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

Answer:

The  t test statistics = 6.1357

Step-by-step explanation:

Given that:

sample (n) = 6

r = $\sqrt{\frac{SSR}{SST} }$

r = $\sqrt{\frac{60}{89} }$

r = 0.821

Therefore; the t test statistic can be calculated as :

$t = r* (\frac{\sqrt{n - 2} }{1 - r^2} ) \\ \\ t = 0.821 * (\frac{\sqrt{6 - 2} }{1 - 0.821^2} )\\\\ t = 0.821 * (\frac{\sqrt{4} }{1 - 0.674041} ) \\ \\ t = (\frac{\sqrt{4} }{0.325959})\\ \\ t = (\frac{ 2 }{0.325959}) \\ \\ t = 6.1357$