Question

Consider the following table of paired data. a. Calculate the correlation coefficient r. b. Use your answer from a, to determine if there is a linear correlation at a significance level of 0.05.

Answer 1

a) For the given paired data to calculate the correlation coefficient we need to do the following table calculation as:

Sum =

The regression equation is calculated as;

r= SSXY SSxx SSyy

based on the table calculation the sum of squares are calculated as:

I=? () (); xx es

(༨) I K=46s (《) སྣརོ=3ygs

based on the sum of squares the regression equation is calculated as:

SSxy = 205 - ? (26 x 34) = 28.2

SSxx = 158 – (26)2 = 22.8 S543 = 270 – $(31)2 = 38.8

r = SSXY SSXX SSyy 28.2 22.8 x 38.8 = = 0.948

b) The sample size is n = 5 for the paired data.

The hypotheses that are assumed:

$Ho: \rho=0$

$Ho: \rho\neq0$

Rejection region:

The degrees of freedom is df = n-2 = 5 - 2 = 3, and using the critical value table for correlation coefficient at significance level 0.05 we create the rejection region as if r is less than -0.878 or greater than 0.878.

So, reject the Ho if r is less than -0.878 or greater than 0.878.

Conclusion:

As we can see that the r calculated in part a is 0.948 which is greater than 0.878 hence we can reject the null hypothesis.

So, we can conclude that there is a significant correlation between the variables at 0.05 level of significance.