Question 3

Cathy Bostic

Florida reappraises real estate every year, and the county appraiser’s Web site lists the current “fair market value” of each piece of property. Property usually sells for somewhat more than the appraised market value. Here are the appraised market values and actual selling prices of condominium units sold in a beachfront building over a 19-month period (in thousands of dollars):

Selling Price	Appraised value	Month	Selling price	Appraised value	Month
850	758	0	790	605.9	13
900	812.7	1	700	483.8	14
625	504	2	715	585.8	14
1075	956.7	2	825	707.6	14
890	747.9	8	675	493.9	17
810	717.7	8	1050	802.6	17
650	576.6	9	1325	1031.8	18
845	648.3	12	845	586.7	19

(a) Make a scatterplot. It appears that appraised market value can be used to predict selling price.

According to the scatter plot the appraised market value can be used to predict selling price. There is a strong linear relationship between the two.

(b) Find the least-squares line for predicting selling price from appraised value. Add this line to your scatterplot. Another unit in this building has appraised value $802,600. What do you predict that it will sell for?

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9277
R Square	0.8606
Adjusted R Square	0.8506
Standard Error	69.7299
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	420072.1418	420072.1418	86.3945	0.0000
Residual	14	68071.6082	4862.2577
Total	15	488143.7500
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	127.2705	79.4892	1.6011	0.1317	-43.2168	297.7578
Appraised value	1.0466	0.1126	9.2949	0.0000	0.8051	1.2881

The least-squares line for predicting selling price from appraised value is;

Selling price = 127.2705+1.0466* Appraised value

The predicted selling price of the building has appraised value $802,600,

Selling price = 127.2705+1.0466* 802.6 = 967.27166 thousand dollar or $967,271.66