SOA SRMStatistics for Risk Modeling

A regression with $n=50$ observations and $p=4$ predictors has $SSE=40$ and $SST=200$. Calculate the adjusted $R^2$.

A logistic model has $\text{logit}(p)=-1+0.5x$. Calculate the predicted probability at $x=2$.

Regressing predictor $x_3$ on the other predictors gives $R^2=0.80$. Calculate the variance inflation factor for $x_3$.