Question

2) The following data gives the selling price, square footage, number of bedrooms, and the age of a house in years. These houses have been sold in a specific neighborhood over the last six months.

Selling Price ($)	Square Footage	Bedrooms	Age (years)
84,000	1,670	2	30
79,000	1,339	2	25
91,500	1,712	3	30
120,000	1,840	3	40
127,500	2,300	3	18
132,500	2,234	3	30
145,000	2,311	3	19
164,000	2,377	3	7
155,000	2,736	4	10
168,000	2,500	3	1
172,500	2,500	4	3
174,500	2,479	3	3
175,000	2,400	3	1
177,500	3,124	4	0
184,000	2,500	3	2
195,500	4,062	4	10
195,000	2,854	3	3

a) Using square footage develop a model to predict the selling price of the house. How well does the model fit the data? What percentage of the selling price is explained by the model?

b) Using the number of bedrooms develop a model to predict the selling price of the house. How well does the model fit the data? What percentage of the selling price is explained by the model?

c) Using the age of the house develop a model to predict the selling price of the house. How well does the model fit the data? What percentage of the selling price is explained by the model?

d) Which of the models estimated in parts a – d best fits the data? Why did you select that model?

Answer 1

Q.a) ans

X=square footage

Y= selling price

correlation coefficient is 0.8363

The percentage of the selling price is explained by the model is (correlation coefficient)^2 = (0.8363)^2 = 0.6994

69.9% of selling price is explained by model

Q.b) ans

Here X : number bedrooms

Y: selling price

Correlation coefficient = 0.6577

The percentage of selling price explained by the model is given by (0.6577)^2 = 0.4325 = 43.2%

Q.c) ans

X : age of the house

Y : selling Price

Correlation coefficient = -.8385

The percentage of selling price explained by the model is given by (-0.8385)^2 = 0.70308 = 70%

Q.d) ans

As we known higher the value of coefficient indicator of goodness of fit.

70.3% variation in selling price explained by model in part c i.e. regression model of age of the house & selling price

Most of the points in part in regression line plot are lies on regression line..so it indicates goodness of fit.

Model in part c (regression model of age of house & selling price) is best model.