Question

A sociologist conducted a study to determine whether there is a linear relationship between family income level (in thousand of dollars) and percent of income donated to charities.

Income level                           42        48        50        59        65        72

(in 1000’s of $)

Donating percent                    9          10        8          5          6          3

A) Calculate the correlation coefficient

B) Using = 0.05 is there enough evidence to conclude that there is a significant linear correlation between the income level and the donating percent?

C) Find the centroid

D) Find the regression equation.

E) Find the donating percentage for a person whose income level is 45 thousand. (give units to the answer)

Work shown in step by step and please write clearly by hand. Include the formulas. Thanks

Answer 1

a) From the given data

B) Test for correlation coefficient:

H0: There is no significant linear correlation between the income level and the donating percent

H1: There is a significant linear correlation between the income level and the donating percent

i.e.

Thus we conclude that there is a significant linear correlation between the income level and the donating percent

c) Centroid point is mean of X and Y :

d) Regression Equation:

E) Find the donating percentage for a person whose income level is 45 thousand.

i.e. X = 45

Y = -0.2134*45 +18.7835

    = 9.181 (in 1000’s of $ )