Question

The following data on sale price, size, and land-to-building ratio for 10 large industrial properties appeared in a paper.

Property	Sale Price (millions of dollars)	Size (thousands of sq. ft.)	Land-to- Building Ratio
1	10.5	2166	1.9
2	2.5	752	3.6
3	30.4	2422	3.7
4	1.7	223	4.8
5	20.0	3917	1.6
6	8.1	2867	2.3
7	10.1	1698	3.1
8	6.7	1046	4.7
9	5.8	1109	7.5
10	4.6	405	17.1

(a) Calculate the value of the correlation coefficient between sale price and size. (Give the answer to three decimal places.)
r =  

(b) Calculate the value of the correlation coefficient between sale price and land-to-building ratio. (Give the answer to three decimal places.)
r =  
(c) If you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use?

Size

Land-to-building ratio  

(d) Based on your choice in Part (c), find the equation of the least-squares regression line you would use for predicting y = sale price. (Give answers to three decimal places.)
y= .... +.... x

Answer 1

a) mean of sale price is- 10.04

Mean of size is= 1660.5

Covariance of sale price and size is = 1/10* (sum ((sale price-mean of sale price)*(size-mean of size)))= 6593.26

Var(sale prize)= 70.2844

Var(size)= 1253407.45

r= cov(sale price, size)/√(var(sale price)*var(size))

=6593.26/√(70.2844*1253407.45)

=0.702.

b)mean of land is = 5.03

Var(land)= 18.8501

Cov(land,price)= -11.9832

r= cov(land,price)/√(var(land)*var(price))

=-11.9832/√(18.8501*70.2844)

=-0.329

c) if I can use any one of the land and size I will select size to predict the sale price as the association between sale price and size is much higher than sale price and land-to-building ratio.

d) As my choice in part c is size the intercept and slope of the regression line for predicting the sale price can be obtained from the following formula-

Slope= r(size,sale price)* sd( sale price)/sd(size)

And

intercept= mean( sale price)-slope*mean(size)

So ,

slope= (0.702*√70.2844)/√1253407.45)=0.005

Intercept=10.04-(slope*1660.5)

=1.738

So the regression line is-

Sale price= 1.738+ 0.005* size