Question

Earnings per​ share, x	Dividends per​ share, y
1.55	1
4.39	0.48
3.92	2.2
8.79	1.22
2.16	0.78
3.16	1.72

​(b) Calculate the sample correlation coefficient r.

requals=nothing

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

​(c) Describe the type of​ correlation, if​ any, and interpret the correlation in the context of the data.

There is

▼

(Blank)

Answers choices below

a moderate negative

a strong negative

a strong positive

a moderate positive

no

a perfect positive

a perfect negative

linear correlation.

Interpret the correlation. Choose the correct answer below.

A.

As​ companies' earnings per share​ increase, their dividends per share tend to decrease.

B.

Based on the​ correlation, there does not appear to be a linear relationship between​ companies' earnings per share and their dividends per share.

C.

Based on the​ correlation, there does not appear to be any relationship between​ companies' earnings per share and their dividends per share.

D.

As​ companies' earnings per share​ increase, their dividends per share tend to increase.

E.

Increases in​ companies' earnings per share cause their dividends per share to decrease.

F.

Increases in​ companies' earnings per share cause their dividends per share to increase.

​(d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let

alphaαequals=0.01.

The critical value is

nothing.

​Therefore, there

▼

is

is not

sufficient evidence at the

11​%

level of significance to conclude that

▼

(Blank)

there is no correlation

there is a significant linear correlation

between​ companies' earnings per share and their dividends per share.

Answer 1

b)

​(c) Describe the type of​ correlation, if​ any, and interpret the correlation in the context of the data.

There is no

linear correlation.

d)

Since, we know that

Degree of freedom (df) can be found out by n-2, where n is number of data points

df = n-2

df = 6-2

df = 4

critical value @ (df = 4 and \alpha = 0.01) = 0.917

Since, r = 0.069 is between -0.917 and 0.917. Therefore, r is not significant

​Therefore, there is not sufficient evidence at the there is no correlation  

between​ companies' earnings per share and their dividends per share.