3.18 real estate near rails-to-trails. consider the railstrails data, which gives 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 (distance from a bike trail) and squarefeet (size of home, in 1000s) 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 squarefeet to the model, we hope to address this impact, controlling for the size of the home.

first fit the simple linear regression model of adj2007 on distance.

next, fit a regression model with both explanatory variables. has the addition of squarefeet changed our estimate of the distance relationship to adj2007? use both the estimated coefficient and r2 in your answer.

find 95% confidence intervals for the distance coefficient from each model and compare them.

using the two-predictor model, give a prediction for the price of a particular home that goes on the market and that has 1500 square feet of space and is 0.5 mile from a bike trail.