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
21928	2438
17356	2455
18214	1871
15652	1063
43957	5715
33631	2567
15131	2260
16698	1824
18277	2010
16038	1438
15198	1337
36089	3049
31008	2843
42044	3411
14414	1454
38940	4057
25329	3939
22907	2505
16152	3547
29213	2835

Taxes	Size
21,928	2,438
17,356	2,455
⋮	⋮
29,213	2,835

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 Property Taxes increase by 1 dollar, the size of the house increases by 6.85 ft.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.85.

c. Predict the property taxes for a 1,300-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

  TaxesˆTaxes^               

rev: 12_08_2018_QC_CS-150875

Answer 1

	Size X	Taxes Y	X * Y
	2438	21928	53460464	5943844	480837184
	2455	17356	42608980	6027025	301230736
	1871	18214	34078394	3500641	331749796
	1063	15652	16638076	1129969	244985104
	5715	43957	251214255	32661225	1932217849
	2567	33631	86330777	6589489	1131044161
	2260	15131	34196060	5107600	228947161
	1824	16698	30457152	3326976	278823204
	2010	18277	36736770	4040100	334048729
	1438	16038	23062644	2067844	257217444
	1337	15198	20319726	1787569	230979204
	3049	36089	110035361	9296401	1302415921
	2843	31008	88155744	8082649	961496064
	3411	42044	143412084	11634921	1767697936
	1454	14414	20957956	2114116	207763396
	4057	38940	157979580	16459249	1516323600
	3939	25329	99770931	15515721	641558241
	2505	22907	57382035	6275025	524730649
	3547	16152	57291144	12581209	260887104
	2835	29213	82818855	8037225	853399369
Total	52618	488176	1446906988	162178798	13788352852

Equation of regression line is


b = 6.85

a =( 488176 - ( 6.846 * 52618 ) ) / 20
a = 6397.78
Equation of regression line becomes

As Size increases by 1 square foot, the property taxes are predicted to increase by $6.85.

When X = 1300
= 6397.776 + 6.846 X
= 6397.776 + 6.846 * 1300
= 15297.58