High School

A real estate agent wishes to estimate the monthly rental for apartments based on the size (square footage) and location of the apartments. She chose the model [tex]y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + e[/tex], where [tex]x_1[/tex] represents the square footage of the apartment and [tex]x_2[/tex] indicates whether it is located in the town center or not. This linear regression model was fitted to a sample of size 50 to produce the regression equation below:

[tex]y = 145 + 1.4x_1 + 300x_2[/tex]

a. Predict the average monthly rent for an apartment located in the town center that has 1,300 square feet. (Simplify your answer.)

b. Predict the average monthly rent for an apartment located in the suburbs that has 1,300 square feet. (Simplify your answer.)

Answer :

An apartment of 1300 square feet in the town center is estimated to cost $1,965, while the same size apartment in the suburbs would cost $1,665.

To estimate the monthly rent for an apartment, we substitute the values into the linear regression equation.

The equation is given as y = 145 + 1.4x + 300x where x1 represents the square footage, and x2 is 1 if the apartment is located in the town center and 0 otherwise.

a) For an apartment with 1,300 square feet in town center:

We use the values x1=1300 and x2=1.

The monthly rent is calculated as y = 145 + 1.4(1300) + 300(1) = $1,965

b) For an apartment with 1,300 square feet in the suburbs:

We use the values x1=1300 and x2=0.

The monthly rent is calculated as y = 145 + 1.4(1300) + 300(0) = $1,665

To know more about linear regression:

https://brainly.com/question/32900914

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