I am estimating an OLS regression with 158 observations and about 140 regressors (some unstructured data features to personality measure). Below is the bottom output I get from OLS. Some of the regressors turn out to be significant at 0.05 level. But I am wondering why may there be a case when adjusted R-squared is reasonable but p-value for F-test is not. Does this mean that the model is not valid even though some of the regressors are significant and adjusted R-square is reasonable?
And what could be the reason causing this and how to remedy this?
Residual standard error: 0.5457 on 19 degrees of freedom
Multiple R-squared: 0.9083, Adjusted R-squared: 0.2424
F-statistic: 1.364 on 138 and 19 DF, p-value: 0.2205