If the error variable e is normally distributed, the test statistic for testing H ₀: b ₁ = 0 has a Student t -distribution with n - 2 degrees of freedom.

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When the error term (e) in a regression model is normally distributed, the test statistic for testing the null hypothesis that the slope coefficient (b1) equals zero (H0: b1 = 0) indeed follows a Student's t-distribution with n - 2 degrees of freedom, where n is the number of observations. This is because the estimate of the slope coefficient is normally distributed if the errors are normally distributed, and the t-distribution is used when estimating the standard deviation of the coefficient from the sample.

If the Error Variable E Is Normally Distributed, the Test