ARE106SU09HW2 - 1 University of California, Davis...

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1 University of California, Davis Managerial Economic(ARE) 106, Summer 2009 Instructor: John H. Constantine Problem Set #2: Due MONDAY, August 17, 2009 Problem 1 (A table is provided at the end of the assignment to calculate the numbers) : The following data give the daily price (x, ($/unit)) and consumption (y) of some commodity Z; the data were collected at nine shops in Davis that sell Z for a one week period. The objective is to estimate the demand for Z. Obs x y 1 51 0 2 31 5 3 15 8 4 91 2 5 14 6 6 41 8 7 32 2 8 61 4 9 81 1 (a) Plot the data. (b) The PRF for this model is: y i = β 1 + β 2 x i + e i . Use the method of least-squares to estimate (by hand) the sample regression function. You must provide numeric estimates for the following variables: (i) β 1 (ii) β 2 (iii) σ 2 (iv) var( β 2 ) (v) s.e.( β 2 ) (c) State the SRF for the given sample above. Plug in the parameter estimates from part (b) into this equation . (d) What is the economic interpretation of both b 1 and b 2 , the sample estimates of β 1 and β 2 , respectively. (d) Clearly distinguish the terms var(b 2 ) and σ 2 and state what your estimates mean. (e) Plot the data points given in the table and draw in your estimated regression function. (f) Suppose x is 9. What is the predicted y (i.e., y ), as determined by your regression equation? Does this coincide with observation 4, where x = 9 and y = 12? Why or why not? (g) The estimated linear regression line always passes through the mean values x and y (assuming we do not suppress the intercept, which we have not done here.) Verify that this estimated regression line passes through the orgin.
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2 Problem 2 : Consider the following example. Suppose you are hired to be a weight guesser at a local amusement park. Customers pay 50 cents each, which you get to keep if you guess the weight within 10 pounds. If you miss by more than 10 pounds, then you must give the customer a small prize that you buy from the amusement park for 60 cents. As a matter of trickery, the amusement park helps you out by placing makers behind the customer so you can measure the height fairly accurately. Besides height and gender, you have no other information about the customer. On day one of the job you do poorly and lose money. On day two you decide to collect data on height (from your deceptive method) and weight (after the guess the person gets on the scale). Most participants are males, so you limit your data collection to males. You hypothesize the following theoretical relationship:
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ARE106SU09HW2 - 1 University of California, Davis...

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