Question

Hanna Properties, Inc. specializes in custom home resales in Equestrian Estates. A random sample of 8 currently listed homes provided the following information on size of home and the price of the home. The size data are in hundreds of square feet, rounded to the nearest hundred, and the price data are in thousands of dollars, rounded to the nearest thousand.

Size (X)	Price (Y)
26	235
27	249
33	267
29	269
34	345
30	415
40	475
22	195

a) Compute the regression equation for price in terms of size.

b) Interpret the meaning of the regression parameters.

c) Compute r and r².  Interpret these statistics

d) Based upon the model above, what would be the predicted sales price of a home that is 3100 square feet?

Answer 1

a)

from above regression equation : Price= -129.590+14.468*Size

b)

here slope 14.468 tells us that for a unit increase in size, the price increases 14.468 on average

Intercept -129.590 tells us that for a home size of 0 , expected price is -129.590 , which is not meaningful and is meant to support the regression equation.

c)

SST=Syy=		65,463.5000
SSE =Syy-(Sxy)2/Sxx=		20,486.9948
SSR =(Sxy)2/Sxx =		44,976.5052

correlation coefficient r=

Sxy/(√Sxx*Syy)               =

0.829

as correlation coefficient is positive and near to 1, this tells us that there is a strong and positive liner relation between size and price.

Coeffficient of determination R^2 =SSR/SST=

0.687

this tells us that 68.7% of variation in Home price can be explained by variation in size of the home

d)

predicted price =-129.590+14.468*31 =318.92  thousands of dollars