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Real Estate Near Rails to Trails: Home Size Transformation

Consider the RailsTrails data, which provides information about 104 homes sold in Northampton, Massachusetts, in 2007. In this exercise, use the square footage of a home as the explanatory variable and the adjusted 2007 selling price (adj2007, in 2014 dollars) as the response variable.

a. Use a simple linear regression model to predict the selling price of a home (in adj2007 units) if the home is 1500 square feet in size. (Note: the square feet are measured in thousands.) Provide a 95% prediction interval and interpret the interval.

b. Comment on adherence to the model conditions and any effect on the answer from part (a).

c. Redo the regression using log(adj2007) and log(square feet) as the response and explanatory variables. Comment on the logged model, comparing its fit and model conditions to the original model.

d. Redo the prediction interval for the 1500 square foot home. Translate the prediction interval back to dollars from log-dollars and compare the two intervals.

Answer :

regression analysis

a) The predicted selling price of a home with a floor space of 1500 square feet is $_______ with a 95% prediction interval of ($_______, $_______).

To predict the selling price of a home with a floor space of 1500 square feet using a simple linear regression model, we utilize the RailsTrails data, which provides information on home size (square feet) and selling price (in adjusted 2014 dollars). By fitting a regression model to the data, we can estimate the relationship between the two variables and make predictions.

Using the simple linear regression model, we can plug in the value of 1500 square feet for the floor space and obtain the predicted selling price. Additionally, we can calculate a 95% prediction interval around this estimate to account for uncertainty.

To assess adherence to the model conditions and the effect on the answer, we need to evaluate whether the assumptions of linear regression are met. This includes checking for linearity, independence, homoscedasticity, and normality of residuals. Violations of these assumptions can impact the accuracy and reliability of the predictions.

For part (d), we are asked to redo the regression using log(adj2007) and log(squarefeet) as the response and explanatory variables. This involves transforming the variables using logarithms and fitting a new regression model. We need to compare the fit and model conditions of the logged model to the original one.

In part (e), we need to redo the prediction interval for the 1500 square foot home, but this time translating it back to dollars from log-dollars. By exponentiating the interval bounds, we can obtain the prediction interval in dollar amounts and compare it to the previous prediction interval.

Overall, these analyses allow us to explore the relationship between home size and selling price, assess the adequacy of the regression models, and make predictions with corresponding intervals.

Learn more about regression analysis

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