Question

7. 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
21,998	2,317
17,350	2,347
⋮	⋮
29,245	2,892

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 6.92 ft.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.92.

c. Predict the property taxes for a 1,800-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

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ANSWER:

a.

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
-276.95	-2424.4	76701.3025	671437.58
-246.95	-7072.4	60984.3025	1746529.18
-824.95	-6157.4	680542.5025	5079547.13
-1569.95	-8778.4	2464743.003	13781649.08
3032.05	19527.6	9193327.203	59208659.58
-11.95	9251.6	142.8025	-110556.62
-388.95	-9263.4	151282.1025	3602999.43
-763.95	-7725.4	583619.6025	5901819.33
-485.95	-6149.4	236147.4025	2988300.93
-1354.95	-8341.4	1835889.503	11302179.93
-1159.95	-9303.4	1345484.003	10791478.83
517.05	11656.6	267340.7025	6027045.03
123.05	6621.6	15141.3025	814787.88
776.05	17593.6	602253.6025	13653513.28
-1049.95	-10016.4	1102395.003	10516719.18
1386.05	14525.6	1921134.603	20133207.88
1314.05	965.6	1726727.403	1268846.68
-259.95	-1472.4	67574.0025	382750.38
948.05	-8260.4	898798.8025	-7831272.22
298.05	4822.6	88833.8025	1437375.93
		SS: 23319062.95	SP: 161367018.4

Sum of X = 51879
Sum of Y = 488448
Mean X = 2593.95
Mean Y = 24422.4
Sum of squares (SS_X) = 23319062.95
Sum of products (SP) = 161367018.4

Regression Equation = ŷ = bX + a

b = SP/SS_X = 161367018.4/23319062.95 = 6.92

a = M_Y - bM_X = 24422.4 - (6.92*2593.95) = 6472.37

ŷ = 6.92X + 6472.37

b. Here slope is 6.92

So answer here is

c. For x=1800, ŷ = (6.92*1800) + 6472.37=18928.37

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