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	10.6	2165	1.9
2	2.5	751	3.4
3	30.4	2421	3.7
4	1.8	225	4.8
5	20.0	3916	1.7
6	8.0	2865	2.3
7	10.0	1698	3.2
8	6.7	1046	4.9
9	5.7	1109	7.6
10	4.5	404	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?

A) Size

B) 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

Solution

We will use excel to find the solution

(a) Calculate the value of the correlation coefficient between sale price and size.

r = 0.702

	Sale Price	Size
Sale Price	1.000
Size	0.702	1.000

(b) Calculate the value of the correlation coefficient between sale price and land-to-building ratio.

r = -0.329

	Sale Price	land-to-building ratio
Sale Price	1.000
land-to-building ratio	-0.329	1.000

(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?

A) Size

Since Size is highly correlated with Sale Price

(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.

The output for regression from excel is given below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.702
R Square	0.492
Adjusted R Square	0.429
Standard Error	6.682
Observations	10.000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.000	346.484	346.484	7.761	0.024
Residual	8.000	357.152	44.644
Total	9.000	703.636
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.288	3.780	0.341	0.742	-7.430	10.005	-7.430	10.005
Size	0.005	0.002	2.786	0.024	0.001	0.010	0.001	0.010

So the regression equation is

Sale Price = 1.288+0.005*Size