ECON453 Data Analytics and Modeling: Quantitative Analysis for Economic Strategy Fall, 2023 Problem Set 3
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Data Analytics and Modeling: Quantitative Analysis for Economic Strategy
(ECON453)
Fall, 2023
Problem Set 3
Due: Monday, April 9, 2023, 11:49 p.m.
Instructions:
● Submit your well labeled R code as an addendum along with your write-up. Start your R code with a comment with your name, Econ453, pset 3.
● I will look at your handwritten (hopefully typed) answers first. Your handwritten answers should be self contained. I will go over your code to see your technique and to see that your code matches with our answers. Please do not just dump output from R code and expect me to hunt down the answers.
● Where needed, data tables are available on d2L in an EXCEL file.
● Upload your completed homework as a single PDF file to the d2L. Please do not e-mail or submit hard copies.
1. Multiple Regression
You are hired as a marketing and sales analyst for Long Gone Inc. LG Inc. is the largest real estate firm in Metro City with annual sales of about $500 million. Of late, sales of residential homes have not been brisk. Your clients (homeowners) have been bickering that LG Inc. sold their homes for low prices to make a quick buck. The general manager of LG Inc. wants to get to the bottom of this.
It is Friday 4:52 p.m. You are getting ready for a weekend with your old U of A buddies. Just as you are about to leave your desk, you are summoned to the general manager’s office. You walk into his office nervously. There he is sitting in an oversized-stuffed chair with a cigar in his mouth. Apparently, “Arizona smoke free law” has not gotten around to his office yet. Sheepishly you mumble, “Good afternoon, Mr. Dimeworth” and quickly realize he is in no mood for pleasantries. You walk to a chair
but not sure if you should sit.
“Look, Mr. .....?”
“Rukie, Iam Rukie, ” you say.
“Oh. Yes. Iam, I have a task for you. Susan (the personnel manager, who hired you) tells me you are pretty good at statistics, economics, and stuff like that. Lately our clients have been grumbling about what they think are very low selling-prices for their homes. They seem to think that we are selling their homes for less than what market would bear. I want you to investigate this matter. We have this vast data bank in our computers. You can access any information about the houses we have sold in the past. Using this information, I want you to find out the characteristics of a house that influence its price. And be through. You can do this. Can’t you?”
“Yes, sir, Mr. Dimeworth. I will. I mean, I can. I will get onto it immediately, sir.” You are happy for having gotten an opportunity to impress Mr. Dimeworth himself. “I will use ……”
“Good. Report back to me on Monday. That’s all,” interrupted Mr. Dimeworth rudely, not particularly caring to listen to what you have to say.
You return to your desk, quickly cancel your social appointments for that evening, order a Domino’s pizza and start pouring over the problem. You draw a random sample of 50 observations (given in the EXCEL File pset3_data.xlsx; see below) from the vast data set. You start from the premise that size of house (living area in square feet), age of the house, location and swimming pool are important characteristics that explain the selling price. After cursing yourself for not paying more attention in ECON453 class, you vaguely remember that you probably should do a multiple regression analysis to investigate the effects of various characteristics on house prices. You estimate a regression equation
(with selling price of house as your dependent variable).
Use your estimated equation to answer the following questions:
1a) Write your estimated equation. Carefully interpret the meaning of the estimated parameters. Although successful in business, Mr. Dimeworth never completed his college having flunked his statistics courses. He thinks that college education is esoteric, far removed from reality with no practical value, and is for party-minded brats. You feel an obligation to show him that useful and practical applications can be made using econometric techniques.
1b) Does the location of the house matter, i.e., is there a premium for a house located in the prestigious “northern” part of the town?
1c) Does the presence of swimming pool influence the selling price of house?
1d) Does your estimated equation support your hypothesis that “size of house matters?” Interpret the parameter associated with “house size” variable.
1e) Mr. Dimeworth believes that newer houses fetch a greater price, other things being equal. Test his hypothesis.
1f) Do a test of overall significance of the regression equation. State your null hypothesis and conclusion clearly.
1g) What is your best forecast of the price for a 2,000 square foot house built in 1990 with a swimming pool, a fireplace, and a garage?
1h) Considering everything, explain why you think you have a (un)reasonable model?
1i) You present your results to Mr. Dimeworth. Trying not to let his admiration for your work out, he asks, “What does your model tell us about the value of a garage?” Can you use your estimated equation to impute the value of a garage? If not, how do you modify your model so you can measure the value of a garage?
1j) Your estimated equation indicates that the effect of house size on price (i.e., slope parameter associated with area of the house) is the same for houses in all locations (North and not-North). How do you modify your equation so that the effect of house size on price depends on the location? For full credit, estimate a model that allows the effect of house size on house price to vary across the two locations. Write your estimated equation(s) and interpret key parameter estimates. Test the hypothesis that the effect of house size on price is the same for both locations (North and not-North).
1k) Suppose you measure house price in thousands of dollars instead of dollars and rerun the regression. What happens to the estimated coefficients? R-Square? Significance of the parameters?
Use complete sentences in your answers. Remember that you need to provide statistical evidence, where appropriate, to convince Mr. Dimeworth - he does not heed to empty words. You need to do hypothesis testingfor questions 3b – 3f and 3j. Use p-valuesfrom R output where necessary.
Table 3.1 Housing Market in Metro City
Price Area Year Pool Location
224700 |
1778 |
95 |
no |
|
162200 |
1465 |
76 |
no |
Not-North |
212300 |
1805 |
65 |
no |
North |
217300 |
2181 |
80 |
no |
North |
236600 |
1770 |
95 |
yes |
North |
175700 |
1601 |
72 |
no |
Not-North |
207200 |
2065 |
70 |
yes |
Not-North |
219900 |
2177 |
63 |
yes |
North |
214000 |
2303 |
85 |
yes |
Not-North |
243500 |
2028 |
88 |
no |
Not-North |
192700 |
1987 |
65 |
no |
North |
223300 |
2037 |
86 |
no |
Not-North |
243500 |
2143 |
67 |
yes |
North |
227100 |
2496 |
72 |
no |
Not-North |
244700 |
2109 |
83 |
no |
Not-North |
216700 |
1988 |
64 |
yes |
Not-North |
209000 |
1853 |
72 |
yes |
North |
260100 |
2029 |
94 |
yes |
Not-North |
245300 |
2275 |
74 |
yes |
Not-North |
244400 |
2236 |
89 |
no |
Not-North |
195000 |
1987 |
64 |
no |
Not-North |
257900 |
2284 |
68 |
no |
North |
200700 |
2083 |
66 |
no |
Not-North |
178000 |
1628 |
76 |
no |
Not-North |
242700 |
2486 |
85 |
yes |
Not-North |
192300 |
1894 |
65 |
no |
Not-North |
179100 |
1977 |
66 |
no |
North |
234500 |
2121 |
94 |
no |
Not-North |
220200 |
1835 |
80 |
no |
Not-North |
197800 |
2170 |
72 |
no |
Not-North |
192600 |
1880 |
70 |
no |
Not-North |
247800 |
2213 |
78 |
yes |
Not-North |
193200 |
1984 |
75 |
no |
Not-</ |
2023-04-05