Assignment
CASE STUDY: Prices of Homes
We will work with the data for homes for sale in Lafayette and West Lafayette, Indiana. The response (dependent) variable is Price, the asking price of a home. The data set contains the following explanatory (independent) variables:
• SqFt, the number of square feet for the home
• Bedrooms, the number of bedrooms
• Baths, the number of bathrooms
• Garage, the number of cars that can fit in the garage
1. The data set contains 44 homes for sale in zip code 47904. a few homes have prices that are somewhat high relative to the others. Similarly, some values for SqFt are relatively high. Exclude any home with Price greater than $150,000 and any home with SqFt greater than 1800 ft2. After excluding process, how many houses do you have in the data set? (20 p)
2. Regress price (dependent variable) on square feet (independent variable) and write the regression equation.
a. What proportion of the variance in Price variable can be explained by the Square Feet variable?
b. Is this proportion of variance statistically significant at .05 level of significance? Justify your answer.
c. Does Square feet significantly predict the price of the house? Justify your answer.
3. Recode the "Bedrooms" categorical variable to be Bed3 = 1 if the home has three or more bedrooms and Bed3 = 0 if it does not. Bed3 is called as Dummy variable (indicator variable).
a. Run the regression analysis including the variables of price and the dummy variable, Bed3 and write the regression equation.
b. What proportion of variance in the price of the house can be explained by the number of bedrooms of the house? Is this proportion of variance statistically significant at .05 level of significance? Justify your answer.
c. Does number of bedrooms significantly predict the price of the house? Justify your answer.
d. What is the predicted price for homes with two or fewer bedrooms (Bed3 = 0)? What is the predicted price for homes with three or more bedrooms (Bed3 =1)?
4. Recode the "Bath" categorical variable to create two dummy variables B2 and Bh as following:
B2 will be an indicator variable for an extra full bath and Bh will be an indicator variable for an extra half bath. For example, any home with at least one-half bath Bh will be equal to 1 and zero otherwise. If a home has at least 1 full additional bath, then B2 should be equal to 1 and zero otherwise. Note that, for homes with both an additional half bath and an additional full bath, both Bh = 1 and B2 = 1. (45 p)
a. What proportion of variance in the price of the house can be explained by the combination of Bh and B2 variables?
b. Is this proportion of variance statistically significant at .05 level of significance? In other words, is the overall model statistically significant at .05 level of significance? Justify your answer.
c. Find the corresponding regression equation. Does each variable (Bh and B2) significantly predict the price of the house? Justify your answer and report coefficients and p values for each variable.
d. What is the predicted price for the house that has an extra full bath?
e. What is the predicted price for the house that has an extra half bath?
5. Run the multiple regression analysis including all explanatory variables: Square Feet, the dummy variable Bed3, the dummy variables Bh and B2. (36 p)
a. What proportion of variance in the price of the house can be explained by the combination of all these explanatory variables? Is this proportion of variance statistically significant at .05 level of significance? In other words, is the overall model statistically significant at .05 level of significance? Justify your answer.
b. Find the corresponding regression equation. Does each variable (SqFt, Bed3, Bh and B2) significantly predict the price of the house? Justify your answer and report coefficients and p values for each variable.
c. Is there any variable in the data that does not significantly contribute to the model? If so, explain the reason for that and exclude the nonsignificant variable from the model and re-run the multiple regression analysis.
d. Do you observe any changes after excluding the variable in the model? Does the overall model fit the data well? Justify your answer and report the coefficient of determination for the model and the coefficient for each variable. Comment on the statistical significance of each variable.
6. Regress the explanatory variable of price on SqFt, and Bh (the half bathroom dummy we created in question 5), and the interaction between these variables.
a. What proportion of variance in the Price of the house can be explained by the combination of these explanatory variables and the interaction of these variables?
b. Is this proportion of variance statistically significant at .05 level of significance? In other words, is the overall model statistically significant at .05 level of significance? Justify your answer.
c. Does the interaction term (SqFt*Bh) significantly predict the price of the house? Justify your answer and report coefficients and p values for the interaction term.
d. What is the predicted price for the homes that lack an extra half bath (Bh = 0)?
e. What is the predicted price for the homes that have an extra half bath, (Bh=l)?
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.
Attachment:- Case-Study-Data-for-Assignment.rar