In a multiple regression, if the F statistic is high, but one or more of the T statistics is not, what does this mean? I’m not entirely clear how to interpret conflicting results. - Robert
multicolinearity’s major diagnostic: T stats for individual coefs are insignificant, however F and R-squared are large and significant then you need to correct the regression by removing one or more corelated indep vars
it means that the t stats individually are not significent but together they become significent (F test) so that means there is high correlation among the independent variable… due to which the become significant when combined(multicollenearity)
think the whole “model” is significant (b/c F-test is), but the individual parts (t-stats) are insignificant. This is bad, they are both supposed to be significant.
Why then do we bother showing t-stats at all, if the F-stat tells us what we need to know? Alternatively, if all the t-stats are significant, why would we care about F?
because you need the t-stats to deduce multicolinearity If they didnt give you the t-stats and the f-stat was significant that could just mean that the individual t-stats were significant and therefore the ‘overall’ f-stat is significan OR the t-stats are insignificant but the f-stat is significant, because of the high correlation between some of the independent variables Hope that was clear
Another reason why we need the individual t-tests… page 365 of book 1 says “To test the null hypothesis that all of the slope coefficients in the multiple regression model are jointly equal to 0 against the alternative hypothesis that AT LEAST ONE slope coefficient is not equal to 0 we must use an F-test.” So I interpret this as saying that the F-test doesn’t tell us if all the independent variables are significant, so that’s why we still need the individual t-tests.
Lovely. What in the world does all that mean?