Question

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

Taxes	Size
21972	2330
17347	2427
18263	1873
15636	1098
43971	5639
33623	2429
15188	2332
16750	1898
18236	2108
16089	1245
15126	1227
36053	3027
31050	2814
42032	3329
14362	1635
38961	4074
25312	4016
22960	2470
16162	3584
29264	2879

Taxes	Size
21972	2330
17347	2427
18263	1873
15636	1098
43971	5639
33623	2429
15188	2332
16750	1898
18236	2108
16089	1245
15126	1227
36053	3027
31050	2814
42032	3329
14362	1635
38961	4074
25312	4016
22960	2470
16162	3584
29264	2879

Taxes	Size
21,972	2,330
17,347	2,427
⋮	⋮
29,264	2,879

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

TaxesˆTaxes^ =  +  Size.

b. Interpret the slope coefficient.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.67.

• As Property Taxes increase by 1 dollar, the size of the house increases by 6.67 ft.

c. Predict the property taxes for a 1,600-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

  TaxesˆTaxes^               

Answer 1

a.

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
-291.7	-2445.85	85088.89	713454.445
-194.7	-7070.85	37908.09	1376694.495
-748.7	-6154.85	560551.69	4608136.195
-1523.7	-8781.85	2321661.69	13380904.85
3017.3	19553.15	9104099.29	58997719.5
-192.7	9205.15	37133.29	-1773832.405
-289.7	-9229.85	83926.09	2673887.545
-723.7	-7667.85	523741.69	5549223.045
-513.7	-6181.85	263887.69	3175616.345
-1376.7	-8328.85	1895302.89	11466327.8
-1394.7	-9291.85	1945188.09	12959343.2
405.3	11635.15	164268.09	4715726.295
192.3	6632.15	36979.29	1275362.445
707.3	17614.15	500273.29	12458488.3
-986.7	-10055.85	973576.89	9922107.195
1452.3	14543.15	2109175.29	21121016.75
1394.3	894.15	1944072.49	1246713.345
-151.7	-1457.85	23012.89	221155.845
962.3	-8255.85	926021.29	-7944604.455
257.3	4846.15	66203.29	1246914.395
		SS: 23602072.2	SP: 157390355.1

Sum of X = 52434
Sum of Y = 488357
Mean X = 2621.7
Mean Y = 24417.85
Sum of squares (SS_X) = 23602072.2
Sum of products (SP) = 157390355.1

Regression Equation = ŷ = bX + a

b = SP/SS_X = 157390355.1/23602072.2 = 6.67

a = M_Y - bM_X = 24417.85 - (6.67*2621.7) = 6935.05

ŷ = 6.67X + 6935.05

b. As we see that size is independent variable and taxes are dependent variable. So slope is rate of change in y, for constant change in x. Hence answer is as below.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.67.

c. For x=1600, ŷ = (6.67*1600) + 6935.05=17607.05