Question

Test if the variables are linearly correlated. (Show all four steps use a = .01, .05 and .10).

N=11, Coefficient of Correlation, r: 0.89, Y-intercept, a: 72.1, Slope, b: 15.2

Answer 1

Solution:

Here, we have to use t-test for checking whether the variables are linearly correlated or not.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H₀: Given variables are not linearly correlated.

Alternative hypothesis: H_a: Given variables are linearly correlated.

H₀: ? = 0 vs. H_a: ? ? 0

We are given level of significance = ? = 0.01, 0.05, 0.10

Y-intercept = a = 72.1, slope = b = 15.2   

N = 11, df = N – 2 = 11 – 2 = 9

Correlation coefficient = r = 0.89

Test statistic = t = r*sqrt(n – 2)/sqrt(1 – r^2)

Test statistic = t = 0.89*sqrt(11 – 2)/sqrt(1 – 0.89^2)

Test statistic = t = 5.85577

P-value = 0.0002

(by using t-table or excel)

? = 0.01, 0.05, 0.10

P-value < ? = 0.01, 0.05, 0.10

So, we reject the null hypothesis H₀ at 1%, 5%, and 10% level of significance.

There is sufficient evidence to conclude that there is a significant linear relationship or correlation exists between the given two variables.