Question

Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help appraise residential housing in the Lake Charles Area. The model was developed using recently sold homes in a particular neighborhood. The price (y) of the house is based on the square footage (x) of the house. The model is:

Y=33,478+62.4X

The coefficient of correlation for the model is 0.63.

(a) Use the model to predict the selling price of a house that is 1,860 square feet.

(b) A house with 1,860 square feet recently sold for $165,000. Explain why this is not what the model predicted.

(c) If you were going to use multiple regression to develop an appraisal model, what other quanititative variables might be included in the model?

(d) What is the coefficient of determination for this model?

Answer 1

Explanation:

Hello!

Given the variables:

Y: Price of a house on sale

X: Square feet of a hose on sale

Y= 33.478 + 62.4X

r= 0.63

a)

To use the model to predict the price of a house with X= 1860 square feet you have to replace that value in the estimated equation:

^Y= 33478 + 62.4*1860= $149542

b)

The model predicts the estimated average value of Y given a certain value of X, that's why the value the house was sold for is different.

c)

Any variable that may vary the price of the house can be included in the model, for example:

X: Age of the house

X: Number of bedrooms

X: Type of neighborhood (residential area, industrial area, commercial area, etc...)

d)

Mathematically the coefficient of determination is equal to the square of the correlation coefficient:

R²= (r)²= 0.63²= 0.3969

This means that 39.69% of the variability of the house price is explained by the square footage of the house under the model: ^Y= 33.478 + 62.4X

I hope this helps!