Question

Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in.
a) Create a scatter plot and find a regression equation between house value and rental income.
b) Then use the regression equation to find the rental income for
a house worth $230,000 and for a house worth $400,000.
c) Find the correlation coefficient.

Data of House Value versus Rental

Value	Rental		Value	Rental
67500	6864		170000	9568
77000	4576		174000	10400
85000	7072		190000	8320
94000	8736		200000	12272
104000	7904		200000	10400
115000	7904		208000	10400
125000	7904		225000	12480
130000	9776		240000	12064
135000	7488		244500	11232
140000	9152		270000	12896
148000	8320		300000	12480
165000	13312		310000	12480

Answer 1

a)

Scatterplot 16000 14000 12000 10000 > 8000 6000 4000 2000 0 0 50000 100000 150000 200000 250000 300000 350000 X

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	4117000.00	234000.00	109374458333	123242912	3065946000
mean	171541.67	9750.00	SSxx	SSyy	SSxy

Sample size,   n =   24      
here, x̅ = Σx / n=   171541.667          
ȳ = Σy/n =   9750.000          
SSxx =    Σ(x-x̅)² =    109374458333.3330      
SSxy=   Σ(x-x̅)(y-ȳ) =   3065946000.0      
              
estimated slope , ß1 = SSxy/SSxx =   3065946000/109374458333.333=   0.0280      
intercept,ß0 = y̅-ß1* x̄ =   9750- (0.028 )*171541.6667=   4941.4049      
              
Regression line is, Ŷ=   4941.405   + (   0.028   )*x

b)

Predicted Y at X=   230000   is          
Ŷ=   4941.40488   +   0.02803   *230000=   11388.68

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Predicted Y at X=   400000   is          
Ŷ=   4941.40488   +   0.02803   *400000=   16154.06

c) correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.83508