The regression model specifies that winning bid and shipping cost are linearly r
ID: 3153005 • Letter: T
Question
The regression model specifies that winning bid and shipping cost are linearly related. Conduct a t test (at the significance level a = 0.10) 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_, and you_conclude that there is a significant linear relationship between shipping cost and winning bid. The result of the significance test_consistent with the notion that buyers don't pay attention to a surcharge when it is levied by a high-reputation seller. The 90% confidence interval estimate of Pi is_to_. Since 0 is_in the confidence interval, you_conclude that there is a significant linear relationship between shipping cost and winning bid. This result_consistent with the notion that buyers don't pay attention to a surcharge when it is levied by a high-reputation seller. Conduct an F test (at a significance level a = 0.10) of overall significance for the regression. (With 1 degree of freedom in the numerator and n-2 = 90 -2 = 88 degrees of freedom in the denominator, F = 2.763 provides an area of 0.10 in the upper tail.) The test statistic is_, and you_conclude that there is a significant linear relationship between shipping cost and winning bid. 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: The following equation lists the estimation results obtained for the sample of 90 high-reputation sellers: These results do not exactly duplicate Cheema's results but are representative of the Cheema study. The mean square due to error (MSE) s^2 is an unbiased estimator of a^2, the variance of the error variable epsilon in the regression model. In this regression analysis, the MSE equals 46.0532, and the standard error of estimate equals 4.54. For the next question, sigma(X_i - 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 bi as the current sample. So bi is a randomExplanation / Answer
Given that,
y = winning bid
x = shipping cost
The regression equaltion is,
y^ = 29.95 - 0.35x
SSR = 50
SSE = 5500
n = 90
F = 2.763
MSE = 46.0532
standard error = 4.54
Here first we have to test linear relationship between x and y.
The hypothesis for the test is,
H0 : There is no linear relationship between x and y.
H1 : There is a linear relationship between x and y.
The test statistic is,
t = r*sqrt(n-2) / sqrt(1-r^2)
where r is sample correlation coefficient.
r we can find by using following formula,
r2 = SSR / SST
SST = SSR + SSE = 50 + 5500 = 5550
r2 = 50/5550 = 0.0090
r = sqrt(0.0090) = 0.0949
t = 0.0949*sqrt(90-2) / sqrt(1-0.09492)
t = 0.8904 / 0.9955 = 0.8944
P-value we can find by using EXCEL.
syntax is,
=TDIST(x, deg_freedom, tails)
where x is test statistic value.
deg_freedom = n-2 = 90-2 = 88
tails = 2
P-value = 0.3735
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is no linear relationship between x and y.
90% confidence interval for B1 is,
b - E < B1 < b + E
where b is slope coefficient in regression line = -0.35
E is the margin of error.
E = tc*SE / sqrt(SSx)
SE = 4.54
SSx = sqrt(4.54) = 2.131
tc we can find by using EXCEL.
syntax is,
=TINV(probability, deg_freedom)
where probability = 1 - c
c is confidence level = 90% = 0.90
deg_freedom = n-2 = 88
tc = 1.662
E = (1.662*4.54) / 2.131 = 3.542
lower limity = b - E = -0.35 - 3.542 = -3.892
upper limit = b + E = -0.35 + 3.542 = 3.192
90% confidence interval for slope is (-3.892, 3.192).
We are 90% confident that the population slope for x is lies between -3.892 and 3.192.