Both X variables in a multiple linear regression are individually insignificant, but the model has an extremely high R-squared value, rejecting the hypothesis that the variables are jointly insignificant. This is possible because significance of individual variables is determined by t-statistics, while significance of the full model is determined by the F-statistic, so the model can be significant even if individual variables are not.

1. Suppose that you have a multiple linear regression with two X variables. Both are statistically
insignificant in the regression (i.e., you do not reject that either slope is equal to zero at a 5%
level). Your R-squared value, however, is extremely high (0.95), so you overwhelmingly reject
the null hypothesis that the variables are jointly insignificant (the null would be written H0:
ß1=ß2=0). How could this be possible?
thanks
Solution
The Fsig is less than .05 for the model and the model explains the .95 of the variance. When you
are determining the significance of a single variable you use Tsig, but when you are determining
the significance of the entire model you are using Fsig. To reject the hypothesis only one Bi must
not equal zero.