Warning : Rod Made a Mistake!

Hey Folks

I made a mistake in my solutions to assignment #2.

In the second part of that solution set, I told you that because the t-test on the intercept was insignificant, you should drop the intercept from the equation.

Generally, you shouldn't actually do this. If a variable is insignificant, then drop it, but if the intercept is insignificant, while it is a good thing to mention in the result in a write-up, it is not a good idea to drop it from the equation.

An explaination of why this is so.

Normally, if the t-statistic indicates that a coefficient is statistically insignificantly different from zero, we normally accept the null hypothesis that the coefficient is equal to zero.

H₁ : b₁ = 0

So, for instances, if the original equation looked like this

Y = a + b₁ X₁ + b₂ X₂ + e

And we accepted the null hypothesis above, we would then say that the estimated equation is:

Y = a + b₂ X₂ + e

However, when is comes to the intercept, we usually do not drop the intercept from the equation, even if it appears to be statistically insignificant. There are some fancy statistically reasons for this, that have to do with making sure that we can still use the Uncentered R-squared. There are actually four different types of R-Squared. You use two of them, the Centered R-squared, which is normally refered to as just the R-squared and the Centered-Adjusted R-Squared. As BUEC333 students you do not have to know these details.

However, there is an easy intuitive explanation, that should make sense. If we have a low t-test on X₁, it means that X₁ doesn’t help to explain Y, therefore we should not include x1 in the regression. The intercept is not an observation, like X₁ or X₂. Instead, the intercept is just a theoretical construct, much like the regression line itself. Thus, dropping it isn’t always useful.

			rboothby@sfu.ca