Question

You estimate a model with 9 explanatory variables and an intercept from a data set with 100 observations. To test hypotheses on this model you should use a t-distribution with how many degrees of freedom?

Select one:

a. 1 b. 10 c. 9 d. 90

Answer 1

We know that in general t-test the number of degrees of freedom is (n -1).

But here, (n -1) is actually the degrees of freedom equal to the number of observations minus the number of parameters being estimated. Since each estimated parameter consumes a single degree of freedom.

In general t-test, the degrees of freedom (n -1) where "n" is the number of observations, and "1" is for the mean which is estimated.

Similarly, in the above regression analysis, the number of observations is 100 and we estimate explanatory variables(which is the parameters) which is 9 that will consume 9 degrees of freedom from 100, as well as intercept is also estimated in regression so for that 1 extra degree of freedom will also consume.

So,

Overall we get

Thus, the degrees of freedom = 100 - 9 - 1 = 90.

Thus, the correct answer is an option (d) which is 90.

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