 5.35824E-08 Regression Residual Total 1 28 SS 5057.55429 2625.16618 7682.72047 MS F 5057.55429 53.94383076 93.755935 29 Intercept Dividend Coefficients Standard Error t Stat P-value 27.01539841 3.922013976 6.888144349 1.73892E-07 2.408166727 0.327880554 7.344646401 5.35824E-08 Lower 95% Upper 95% Lower 95.0% Upper 95.0% 18.98151707 35.04927974 18.98151707 35.04927974 1.736533869 3.079799586 1.736533869 3.079799586

Using the above regression output, segression equation can be given The Price = 27.0154 + 2.4082 Dividend. line Now the test the significance of slope B Parameter : let ß bethe slope of regression Hypothesis : Ho: The elope of regression line is equal to o.. There is no pignificant linear_relationship beth Price 4 dividend. us. Huilhe of blope regression line is not equal to 0. There is significant linear relationship beth price Symbolically Ho: B and dividend. VIS H: B to. Jest statistic : tal = Sbi bi- ß wton-2, 2/2) (12 because the testis hoo sided). bere bi is the slope & sbi is the standard erios which we get from the regression output. from the above output, be 2. 4082 & sbi = 0.3279 so under Hor B=0 test statistic becomes, tral= 0.3279 2.4082 tral 7.3446.

Decision : Reject Reject Ho if I teall > #0-2,412) here x = 0.05 = 0.025 2 do tem-2,212) + 30-2, 0.025) = 728,0·025) = 2.0484 oo here Itali s 7. 3446 > RD- 2,82) 2.0484 xeject HO so we Conclusion : ß 70 There be be significant linear relation beth price & dividend. may = 0 Ansioeus: a). Price 27.0154 + 2-4082 Dividend 611 ). Ho: B vis Hi:ß 70. 62) Reject Mo if t is not between $ 2.048 63). Jest statistic - tal = 7.3446 b4). Reject Ho. b5). Yes, we can conclude slope io not equal to zero.