7. Significance testing in simple linear regression Aa Aa Buying an item sight u

Question

7. Significance testing in simple linear regression 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 xshipping cost (in dollars) The following equation lists the estimation results obtained for the sample of 90 high-reputation sellers: The estimated regression equation: y = 29.95-0.35x SSR 50 SSE: 5,500 (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 Hint: For the next question, (Xi-X)2-(n-1)(sample variance of shipping cost). 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 bi is a random variable. Its sampling distribution has an estimated standard deviation of

Explanation / Answer

Solution

Taking the sample size to be 90 [a third of 271 given approximately equal among 271 auctions], degrees of freedom for Error SS is (90 - 1) - (1) = 88 and hence

MSE = 5500/88 = 62.5 and hence standard error of estimate = sqrt(62.5) = 7.91. ANSWER 1 & 2.

Standard Error of b1 is sb1, where sb12 = s2/Sxx = 62.5 [as obtained above]/4.54 [given]

= 13.76 ANSWER 3

To test = 0

Test statistic is: t = (b1 - 0)/SE(b1) tn – 2

t = (- 0.35 – 0)/13.76

= - 0.0254 ANSWER 4

Given = 0.01,the critical value = 0.005 point of t88 = 2.633.

Since |t| = 0.0254 < 2.633, the null hypothesis that the regression coefficient b1 = 0 is accepted.

So, we cannot conclude that there is significant relationship between shipping cost and winning bid. The result ……… is consistent ……… high reputation seller. ANSWER 5 & 6

DONE

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