Let’s get some more experience with the six steps in applied regression. Suppose that you’re interested in buying an Apple iPod (either new or used) on eBay (the auction website) but you want to avoid overbidding. One way to get an insight into how much to bid would be to run a regression on the prices¹¹ for which iPods have sold in previous auctions.

The first step would be to review the literature, and luckily you find some good material—particularly a 2008 article by Leonardo Rezende¹² that analyzes eBay Internet auctions and even estimates a model of the price of iPods.

The second step would be to specify the independent variables and functional form for your equation, but you run into a problem. The problem is that you want to include a variable that measures the condition of the iPod in your equation, but some iPods are new, some are used and unblemished, and some are used and have a scratch or other defect.

a. Carefully specify a variable (or variables) that will allow you to quantify the three different conditions of the iPods. Please answer this question before moving on.

b. The third step is to hypothesize the signs of the coefficients of your equation. Assume that you choose the following specification. What signs do you expect for the coefficients of NEW, SCRATCH, and BIDRS? Explain.

PRICE_i = β₀ + β₁NEW_i + β₂SCRATCHi + β₃BIDRSi + ε_i

Where:

PRICE_i = the price at which the ith iPod sold on eBay

NEW_i = a dummy variable equal to 1 if the ith iPod was new, 0 otherwise

SCRATCH_i = a dummy variable equal to 1 if the ith iPod had a minor cosmetic defect, 0 otherwise

BIDRS_i = the number of bidders on the ith iPod

c. The fourth step is to collect your data. Luckily, Rezende has data for 215 silver-colored, 4 GB Apple iPod minis available on a website, so you download the data and are eager to run your first regression. Before you do, however, one of your friends points out that the iPod auctions were spread over a three-week period and worries that there’s a chance that the observations are not comparable because they come from different time periods. Is this a valid concern? Why or why not?

d. The fifth step is to estimate your specification using Rezende’s data, producing:

Do the estimated coefficients correspond to your expectations? Explain.

e. The sixth step is to document your results. Look over the regression results in part d. What, if anything, is missing that should be included in our normal documentation format?

f. (optional) Estimate the equation yourself (Datafile = IPOD3), and determine the value of the item that you reported missing in your answer to part e.