Explain how you would test the null hypothesis that \(\beta_{1}=0\) in the multiple regression model \(Y_{i}=\beta_{0}+\beta_{1} X_{1 i}+\beta_{2} X_{2 i}+u_{i}\). Explain how you would test the null hypothesis that \(\beta_{2}=0\). Explain how you would test the joint hypothesis that \(\beta_{1}=0\) and \(\beta_{2}=0\). Why isn't the result of the joint test implied by the results of the first two tests?