Real Estate Regression, statistics homework help

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LBYB2013

Mathematics

Description

Complete the Real Estate Regression Exercise Questions.

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 MS F Significance F

Regression 1 3,089,486,315,438.38 3,089,486,315,438.38 67.70 0.000000000000825

Residual 98 4,471,962,614,775.65 45,632,271,579.34

Total 99 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 Footage117203067.9444622.7536

Correlation:

Listing Price ($) Square Footage

Listing Price ($) 1

Square Footage 0.6392056811

Correlation Coefficient 0.639205681


"WITH THE INFORMATION GIVE ABOVE ANSWER THE TWO QUESTIONS BELOW."


Question Set:

(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?

"SEE ATTACHMENT FOR A BETTER UNDERSTANDING OF WHAT IS REQUIRED FOR THE FOLLOWING QUESTIONS"


Unformatted Attachment Preview

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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Explanation & Answer

Here is my answer :)

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...


Anonymous
Great study resource, helped me a lot.

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