Question

An agent for a residential real estate company in a suburb located outside a major city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward the​ goal, the agent would like to use the size of an​ apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 8​ one-bedroom apartments and the data are shown

Monthly Rent ($)   Size (Square Feet)
875                        800
1450                    1200
850                       1050
1500                    1250
2000                     1800
925                         650
1800                    1250
1250                   1100

a ) Use the​ least-squares method to determine the regression coefficients b 0 and b 1 and simple linear regression equation and what does it mean?

b) Predict the mean monthly rent for an apartment that has​ 1,000 square feet.

c) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square​ feet?

d) Two people are considering signing a lease for an apartment in this neighborhood. They are trying to decide between two​ apartments, one with​ 1,000 square feet for a monthly rent of​ $1,275 and the other with​ 1,200 square feet for a monthly rent of​ $1,425. Based on​ (a) through​ (d), which apartment is a better​ deal?

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Answer 1

X	Y	XY	X²	Y²
800	875	700000	640000	765625
1200	1450	1740000	1440000	2102500
1050	850	892500	1102500	722500
1250	1500	1875000	1562500	2250000
1800	2000	3600000	3240000	4000000
650	925	601250	422500	855625
1250	1800	2250000	1562500	3240000
1100	1250	1375000	1210000	1562500
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
9100	10650	13033750	11180000	15498750

a)

Slope, b = SSxy/SSxx = 919375/828750 = 1.1093514

y-intercept, a = y̅ -b* x̅ = 1331.25 - (1.10935)*1137.5 = 69.362745

Regression equation :

ŷ = 69.3627 + (1.1094) x

b)

Predicted value of y at x = 1000

ŷ = 69.3627 + (1.1094) * 1000 = 1178.7142

c)

As the value 500 square feet is outside the range of value of apartment size, so it not be appropriate to use the model to predict the monthly rent.

d)

Residual for apartment size 1000 = y - ŷ = 1275 - 1178.7142 = 96.2858

Predicted value of y at x = 1200

ŷ = 69.3627 + (1.1094) * 1200 = 1400.5845

Residual = y - ŷ = 1425 - 1400.5845 = 24.4155

The apparent with size 1200 square feet is better deal.