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 20.6 50.6 29.3 57.4 31.1 58 31.7 57.7 27.2 55.7 20.1 54.4 16.1 48.6 26.7 50.2 33.1 70 24.5 51.4 24.6 52.4 33.2 49.8 26.8 56.3 18.6 43.9 21.6 55 9 48.3 29.9 58.3 43.3 72.8 21.8 50.5 33.6 52.1 19.7 52.3 21.6 50 30.7 60.9 21.3 43.3 4.7 40.3 22.9 49.9 5 48 11.2 43.4 32.7 63.9 20.7 47.6 23.9 42.3 21.5 46.6 24.2 56.8 23.6 46.7 25.2 59.9 What is the correlation coefficient for this data set? r = (report answer accurate to at least 3 decimal places) To find the p-value for a correlation coefficient, you need to convert to a t-score:t=r⋅√n−21−r2t=r⋅n-21-r2This t-score is from a t-distribution with n−2n-2 degrees of freedom. What is the p-value for this correlation coefficient? p-value = (report answer accurate to at least 4 decimal places) Your final conclusion is that... 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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
20.6	50.6
29.3	57.4
31.1	58
31.7	57.7
27.2	55.7
20.1	54.4
16.1	48.6
26.7	50.2
33.1	70
24.5	51.4
24.6	52.4
33.2	49.8
26.8	56.3
18.6	43.9
21.6	55
9	48.3
29.9	58.3
43.3	72.8
21.8	50.5
33.6	52.1
19.7	52.3
21.6	50
30.7	60.9
21.3	43.3
4.7	40.3
22.9	49.9
5	48
11.2	43.4
32.7	63.9
20.7	47.6
23.9	42.3
21.5	46.6
24.2	56.8
23.6	46.7
25.2	59.9

What is the correlation coefficient for this data set?
r =
(report answer accurate to at least 3 decimal places)

To find the p-value for a correlation coefficient, you need to convert to a t-score:t=r⋅√n−21−r2t=r⋅n-21-r2This t-score is from a t-distribution with n−2n-2 degrees of freedom.

What is the p-value for this correlation coefficient?
p-value =
(report answer accurate to at least 4 decimal places)

Your final conclusion is that...

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.

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