An agent for a residential real estate company in a suburb located outside a maj
ID: 3178712 • Letter: A
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. Complete parts below
Monthly Rent ($) Size (Square Feet)
900 750
1,550 1,200
800 1,050
1,600 1,250
2,000 2,000
925 700
1,750 1,350
1,250 950
b. Use the least-squares method to determine the regression coefficients
B0 and B1.
B0=
b1=
Now interpret B0,B1 in this problem
c. Predict the mean monthly rent for an apartment that has 1,000 square feet.
Use the equation
Y^i=b0+b1(Xi)
D. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?
When using a regression model for prediction purposes, consider only the range that includes all values from the smallest to the largest X-value used in developing the regression model.
f. 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?
Compare the model's predicted rents for the two apartments to their actual rents. The apartment whose rent differs from this prediction by the lesser amount is the better deal.
Calculate the difference between the actual and predicted rent values for a 1,000 square foot apartment.
Actual -predicted=
Explanation / Answer
x = Size
y = Monthly Rent
x
y
750
900
1200
1550
1050
800
1250
1600
2000
2000
700
925
1350
1750
950
1250
We go to excel and the we go to Data option. There we select Data Analysis. Under Data Analysis we select Regression. We select data for x and y, then we click on OK. We get the Regression Output:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.870088452
R Square
0.757053914
Adjusted R Square
0.716562899
Standard Error
236.4312656
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
1045148.415
1045148
18.697
0.0050
Residual
6
335398.4601
55899.74
Total
7
1380546.875
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
261.9966
264.4565
0.9907
0.3601
-385.1050
909.0982
X Variable 1
0.9383
0.2170
4.3240
0.0050
0.4073
1.4692
b.
The line of regression is,
y^ = 261.9966 + 0.9383x
Here the value of the intercept is 261.9966 (B0) and the value of the slope (B1) is 0.9383.
The value of the slope tells us that if there is one unit increment is size then the rent amount is going to be increased by 0.9383 units.
The value of the intercept is 261.9966; this is the rent amount when the size of the house is 0.
c)
Here x = 1000
y^ = 261.9966 + (0.9383*1000)
= 1200.30
The predicted value is $1200.30
d)
The size of 500 is quite far from the smallest number. This is the case of extrapolation where we predict the value of the dependent variable for an independent variable which is outside the range of our data. So only this is not appropriate to use the model to predict the monthly rent for apartments that have 500 square feet.
f)
Here we find the Residuals:
X = 1000
Residual = 1275 – 1200.30 = 74.70
X = 1200
y^ = 261.9966 + (0.9383*1200)
= 1387.96
Residual = 1425 – 1387.96 = 37.04
Here the value of the residual is smaller in case of the 1200 square feet house. So the best deal is 1200 square feet house for a monthly rent of $1425.
x
y
750
900
1200
1550
1050
800
1250
1600
2000
2000
700
925
1350
1750
950
1250
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.