Assignment Task
Assume independent samples and underlying normal distributions. You are in charge of The Home Staging Design company, which is hoping to gain some insights into the market based on recent sales in the area. In particular, you have been asked to make some predictions about prices and values. Remember to submit your Excel data and calculation files. Please use the following independent data items for your multiple regression (see Q1 and Q2 below), to predict the price of the home:
i. Bedrooms
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iii. Square foot interior living space
iv. Square foot of the land space
v. Fireplace vi. Condition
vii. Age
viii. Stage Rating
In conducting the regressions, explain why outliers might have an impact, and whether you needed to exclude any data elements as a result.
1. Develop three possible multiple regression models to predict house prices using only interval data variables. Your models must use at least two, three and four independent, interval data variables. (i.e. you must have one model with at least 2 independent variables, one model with at least 3 independent variables, and one model with at least 4 independent variables). Provide the regression equation for each of these models you have developed. Do all the models meet the assumptions required of a regression? Which model is best? Why? Do you think the model makes sense? Why or why not? Use an alpha of 0.05. Based on the best model you developed, please predict the price of a home with 3 bedrooms, 2.5 baths, 2100 sq ft interior living space, 2500 sq ft land space, 18 years old, with a fireplace. Also, predict with a 95% confidence interval, the price of a specific home with these characteristics, as well as the average home with these characteristics.
2. Based on the best model you developed, add model cases where you include nominal and ordinal data as independent variables (i.e. you may use any of the nominal or ordinal data in the dataset). What are the regression equations for these models? Do they all meet the assumptions required of a regression? Of these additional models, which is best? How do these models compare to those you developed in the previous question? Are you surprised? Please explain. Use an alpha of 0.10. Based on the best model you developed with nominal and ordinal numbers, please predict the price of the average home with 3 bedrooms, 2.5 baths, 2100 sq ft interior living space, 2500 sq ft land space, built 45 years ago, without central air or a fireplace. Also, predict with a 90% confidence interval, the price of a specific home with these characteristics, as well as the average home with these characteristics.
3. Is lot size a good predictor of land value? Explain. Ensure you have evaluated the assumptions of the analysis you do. If the, what is the predicted based on your analysis? Why? (i.e. what is the equation?) What is the 99% confidence interval of land value for a specific individual home with a lot size of 0.64. What is the 99% confidence interval for land value for the average home whose lot size is 0.64. Use an alpha of 0.01.
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