Table 2 presents the summary of the regression outcome using “lm” command. You s

Question

Table 2 presents the summary of the regression outcome using “lm” command. You should notice that the p-values (the bold areas) are the same for both t and F test statistic. Meanwhile, the square of the t test statistic for the slope (4.563) is exactly same as the value of the F test statistic (20.82) [i.e. 4.5632 = 20.82]. Please explain what’s going on here. Is this a coincidence?

Table 2

Coefficients Estimate Std. Error T Value Pr(>|t| (Intercept) 57.7012 3.2904 17.536 1.14e-07 X 3.8383 0.8412 4.563 0.00184

Explanation / Answer

It is not coincidence. It can be done for every regression mode.

Since the square of t distribution is follows F-distribution.

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