A sample of 6 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample r

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.

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Vivian 1 week 2021-11-19T15:16:27+00:00 1 Answer 0 views 0

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    2021-11-19T15:18:23+00:00

    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

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45:7+7-4:2-5:5*4+35:2 =? ( )