Question

A sample of 6 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.SSR=60, SST=89, summation (x_i-xbar)2=28, summation (x_i-xbar)(y_i-ybar)=45.Calculate the t test statistics to determine whether a statistically linear relationship exists between x and y.

Answer 1

The t test statistics = 6.1357

Explanation:

Given that:

sample (n) = 6

r =
`\sqrt{(SSR)/(SST) }`

r =
`\sqrt{(60)/(89) }`

r = 0.821

Therefore; the t test statistic can be calculated as :

`t = r* ((√(n - 2) )/(1 - r^2) ) \\ \\ t = 0.821 * ((√(6 - 2) )/(1 - 0.821^2) )\\\\ t = 0.821 * ((√(4) )/(1 - 0.674041) ) \\ \\ t = ((√(4) )/(0.325959))\\ \\ t = (( 2 )/(0.325959)) \\ \\ t = 6.1357`