Real Estate Regression Exercise
You are consulting for a large real estate firm. You have been asked to construct a model that can
predict listing prices based on square footages for homes in the city you’ve been researching. You have
data on square footages and listing prices for 100 homes.
1.
Which variable is the independent variable (x) and which is the dependent variable (y)?
Answer- We believe the independent variable (x) is the square footage of the home. It is
because the price depends on the square footage. The square footage of the house will
drive the price. The dependent variable (y) is the price of the house. The x variable of the
square footage will change the value of y, the price of the home
2. Click on any cell. Click on Insert→Scatter→Scatter with markers (upper left).
To add a trendline, click Tools→Layout→Trendline→Linear Trendline
Does the scatterplot indicate observable correlation? If so, does it seem to be strong or weak?
In what direction?
Answer- This scatter graph does show a correlation that if the square footage increases so
does the price. If there are some properties that are not in line (for example higher prices
with lower square footages), this would be due to location of the property and
surrounding area. Other than that, the chart is showing with the higher square footages
and the higher the prices.
Please note all data on excel file (wk5-RealEastate_April 4, 2017, under Scatter tap).
3. Click on Data→Data Analysis→Regression→OK. Highlight your data (including your two
headings) and input the correct columns into Input Y Range and Input X Range, respectively.
Make sure to check the box entitled “Labels”.
Regression:
Copyright © 2016 by University of Phoenix. All rights reserved.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.639205681
R Square
0.408583903
Adjusted R Square
0.402549045
Standard Error 213617.1144
Observations 100
ANOVA
df
SS
Regression
1
0.000000000000825
Residual
98
Total
99
MS
F
Significance F
3,089,486,315,438.38 3,089,486,315,438.38
4,471,962,614,775.65
67.70
45,632,271,579.34
7,561,448,930,214.03
Coefficients
Standard Error t Stat P-value Lower 95%
Upper 95%
Lower
95.0% Upper 95.0%
Intercept
232837.5203
57,396.80
4.06
0.00010005608601
118,935.44
346,739.60
118,935.44
346,739.60
Square Footage
263.6011472
32.04 8.23
0.00000000000082
200.03
327.18 200.03
327.18
Covariance:
Listing Price ($) Square Footage
Listing Price ($) 75614489302
Square Footage
117203067.9 444622.7536
Correlation:
Listing Price ($) Square Footage
Listing Price ($) 1
Square Footage
0.639205681 1
Correlation Coefficient 0.639205681
(a) What is the Coefficient of Correlation between square footage and listing price?
Answer- The coefficient of the correlation is 0.639205681.
Please note all data on excel file (wk5-RealEastate_April 4, 2017, under regression tap).
(b) Does your Coefficient of Correlation seem consistent with your answer to #2 above?
Why or why not?
Answer- The coefficient of correlation is consistent with the scatter plot in question
#2 as the number was positive. The two variables have a positive and somewhat
Copyright © 2016 by University of Phoenix. All rights reserved.
strong relationship which is what the scatter plot in question #2 proved to be
corrected.
Please note all data on excel file (wk5-RealEastate_April 4, 2017, under regression tap).
(c) What proportion of the variation in listing price is determined by variation in the square
footage? What proportion of the variation in listing price is due to other factors?
(d) Check the coefficients in your summary output. What is the regression equation relating
square footage to listing price?
(e) Test the significance of the slope. What is your t-value for the slope? Do you conclude
that there is no significant relationship between the two variables or do you conclude that
there is a significant relationship between the variables?
P-value of the slope is more than the significance level 0.05. The T-value for the slope is
8.23.
We conclude that there is a significant relationship between the two variables.
(f) Using the regression equation that you designated in #3(d) above, what is the predicted
sales price for a house of 2100 square feet?
Listing price=232837.52+263.60*2100
Listing Price= 489,512,352.00
Copyright © 2016 by University of Phoenix. All rights reserved.
Real Estate Regression Exercise
You are consulting for a large real estate firm. You have been asked to construct a model that can
predict listing prices based on square footages for homes in the city you’ve been researching. You have
data on square footages and listing prices for 100 homes.
1.
Which variable is the independent variable (x) and which is the dependent variable (y)?
Answer- We believe the independent variable (x) is the square footage of the home. It is
because the price depends on the square footage. The square footage of the house will
drive the price. The dependent variable (y) is the price of the house. The x variable of the
square footage will change the value of y, the price of the home
2. Click on any cell. Click on Insert→Scatter→Scatter with markers (upper left).
To add a trendline, click Tools→Layout→Trendline→Linear Trendline
Does the scatterplot indicate observable correlation? If so, does it seem to be strong or weak?
In what direction?
Answer- This scatter graph does show a correlation that if the square footage increases so
does the price. If there are some properties that are not in line (for example higher prices
with lower square footages), this would be due to location of the property and
surrounding area. Other than that, the chart is showing with the higher square footages
and the higher the prices.
Please note all data on excel file (wk5-RealEastate_April 4, 2017, under Scatter tap).
3. Click on Data→Data Analysis→Regression→OK. Highlight your data (including your two
headings) and input the correct columns into Input Y Range and Input X Range, respectively.
Make sure to check the box entitled “Labels”.
Regression:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.639205681
R Square
0.408583903
Adjusted R Square
0.402549045
Standard Error 213617.1144
Observations 100
ANOVA
df
SS
Regression
1
0.000000000000825
Residual
98
Total
99
MS
F
Significance F
3,089,486,315,438.38 3,089,486,315,438.38
4,471,962,614,775.65
67.70
45,632,271,579.34
7,561,448,930,214.03
Coefficients
Standard Error t Stat P-value Lower 95%
Upper 95%
Lower
95.0% Upper 95.0%
Intercept
232837.5203
57,396.80
4.06
0.00010005608601
118,935.44
346,739.60
118,935.44
346,739.60
Square Footage
263.6011472
32.04 8.23
0.00000000000082
200.03
327.18 200.03
327.18
Covariance:
Listing Price ($) Square Footage
Listing Price ($) 75614489302
Square Footage
117203067.9 444622.7536
Correlation:
Listing Price ($) Square Footage
Listing Price ($) 1
Square Footage
0.639205681 1
Correlation Coefficient 0.639205681
(a) What is the Coefficient of Correlation between square footage and listing price?
Answer- The coefficient of the correlation is 0.639205681.
Please note all data on excel file (wk5-RealEastate_April 4, 2017, under regression tap).
(b) Does your Coefficient of Correlation seem consistent with your answer to #2 above?
Why or why not?
Answer- The coefficient of correlation is consistent with the scatter plot in question
#2 as the number was positive. The two variables have a positive and somewhat
strong relationship which is what the scatter plot in question #2 proved to be
corrected.
Please note all data on excel file (wk5-RealEastate_April 4, 2017, under regression tap).
(c) What proportion of the variation in listing price is determined by variation in the square
footage? What proportion of the variation in listing price is due to other factors?
(d) Check the coefficients in your summary output. What is the regression equation relating
square footage to listing price?
(e) Test the significance of the slope. What is your t-value for the slope? Do you conclude
that there is no significant relationship between the two variables or do you conclude that
there is a significant relationship between the variables?
P-value of the slope is more than the significance level 0.05. The T-value for the slope is
8.23.
We conclude that there is a significant relationship between the two variables.
(f) Using the regression equation that you designated in #3(d) above, what is the predicted
sales price for a house of 2100 square feet?
Listing price=232837.52+263.60*2100
Listing Price= 489,512,352.00
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