3. Assessing the model - Testing the slope Buying an item sight unseen on the Internet requires a significant amount of trust in the seller. Consider this hypothesis: Potential buyers tend 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: ywhereyx=0+1x+1=winningbid(indollars),and=shippingcost(indollars). The following equation lists the estimation results obtained for the sample of 90 high-reputation sellers: (Note: These results do not exactly duplicate Cheema's results but are representative of the Cheema study.) The mean square due to error (MSE) s2 is an unbiased estimator of 2, the variance of the error variable in the regression model. In this 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 4.54 . A different sample of eBay auctions cannot be expected to provide the same value of b1 as the current sample. So b1 is a random variable. Its sampling distribution has an estimated standard deviation of Use the Distributions tool to help you answer the questions that follow. Use the Distributions tool to help you answer the questions that follow. The regression model specifies that winning bid and shipping cost are linearly related. Conduct a t test (at the significance level a=0.05 ) for a significant linear relationship between shipping cost and winning bid when the seller has a high reputation. The value of the test statistic is winning bid. The result of the significance test by a high-reputation seller. , and you infer that there is a significant linear relationship between shipping cost and consistent with the notion that buyers don't pay attention to a surcharge when it is levied The 95% confidence interval estimate of 1 is to Since 0 is and winning bid. This result seller. in the confidence interval, you consistent with the notion that buyers don't pay attention to a surcharge when it is levied by a high-reputation infer that there is a significant linear relationship between shipping cost consistent with the notion that buyers don't pay attention to a surcharge when it is levied by a high-reputation seller