10.2 (Data file: Highway) 10.2.1 For the highway accident data, use your software to verify the forward selection and backward elimination subsets that are given in Section 10.2.2. 10.2.2 Use as response log(rate x len) and treat 1wid as the focal regressor. Use both forward selection and backward elimination to assess the importance of 1wid. Summarize your results. 10.2.3 Using the identity log(rate x len) = log(rate) + log(len), we can write E(log(ratexlen)lX = x) = Bo + B'x E(log(rate) + log(len)lX =x) = Bo + B'x E(log(rate)lX =x) = Bo + B'x-log(len) In this last equation, the variable log(len) is on the right side of the equation with an implied known regression coefficient equal to -1. A regressor with a known regression coefficient is called an offset, and most modern regression software allows you to include offsets in fitting a model. The difference between an offset and a regressor is that no coef- ficient will be estimated for the offset. Repeat Problem 10.2.2, but use log(rate) as the response and -log(len) as an offset. Is the analysis the same or different? Explain