Question

2. Stocks that consistently pay dividends are popular among investors seeking income. However, the fact that a stocks earning per share is high is not necessarily indicative of a large dividend. A random sample of 20 stocks that have consistently paid dividends yielded the following data on earning per share (EPS) and amount of dividend. Stock EPS ($) Dividend ($)

1 1.85 .32

2 5.55 1.52

3 3.69 1.00

4 4.97 1.68

5 3.83 2.40

6 4.00 1.84

7 6.63 2.16

8 6.34 2.80

9 3.38 2.16

10 1.74 1.68

11 4.26 2.96

12 3.58 1.40

13 7.42 3.60

14 4.12 1.68

15 2.68 1.00

16 2.58 .84

17 4.27 2.00

18 2.93 1.12

19 8.80 3.28

20 2.87 1.40

a. What is the estimated coefficient of correlation between EPS and amount of dividend paid? Comment on the strength and direction of the relationship.

b. Conduct an appropriate test of hypothesis at 0.1 level of significance to determine if there is a significant correlation between EPS and amount of dividend. Formulate the hypothesis, show your work, and provide a conclusion in non-technical language

c. Develop the least square regression line to predict the stock dividend based on the stock’s earning per share.

d. Interpret the slope of the regression line.

e. What would be the estimated average dividend for stocks earning $2 per share

f. Develop 99% confidence interval for the estimated average dividend of stocks earning $2 per share. Interpret your result.

g. What percentage of variation in stock dividend can be explained by stock’s earning per share

Answer 1

The calculations are given below

stockEPS (x)	dividend (y)	s1=(y-ybar)^2	s2=(x-xbar)^2	s3=(x-xbar)*(y-ybar)	yhat=b0+b1*x	e2=(y-yhat)^2
1.85	0.32	2.3165	5.8782	3.6901	0.9843	0.4413
5.55	1.52	0.1037	1.6269	-0.4107	2.2932	0.5978
3.69	1	0.709	0.3416	0.4921	1.6352	0.4035
4.97	1.68	0.0262	0.4837	-0.1127	2.0881	0.1665
3.83	2.4	0.3114	0.1976	-0.248	1.6847	0.5117
4	1.84	0	0.0754	0.0005	1.7449	0.009
6.63	2.16	0.1011	5.5484	0.749	2.6753	0.2655
6.34	2.8	0.9178	4.2663	1.9787	2.5727	0.0517
3.38	2.16	0.1011	0.8001	-0.2845	1.5255	0.4026
1.74	1.68	0.0262	6.4237	0.4106	0.9453	0.5398
4.26	2.96	1.2499	0.0002	-0.0162	1.8369	1.2614
3.58	1.4	0.1954	0.4823	0.307	1.5963	0.0385
7.42	3.6	3.0906	9.8942	5.5298	2.9548	0.4163
4.12	1.68	0.0262	0.0239	0.025	1.7873	0.0115
2.68	1	0.709	2.5424	1.3426	1.2779	0.0772
2.58	0.84	1.004	2.8713	1.6979	1.2425	0.162
4.27	2	0.025	0	-0.0007	1.8404	0.0255
2.93	1.12	0.5213	1.8077	0.9707	1.3663	0.0607
8.8	3.28	2.0678	20.4802	6.5077	3.443	0.0266
2.87	1.4	0.1954	1.9726	0.6208	1.3451	0.003
xbar=sum(x)/20	ybar=sum(y)/21	sy=sqrt(sum(s1)/19))	sx=sqrt(sum(s2)/19))	sxy=sum(s3)/19		Ssres=sum(e2)
4.2745	1.842	0.8491	1.8598	1.22366842105263		5.4721
	r=sxy/sx*sy	r2=r^2	b1=sxy/sx*sx	b0=ybar-b1*xbar	sxx=19*sx*sx	MSE=Ssres/18
	0.7749	0.6005	0.3538	0.3298	65.7183	0.3040