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