Question

For the following data​ (a) display the data in a scatter​ plot, (b) calculate the sample correlation coefficient​ r, and​ (c) make a conclusion about the type of correlation. Use technology.

The earnings per share​ (in dollars) and the dividends per share​ (in dollars) for

six

medical supplies companies in a recent year are shown in the data set below.

a) choose the correct scatter plot. Use technology.

​(b) The correlation coefficient r is

_____

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

​(c) Which of the following best describes the type of correlation that exists between earnings per share and dividends per​ share?

A. strong positive linear correlation

B. strong negative linear correlation

C. No linear correlation

D. Weak negative linear correlation

E. weak positive linear correlation

Earnings_per_share,_x   Dividends_per_share,_y
2.74   0.51
5.05   2.44
4.52   1.41
3.03   0.85
3.73   1.05
2.19   0.29

Answer 1

scatter plot is given as

b) X Values
∑ = 21.26
Mean = 3.543
∑(X - M_x)² = SS_x = 5.999

Y Values
∑ = 6.55
Mean = 1.092
∑(Y - M_y)² = SS_y = 2.96

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 4.011

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 4.011 / √((5.999)(2.96)) = 0.952

r = 0.952

c)A. strong positive linear correlation