Week 2 Multiple Regression

Assignment "Realtor’s Challenge"

Group Task:

Assume that you are a real estate agent and your client wants an estimate on his house. The house size is 2,100 square feet. It has 3 bedrooms and 2 bathrooms. It is a 15 years-old property. Your client also wants to know whether the home renovation (adding a bathroom) will increase the value of his house and by how much.

You have collected information on properties located in the same area as your client’s house. You will use this information to build a model to predict sales prices for residential property. Armed with the model results, you will prepare a report to your client addressing his questions. You will put all technical information about particulars of regression analysis into a technical note.

Group Question: Estimate a house price for your client and make suggestions on whether adding a bathroom will increase the value of your clients’ house

Use the following questions as a guide when formulating your response. Include detailed answers to these questions along with figures, tables and/or equations, if necessary, into the Technical Note of your report:

1. Describe the data you collected and presented in the "Data" worksheet. The dependent variable Price is the property market value. There are four independent variables representing different characteristics of the property.

• How many properties (observations) did you use in the analysis?
• Locate quantitative variables. What was the average selling price for properties in the dataset? Average age and size? What were the highest and the lowest price in your data set?
• Locate two categorical variables: number of bedrooms and bathrooms. Note that these variables were appropriately transformed into binary variables for the purposes of regression modeling. How many recently sold houses had one or two bedrooms and how many had more than 2 bedrooms? How many properties had 1-2 bathrooms? More than two bathrooms?
• Describe your variables. Do you think that this data is appropriate for the estimation of the selling price of your client’s house?

2. Navigate to your individual question . At this step, each student in your group will test different hypothesis about discount means. This is an individual assignment; however, its results are important for success of your group assignment. Therefore, start working on it as early as possible. Ask for the help of your group members if needed. See calendar to find out when Individual questions are due.

3. Each of you in the team has estimated different models. Compare the results of your individual questions and select the best model.

• Use R square value as a criterion. Large values of R square indicate the large explanatory power of the model.
• CAUTION: Remember that the addition of new variable(s) ALWAYS increases R square, even if the model has multicollinearity problem. When evaluating the model with highly collinear variables, pay attention to the correlation between independent variables and look for the instability in the regression estimates. Avoid including highly correlated explanatory variables into the model even if its R square is large – the R square is meaningless in this situation.

4. Select the best model and analyze the results of your regression:

• What value did you obtain for the intercept? What is its meaning?

• One would expect that houses of larger sizes and with greater number of baths would be selling at higher prices. Do the estimated coefficients of the Size and Bathrooms variables have expected signs (i.e. do square footage and number of baths matter and if yes do they increase or decrease the selling price)? How about Age and Bedrooms variables? How would you interpret the signs of Age and Bedroom variables?
• What is the effect of property size on the selling price. By how much the selling price of houses of the same age and with the same number of bedrooms and baths, will increase due to a 1-square-foot increase in the size of the house?
• What is the effect of property age? How different will be the selling price of 10-year house from the selling price of 11-year house with similar?

• How much variation in Price variable does your winning model explain, i.e. what is the value of R square?

5. Estimate the predicted value of your client’s property and make suggestions:

• Estimate the predicted value of your client’s house.
• Would you suggest adding a bathroom to increase the value of your client’s house? By how much will this addition increase the selling price?

Price: $25.8

Solution: The downloadable solution consists of 13 pages, 1280 words.
Deliverable: Word Document