Question 1
\nSuppose that you work for a firm that operates stores across multiple markets, and you want to understand the revenues earned by specific store locations. To that end, you collect different pieces of information about each store, and run the following regression:
\ncase:
\n(i) \u201cRevenue\u201d is the revenue (per employee) per week for each store in thousands of dollars
\n(ii) \u201cSize of Store\u201d is the area of the store\u2019s floorplan (in square metres).
\n(iii) \u201cDistance to Nearest Major Road\u201d is the distance (in hundreds of metres) to the nearest 4-lane (or larger) road leading to the store.
\n(iv) \u201cMarket Size\u201d is the number of people, in thousands, who reside in the market served by each store.
\nThe regression results from the data you\u2019ve acquired are displayed below:
\nCoefficient Standard Error of Coefficient
\nIntercept 4 1
\nSize of Store 0.1 0.02
\nDistance to Nearest Major Road \u20131 0.25
\nMarket Size 0.5 0.1
\nThe questions related to these results are displayed on the following page.
\n(a) What is the proper, technical interpretation of the coefficient on \u201cSize of Store\u201d in the multiple regression? (5 marks)
\n(b) In this multiple regression setting, how would you test the hypothesis that the effect of \u201cSize of Store\u201d on revenues was zero at the 5% level of significance for all markets in which your company operates? (5 marks)
\n(c) Again, in this multiple regression setting, test (at the 5% level of significance) the hypothesis that the variable \u201cDistance to Nearest Major Road\u201d no effect on a store\u2019s revenues.
\n(5 marks)
\n(d) Now suppose that you acquire one other piece of information: the weekly advertising budget (in thousands of dollars) for each particular store. You represent this information with the variable \u201cAdvertising Budget\u201d, and your regression is now specified as:<\/p>\n
Using this new regression, you obtain the following results:
\nCoefficient Standard Error of Coefficient
\nIntercept 4 1
\nSize of Store 0.01 0.02
\nDistance to Nearest Major Road \u20131 0.25
\nMarket Size 0.5 0.1
\nAdvertising Budget 2 0.4
\nIn this case, test the hypothesis that the effect of \u201cSize of Store\u201d on revenues was zero at the 5% level of significance for all markets in which your company operates? (5 marks)
\n(e) Explain why the coefficient value on \u201cSize of Store\u201d and the hypothesis test on this coefficient is different in part (d) than in part (a) and (b). (10 marks)
\nQuestion 2
\nYou\u2019ve been contracted by a computer manufacturer to study the price of laptop computers in the market. You are asked to analyze the determinants of these prices, and so you collect data on the characteristics of various laptops sold by different companies, and use a regression to explore this issue:
\nIn this case:
\n(v) \u201cPrice\u201d is the price of the laptop (in dollars)
\n(vi) \u201cSize of screen\u201d is the area, in square centimetres, of the laptop\u2019s screen.
\n(vii) \u201cProcessor Speed\u201d is the computer\u2019s processing speed in GHz. (viii) \u201cRAM\u201d is computer\u2019s memory in GB.
\nThe regression results from the data analyzed by the internal research team are displayed below:
\nCoefficient Standard Error of the Coefficient
\nIntercept 500 100
\nSize of screen \u20135 2
\nProcessor Speed 200 50
\nRAM 100 10
\nStandard Error of the Regression = 150
\n(a) Provide a definition of the coefficient on \u201cProcessor Speed\u201d, and using the 5% level of significance, test the hypothesis that this variable has an effect on the price of the laptop. (10 marks)
\n(b) Suppose that a new laptop has been made by this company that has: (i) a screen whose area is 120 square centimetres, (ii) a processor speed of 4 GHz, and (iii) 8 GB of RAM. If the company believed that a laptop like this would have a price of $1000, respond to this assertion by using the information from the regression as well as formal hypothesis testing techniques. (10 marks)
\n(Please see the following page for the next part of this question)
\n(c) Now suppose that you do some more analysis of the price of laptops by adding some information to the regression used in parts (a) and (b). In particular, you estimate:<\/p>\n
In this case, \u201cWeight\u201d is the weight of the laptop (in grams). The results from this regression are displayed below:
\nCoefficient Standard Error of the Coefficient
\nIntercept 500 100
\nSize of screen \u20131 2
\nProcessor Speed 200 50
\nRAM 100 10
\nWeight \u20132 0.5
\nStandard Error of the Regression = 100
\nIn this case, the coefficient on \u201cSize of Screen\u201d changed in this regression compared to the regression in part (a). How can you explain this coefficient\u2019s change, while incorporating the correlation between \u201cSize of Screen\u201d and \u201cWeight\u201d into your answer? (10 marks)
\n(d) Suppose that the company intends to manufacture the same laptop specified in part (b), but has a specific weight in mind. Specifically, the laptop it will make has: (i) a screen whose area is 120 square centimetres, (ii) a processor speed of 4 GHz, (iii) 8 GB of RAM, and (iv) a weight of 400g. If, again, the company believed that a laptop like this would have a price of $1000, respond to this assertion by using the information from the regression as well as formal hypothesis testing techniques. (10 marks)
\nQuestion 3
\n(a) You work for a large company that wants to compare the performance of two sales teams
\n(we\u2019ll call them \u201cTeam A\u201d and \u201cTeam B\u201d) working at the firm. To formalize this comparison, you gather a sample of data on the weekly revenue created by each team. You then use this data to estimate the following regression:<\/p>\n
In this case, \u201cRevenue\u201d represents the weekly revenue (in dollars) generated by the sales team, and \u201cTeam A\u201d is a dummy variable equal to one if the revenue is created by \u201cTeam A\u201d, and zero if it\u2019s created by \u201cTeam B\u201d. Your regression results are listed below:
\nCoefficient Standard Error of Coefficient
\nIntercept 4000 1000
\nTeam A 800 200
\n(i) Interpret the meaning of the intercept in the above regression. (5 marks)
\n(ii) Interpret the meaning of the coefficient on the variable \u201cTeam A\u201d in the above regression. (5 marks)
\n(iii) Use these regression results to determine the average weekly revenue generated by Team A. (5 marks)
\n(iv) Use your statistical training to rigorously test whether or not the two teams generate similar or different levels of weekly revenue. (5 marks)
\n(b) Suppose that instead of running the regression listed above, you instead estimate the following regression:<\/p>\n
In this regression, \u201cRevenue\u201d is still defined in the same way as before, but \u201cTeam B\u201d is a dummy variable equal to one if the revenue is created Team B, and zero if it was created by Team A. In this case:
\n(i) Use the estimated coefficients from part (a) to determine the value of the intercept term in this regression (here in part (b)). Interpret the meaning of the intercept in this case. (5 marks)
\n(ii) Use the estimated coefficients from part (a) to determine the value of the coefficient on the dummy variable \u201cTeam B\u201d in this regression (here in part (b)). Interpret the meaning of the coefficient on \u201cTeam B\u201d in this case. (5 marks)<\/p>\n","protected":false},"excerpt":{"rendered":"
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