Question

You wish to determine if there is a positive linear correlation between the two variables at...

You wish to determine if there is a positive linear correlation between the two variables at a significance level of α=0.01α=0.01. You have the following bivariate data set.

x y
54.5 82.1
45.8 20.9
46.4 22.7
44.8 -5.5
38.8 -5.4
35.4 83.5
44.3 96.3
25 -45.1
47.8 29.8
48.8 6
49.9 40.6
50.2 62.7
42.1 20.4
32.3 -40.2
45.1 30.5
49.3 3.4
29.4 27.7
44 2.3
39.2 18.2
37.5 1
44.1 27.1
50.6 -41.3
42.9 90.5
39.2 4.5
40.2 -60.7
34 -39.3
50 107
39.3 -36.4
38.4 39.8
40.8 13.8
49.1 86.8
42.3 41.5
28.2 22

What is the correlation coefficient for this data set?
r =

To find the p-value for a correlation coefficient, you need to convert to a t-score:

t=√r2(n−2)1−r2t=r2(n-2)1-r2

This t-score is from a t-distribution with n–2 degrees of freedom.

What is the p-value for this correlation coefficient?
p-value =

• There is insufficient sample evidence to support the claim the there is a positive correlation between the two variables.
• There is sufficient sample evidence to support the claim that there is a statistically significant positive correlation between the two variables.

Note: In your calculations, round both r and t to 3 decimal places in ALL calculations.

We have given the below data and we have to compute correlation coefficient between x and y .

x y
54.5 82.1
45.8 20.9
46.4 22.7
44.8 -5.5
38.8 -5.4
35.4 83.5
44.3 96.3
25 -45.1
47.8 29.8
48.8 6
49.9 40.6
50.2 62.7
42.1 20.4
32.3 -40.2
45.1 30.5
49.3 3.4
29.4 27.7
44 2.3
39.2 18.2
37.5 1
44.1 27.1
50.6 -41.3
42.9 90.5
39.2 4.5
40.2 -60.7
34 -39.3
50 107
39.3 -36.4
38.4 39.8
40.8 13.8
49.1 86.8
42.3 41.5
28.2 22