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The data set contains information on sales of 1oz gold coins on eBay. Further details will be available in the key after the exam ends. The file contains the following variables:
DATE: date of the sale
SALE: final selling price of the coin
GOLDPRICE: price of gold, one ounce, at the end of trading on the date of the sale, or, if the sale is on a weekend or holiday, the end of the previous day of trading.
BIDS: the number of bids submitted for the auction (these eBay sales were in an auction format)
TYPE: E for Eagle or a US coin, KR for Krugerrand or a South African coin and ML for Maple Leaf or a Canadian coin.
SHIPPING: cost of shipping; this is an additional fee the buyer must pay so that SALE+SHIPPING is the total cost to the buyer.
SLABBER: P for PCGS, N for NGC or U for not slabbed; a slabbed coin is a coin inside a tamper proof holder that also indicates the coin’s condition or grade.
GRADE: the grade of slabbed coins. If SLABBER=’U’ then this is 0.
other: additional characteristics of slabbed coins are noted here; example FD means the “slab” or coin holder notes that the coin was minted on the first day of minting and FDIFLAG means that it is labeled was first day of issue and the holder has an image of a flag on it.
a) What is the average for SALE?
[ Select ] [“1915”, “1651”, “1654”, “1930”] .
b) What is the maximum for BIDS?
[ Select ] [“55”, “60”, “57”, “62”] .
c) Create a boxplot of SALE. You should see that there are 3 (three) outliers. Look at those three observations and choose the correct statement. (i) the observations either have only 1 bid or other=”BURNISHED”, (ii) the observations all have SLABBER=”P”, (iii) the observation(s) with low value(s) for SALE has/have only 1 or 2 bids while the observation(s) with high value(s) for SALE has/have numbers of bids near the maximum, say within 5 of the maximum, (iv) the observations either have other=”ME” or “LD”.
[ Select ] [“(ii)”, “(iii)”, “(i)”, “(iv)”] . d) In R type the following command, table(yourdataset$other), where yourdataset is the name you gave to the dataset with the ebay coin sales. This will produce a table showing the value for “other” and the number of observations which have that value. For example, it will show the value “0” and under that the number 20, meaning that there are 20 observations where other is 0 and then it will show BURNISHED and under that a 2, meaning there are 2 coins where other is BURNISHED. How many observations are there where other is “LD”?
[ Select ] [“4”, “6”, “1”, “2”] .
e) Run a regression where SALE is the dependent variable and GOLDPRICE, BIDS, and SHIPPING are the explanatory variables. Consider the following statements and select which ones are correct (1) although there is little explanatory power the model is basically a good model (2) the model has minimal explanatory power (3) none of the independent variables have statistically significant coefficients at standard levels of significance (4) at least 1 of the estimated coefficients has the wrong sign, (5) some combination of items (2), (3) and (4) suggest this is not a good model.
[ Select ] [“(1), (2) and (3)”, “(1) and (3)”, “(2) and (4)”, “(1) and (2)”, “(2) and (3)”, “(2), (3), (4) and (5)”] .
f) Run a regression where SALE is the dependent variable and GOLDPRICE, BIDS, SHIPPING and a set of dummy variables for the values of other are the explanatory variables. NOTE: remove the observations where other=”ME” since there is only one such observation. Because there is only one observation with “ME” it will have a residual of 0 since the “ME” will perfectly explain why it is different from all other observations. This means that your regression is run with only 46 observations and you should see the df for the F statistic being 10 and 35.
What is the R2 value for this regression?
[ Select ] [“0.6268”, “0.6801”, “0.431”, “0.5527”, “0.3496”] .
g) Using this model what is the expected value for SALE for an auction with a gold price of $1650, 5 bids, free shipping (SHIPPING=0), and other= FDIFLAG?
[ Select ] [“$1988”, “$1945”, “$1956”, “$1919”, “$1972”] .
h) Is the coefficient on FDIFLAG statistically significant at the 0.05 level?
[ Select ] [“NO”, “YES”] .
i) Examine the residual plots. Find the observation with the largest absolute residual and the observation with the largest Cook’s Distance. Identify the correct statement. (i) the observation with the largest absolute residual is an outlier in the residual space and this is due to an extremely low sale price which might relate to only receiving one bid (ii) the observation with the largest Cook’s Distance is influential and has high leverage which might be because it has an unusual grade, GRADE, for a slabbed coin (iii) the observation with the largest absolute residual is an outlier in the residual space and this is due to an extremely high sale price which might relate to the unusually high price for gold at the time of the sale (iv) the value for the largest absolute residual is not an outlier and the largest value for Cook’s Distance does not qualify as being influential.
[ Select ] [“(i)”, “(iii)”, “(ii)”, “(iv)”] .
j) Remove the observations or observation from part (i) that had the largest absolute residual and the largest Cook’s Distance. If those are the same observation then remove only one observation. If they are different then remove them both, i.e., two observations. With this smaller dataset (which also has other=”ME” removed from before) regress SALE on GOLDPRICE, BIDS, SHIPPING and a set of dummy variables for the values of other. The estimated coefficient on GOLDPRICE is [ Select ] [“2.5083”, “1.5076”, “2.1763”, “1.763”, “2.0756”] .
k) Using the most recent model, from part (j), test the hypothesis that the coefficient on GOLDPRICE is 1. The t test statistic for this test is
[ Select ] [“1.232”, “1.733”, “0.833”, “1.497”] .
l) Examine the model results, from part (j). Based on these results, if you were auctioning off a gold coin to maximize your revenue, would you rather offer free shipping or would you rather charge $7.5 for shipping?
[ Select ] [“Offer free shipping.”, “It doesn’t appear to matter.”, “Charge $7.5 for shipping.”] .
m) Again, using the model from part (j), test whether the errors have constant variance using the test covered in the lectures. What is the p-value?