In the three variable regression model given by population regression function:
a way of determining whether the model as a whole makes sense, i.e. if the independent variables X2 and X3 help in explaining the dependent variable y, is to perform the following t-tests for each of the coefficients
then,if we fail to reject both tests,we must change our model as X2 and X3 do not really explain y.
please make sure to show all your work when carrying out the necessary computations.
- 1 decade agoFavorite Answer
Let me restate the problem clearly. So you wanna test whether the independent
variables are significant in the regression model, y = B0+B1X1+B2X2+B3X3. One
way of testing it is by making null hypothesis H0: Bj = 0 in favor of H1: Bj =/= 0
where j = 1,2,3 and see if we can reject H0 or fail to reject. If we reject H0, which
means B1, B2 B3 are non-zero, we conclude they are significant; however
, if we fail to reject H0, at least one B is zero.
You`ll need t statistics in carrying out the hypothesis testing. Look for the t stat and see if it exceeds t^(n-k-2)(alpha=0.05/2)
*the alpha is the level of significance in which you have to decide, normally it`s 0.05*