Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed

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 () of the house is based on the square footage (X) of the house. The model is Y = 33,478 + 624x 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 quantitative variables might be included in the model? (d) What is the coefficient of determination for this model?

Explanation / Answer

Solution:

Regression equation is

Y = 33478 + 62.4 X

Coeficient of Corelation for this model = 0.63

SOlution1:

Given X = 1860

So Selling Price should be Y = 33478 + 62.4*1860 = 149542

Solution2:

As we can see that model predicted selling price for 1860 square feet is 149542 but actually it sold for 1,65000 which is not pridected by this model.

Solution3:

For multiple regression there could be many quantitative independent variable like Income of the person, Age of the person, Far from the City etc.

Solution4:

Coeficient of determination is the Square of Coficient of Correlation

So R2 = 0.63*0.63 = 0.3969

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