3. Assessing the model Testing the slope Aa Aa Buying an item sight unseen on th

Question

3. Assessing the model Testing the slope Aa Aa Buying an item sight unseen on the Internet requires a significant amount of trust in the seller. Consider this hypothesis: Potential buyers tend to scrutinize the offers posted by sellers with poor reputations more than they do the offers posted by sellers with neutral or good reputations. As a result, if buyers notice a surcharge (such as a shipping fee) levied by a seller with a poor reputation, they reduce the (presurcharge) price they are willing to pay for the item. On the other hand, a surcharge does not affect buyers' (presurcharge) willingness to pay for an item offered by a seller with a neutral or a good reputation. Amar Cheema tested this hypothesis, which was described in a June 2008 paper entitled "Surcharges and Seller Reputation" and published in the Journal of Consumer Research. Cheema collected data on 271 completed eBay auctions for three DVD trilogies: The Godfather, The Lord of the Rings, and Star Wars. For each auction, Cheema recorded the winning bid, the surcharge, and the seller's eBay feedback score. Then he partitioned the 271 auctions into three almost equal-sized samples based on the seller's feedback score. The following is a simple linear regression model estimated for each group: where y winning bid (in dollars), and x = shipping cost (in dollars). The following equation lists the estimation results obtained for the sample of 90 medium-reputation sellers The estimated regression equation : y = 33.04-0.43x SSR: 72 SSE: 4,493 (Note: These results do not exactly duplicate Cheema's results but are representative of the Cheema study.) the variance of the error variable in the regression model. In this The mean square for error (MSE) s is an unbiased estimator of regression analysis, the MSE equals , and the standard error of estimate equals The sample variance of shipping costs for the auctions in the sample is 4.39 A different sample of eBay auctions cannot be expected to provide the same value of bi as the current sample. So bi is a random variable. Its sampling distribution has an estimated standard deviation of

Explanation / Answer

MSE = SSE / 90-2 = 4493/88 = 51.05682

SE = Sqrt(MSE) = 7.1454

The sampling distribution has an estiamted sd of 4.39/88 = 0.05

Test statistic t = -0.43/0.05 = -8.6
You may infer that there is significanct linear relationship between shiping a cost and winning bid

The 90% confidence interval estiamte of beta1 is (-0.43 - 1.6624*0.05,-0.43 + 1.6624*0.05) = (-0.5112,-0.3488)

Since 0 is not contain in the confidence interval, you suggest infer that there is significanct linear relationship between shiping a cost and winning bid
This result is consistent with notation that buyers don't pay attentionto a surchange when it si levied by a medium reputation seller

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