3/48 Real estate near Rails to Trails: nested F-test Consider the RailsTrails data, which give information about 104 homes sold in Northampton, Massachusetts, in 2007. In this exercise, use Adj2007 ( the 2007 selling price in adjusted 2014 thousands of dollars) as the response variable and Distance and GarageGroup as two explanatory variables. The primary interest of the researchers was to ascertain the selling price impact of being close to a bike trail. By adding GaxageGroup to the model, we hope to address the distance- to-trail impact, controlling for whether the home has any garage spaces. The variable GarageGroup is a binary variable, jes or no, On whether the home has any garage spaces at all. ( Rails a. Le comparative boxplots and a t test to decide if having a 414 garage is related to the price of a home. Summarize your results. b. Fit (again) the simple linear regression model of Adj2007 on Distance and summarize the impact of distance to a trail on home price. c. Now fit a model using both GarageGroup and Distance as predictors. Summarize the results. d. Finally, fita model with an interaction term between Distance and GaxageGroup. Use the results of this model to estimate the two rates at which housing price decreases as distance increases. Is this difference in rates statistically significant? Explain e. Le a nested F-test to ascertain whether the terms involving garage space add significantly to the model of price on distance