Question

Before starting their graduate studies, a student wants to rent an apartment near the university. She wants to learn how the distance to the school affects the rent. Statistical software was used to conduct a simple linear regression about the relationship between the rent (in USD) of an apartment and its distance to the university (in miles). The following equation for the regression line was given: RENT = 1200.4326 - 256.2567 DISTANCE Say someone lives 0.43 miles from campus and pays $1,050 a month in rent. What is the resulting residual value? Give your answer to two decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Answer 1

The resulting residual value is e=-40.24.

Explanation:

The residual value e for a regression model is defined as the difference between the real value y and the predicted value yp:

`e=y-y_p`

The predicted value for DISTANCE=0.43 miles is:

`RENT = 1200.4326 - 256.2567\cdot DISTANCE\\\\RENT(0.43) = 1200.4326 - 256.2567\cdot 0.43\\\\RENT(0.43) = 1200.4326 - 110.1904=1090.2422\\\\`

Then, if the real value is $1,050, the residual value is calculated as:

`e=y-y_p\\\\e=1050-1090.2422=-40.2422`