Question

16. 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
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 pl

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

Answer 1

a.

y: Taxes;

x : size

Regression equation

$\widehat{y}$= a + b x

i.e

= a + b size

tares

.Σ.ry _ (Σ.r)(Συ)

$a=\frac{(\Sigma y-b\Sigma x)}{n}$

	y: Taxes	x: Size	xy	x2
	21972	2330	51194760	5428900
	17347	2427	42101169	5890329
	18263	1873	34206599	3508129
	15636	1098	17168328	1205604
	43971	5639	247952469	31798321
	33623	2429	81670267	5900041
	15188	2332	35418416	5438224
	16750	1898	31791500	3602404
	18236	2108	38441488	4443664
	16089	1245	20030805	1550025
	15126	1227	18559602	1505529
	36053	3027	109132431	9162729
	31050	2814	87374700	7918596
	42032	3329	139924528	11082241
	14362	1635	23481870	2673225
	38961	4074	158727114	16597476
	25312	4016	101652992	16128256
	22960	2470	56711200	6100900
	16162	3584	57924608	12845056
	29264	2879	84251056	8288641
Total	$\Sigma$y = 488357	$\Sigma$x = 52434	$\Sigma$xy=1437715902	$\Sigma$x2= 161068290

n = 20

.Σ.ry _ (Σ.r)(Συ)

$\small =\frac{20\times1437715902-52434\times488357}{20\times161068290-52434^{2}}=\frac{3147807102}{472041444}=6.6685$

$\small a=\frac{(\Sigma y-b\Sigma x)}{n}$$\small =\frac{488357-(6.6685\times52434)}{20}=\frac{138700.871}{20}=6935.0436$

Sample regression equation

= 6935.0436 + 6.6685 size

tares

= 6935.04 + 6.67 Size

tares

b.

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

c.

Predict the property taxes for a 1,600-square-foot home;

substitute size = 1600 in the above regression equation:

= 6935.0436 + 6.6685 size

tares

= 6935.0436 + 6.6685 x 1600 = 17604.6436