3. Using $$ \Psi_{s}(X, \lambda)=\left\{\begin{array}{cc} \left(X^{\lambda}-1 ight) / \lambda & \text { if } \lambda eq 0 \\ \log (X) & \text { if } \lambda=0 \end{array}, ight. $$ transform the data in the dataset mtcars to fit $\mathrm{hp}(X)$ as the explanatory variable and $\mathrm{mpg}(y)$ as the response. Find the optimal $\lambda$. Using your model, predict the value of mpg when $h p=100$