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 r = 0.921. Using α = ​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 andweight?b) what proportion of the variation in weight can be explainedby the linear relationship between weight and chest size?

Answer 1

Answer:

There is a linear correlation between chest size and weight,0.8482

Step-by-step explanation:

Given that for a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears.

the value of the linear correlation coefficient is r = 0.921.

i.e. there is a strong positive correlation from the value of r.

$H_0: r=0\\H_1: r\neq 0$

(Two tailed test at 5% level for correlation coefficient)

Test statistic t = $\frac{r\sqrt{n-2 } }{\sqrt{1-r^2}} \\=5.791$

p value <0.00001

Since p is less than 0.05 we reject H0

a) There is a  linear correlation between chest size andweight

b)--  R^2 = 0.8482 proportion of the variation in weight can be explainedby the linear relationship between weight and chest size