Regression Stat Tools

Your submission should consist of only those answers exhibits that are specifically asked for in a single word or pdf document. Please ensure that each exhibit is well edited and appropriately formatted. You may assume that fractional answers are acceptable throughout.

Problem

This assignment is an analysis of house prices in Springfield. You will find data in the file House Prices (Excel file) (Links to an external site.) on 128 recent sales of single-family houses in Springfield has the following variables:

Price:                Price at which house was eventually sold

SqFt:                 Floor area in square feet

Bedrooms:         Number of bedrooms

Bathrooms:        Number of bathrooms

Offers:               Number of offers made on the house prior to the accepted offer

Brick:                 Whether the construction is primarily brick or not (yes or no)

Neighborhood:   One of the three neighborhoods in Springfield (east, west or north)

Use StatTools to conduct the statistical analysis asked below. For questions that ask for a price (or change in price), use zero decimal places in your final numerical answer.

Part A - Linear Regression

Create a regression model for Price using SqFt, Bedrooms, Bathrooms and Offers as the independent (explanatory) variables.  Let us call this Model A.  Include the StatTools regression output as Exhibit A.

1. Write out the estimated regression equation.
2. The coefficient of SqFt is 309.20.  Provide an economic interpretation of this number.
3. Suppose a homeowner adds an extension to her house in the form of a 400 sq ft. bedroom.  What is the increase in the predicted selling price of her house?
4. Estimate the price of a 1720 sq ft. house that has 3 bedrooms, 2 bathrooms and has had 1 offer made on it.
5. Consider house number 39 in the data set.  It has 1720sq ft., 3 bedrooms, 2 bathrooms and has had 1 offer made on it.  Suppose the list price is $656,500.
   • According to Model A, is this house over-priced or under-priced?
   • By how much?

Part B - Adding Categorical Variables

Create a regression model for Price using the quantitative as well as qualitative (categorical) variables in the spreadsheet.

Use “North” as the base (or reference) category for the Neighborhood variable, and “No Brick” as the base category for exterior construction material variable, Brick.

Let us refer to this model as Model B.  Include the StatTools regression output as Exhibit B.

1. According to Model B estimated above, by how much does the average price in the East exceed the average price of a similar house in the North?
2. According to Model B, by how much does the average price in the West exceed the average price of a similar house in the East?
3. Let us define the “brick premium” as the average amount by which the price of a brick house exceeds the price of a similar house made without brick. According to Model B, what is the brick premium in Springfield?      

Part C - Adding Interactions

In Model B the brick premium was defined to be “the average amount by which the price of a brick house exceeds the price of similar house made without brick.”

Next, suppose it is conjectured that the brick premium varies by neighborhood.  To account for this conjecture, we augment Model B with interaction terms as follows:

Price = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers + b5BrickYes + b6East + b7West + b8BrickYes*East + b9BrickYes*West

Let us call this model Model C.

1. Simplify the equation for Model C for the various segments as asked below. In this part, we are looking for algebraic answers, not numerical answers. For simplicity, let S = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers.
   • What is the price of a non-Brick house in the North?
   • What is the price of a Brick house in the North?
   • What is the brick premium in the North
   • What is the price of a non-Brick house in the East?
   • What is the price of a Brick house in the East?
   • What is the brick premium in the East?
   • What is the price of a non-Brick house in the West?
   • What is the price of a Brick house in the West?
   • What is the brick premium in the West?
2. Provide an economic interpretation of b8.
3. Provide an economic interpretation of b9.
4. Run Model C using StatTools. Include the regression output as Exhibit C.
5. Use this output, what is the brick premium in the North, East and West?

Part D - Nonlinear Regression

Run the following regression as Model D:

 Log(Price) = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers + b5BrickYes + b6East + b7West

Recall that for our purposes, “Log” refers to natural logarithms.

1. Include the StatTools output as Exhibit D.
2. Estimate the price of a 1720 sq ft. brick house in the North that has 3 bedrooms, 2 bathrooms and has had 1 offer made on it.
3. From the output, it is seen that b7 = _______________.  Provide an economic interpretation. 
4. Suppose a homeowner adds an extension to her house in the form of a 400 sq ft. bedroom.  According to Model D, what is the increase in the predicted selling price of her house?

Be careful with the units