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In simple linear regression for the problem Y=aX+b; the "goodness" of the coefficient a can be estimated through a hypothesis test which computes the statistic, $t=\frac{a'-0}{SE(a')}$.

Which of the following follows a t distribution:

1- Is it t?

2- Is it a?

3- Is it both?

If one computed some other measure such as $t_2=\frac{2a'-0}{8SE(a')}$, would it also follow a t-distribution as long as it is computed on a sample? why/why not?

Minaj
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  • Why are you subtracting $0$? – Henry Jun 20 '17 at 07:35
  • @Henry The default test for almost all software is a comparison of each coefficient to zero. (It may be misleading, though, to characterize that as an estimate of the "goodness" of the coefficient, whatever that might even mean.) – whuber Jun 20 '17 at 14:08

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