DUE TODAY (ONLY TWO QUESTIONS)

Dec. 19, 2016

Cynthia McCahon

University of Phoenix Material

Real Estate Regression Exercise

Directions: Use the real estate data you used for your Week 2 learning team assignment. Analyze the data and explain your answers.

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)?

The independent variable (x) is square footage and the dependent variable (y) is the listing price. Listing price depends on the homes square footage.

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?

There is positive correlation, a positive slope. The correlation between square footage and listing price is 0.801782. The correlation is strong.

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”.

(a) What is the Coefficient of Correlation between square footage and listing price?

From the Excel regression output, the coefficient of correlation r= 0.801782

(b) Does your Coefficient of Correlation seem consistent with your answer to #2 above? Why or why not?

Yes, the correlation coefficient is consistent with the observable correlation from the scatter plot. As the scatter plot indicates, there seems to be a positive correlation as the listing prices of houses increase with an increase in square footage for most of the points and hence indicates a strong positive correlation.  The correlation coefficient from the Regression output has r=0.801782 which is a strong positive correlation and is consistent with the scatter plot.

(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?

The portion of the variation in listing price that is determined by the variation in the square footage is equal to 0.643 or 64.3%. Please keep in mind that these values have been rounded up to only 3 decimals. The proportion of the variation in listing price due to other factors is equal to 0.357 or 35.7%, which is calculated by subtracting the already obtained proportion from 1. This is done because the correlation proportion is assigned using values between one and negative one, as the way to assign strength in the correlation.

(d) Check the coefficients in your summary output. What is the regression equation relating square footage to listing price?

The coefficients are providing important data regarding the behavior of the slope and the intercept of our sample of square footage and listing price. The regression equation is equal to: Ŷ = 192808.838 + 489.945 (x) where x represents square footage.

(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?

(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?

References

Lind, D., Marchal, W., & Wathen, S. (2015). Statistical Techniques in Business and Economics

(16th ed.). Retrieved from The University of Phoenix eBook Collection database.

Pasadena Single Family Homes for Sale. (2016). Retrieved from