Question

For a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is

requals=0.715

Using

alphaαequals=​0.05,

determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size?

a. Is there a linear correlation between chest size and​ weight?

A.​Yes, because the test statistic falls between the critical values of

negative 0.707−0.707

and 0.707.

B.​Yes, because the absolute value of the test statistic exceeds the critical value

of 0.707

C.​No, because the absolute value of the test statistic exceeds the critical value

of 0.707

D.

The answer cannot be determined from the given information.

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size?

nothing

​

Answer 1

Solution:

We are given

r = 0.715

α = 0.05

n = 8

df = n – 2 = 8 – 2 = 6

So, critical value by using correlation critical values table is given as below:

Critical value = 0.707

r > critical value, so we reject the null hypothesis

There is sufficient evidence to conclude that there is a linear correlation between chest size and weight.

a. Is there a linear correlation between chest size and ​weight?

B.​Yes, because the absolute value of the test statistic exceeds the critical value of 0.707

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size?

We are given r = 0.715

Coefficient of determination = R^2 = r^2 = 0.715^2 = 0.511225 = 51.12%

About 51.12% of the proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size.

Answer: 0.511225