Question

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

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.05α=0.05. You have the following bivariate data set.

x y
43.3 -108.4
21.9 114.3
1.5 113.2
62.4 143.4
-2.2 48.1
20.3 -32.4
36.5 62.5
20.5 93.2
-10 -71.7
31.9 -323.3
30.9 132.5
51.2 -276.3
29.5 -3.4
2.9 -28.1
7.4 277.4
31.7 194.3
25.2 -120.5
12.6 -113.8
33.5 494.4
28.8 -99.9
37.1 229.6
11.7 -196.9
39.1 -295.9
18.7 -192.7
-1.1 -355.2
20.5 219.1
19.3 -106.6
44.1 88.8
50.6 89
11.9 -5.3
48.9 100.4
38.9 -28.8
18.8 107.4
34.8 48.7
57.6 54.8
27.4 85.3
59.5 255.2
18.1 -161.6
29.8

-221.4

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 =

The statistical software output for this problem is :

r = 0.1889

t = 1.1703

P-value = 0.2494

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