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

If she finds an apartment that is 1.2 miles away from school, what is its predicted rent?

Answer 1

The predicted rent, if the school is 1.2 miles away from the apartment is 896.52 USD.

Explanation:

The simple linear regression analysis is used to determine the relationship between the dependent variable (Y) and the independent variable (X).

The general form of a simple linear regression equation is:

`y=\alpha +\beta x`

Here,

α = intercept

β = slope coefficient

A student starting their graduate studies wants to rent an apartment (in USD) near the university.To do this she wants to learn how the distance (in miles) to the school affects the rent.

On conducting the simple linear regression analysis using a statistical software the regression equation obtained is:

`RENT(y)= 1200.4326 - 256.2567* DISTANCE(x)`

Compute the value of y for x = 1.2 as follows:

`y= 1200.4326 - 256.2567* x`

`= 1200.4326 - (256.2567* 1.2)\\=896.52456\\\approx896.52`

Thus, the predicted rent, if the school is 1.2 miles away from the apartment is 896.52 USD.