XR19-49 An auctioneer of antique and semiantique Persian rugs kept records of his weekly auctions in

XR19-49 An auctioneer of antique and
semiantique Persian rugs kept records of his weekly auctions in order to
determine the relationships among price, age of rug, number of people attending
the auction, and number of times the winning bidder had previously attended his
auctions. He felt that with this information, he could plan his auctions
better, serve his steady customers better and make a higher profit overall for
himself. Part of the data are shown in the table at right. Use the Excel
package to estimate the model,

      y = _0 + _1x1
+ _2x2 + _3x3 + _

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XR19-49 An auctioneer of antique and
semiantique Persian rugs kept records of his weekly auctions in order to
determine the relationships among price, age of rug, number of people attending
the auction, and number of times the winning bidder had previously attended his
auctions. He felt that with this information, he could plan his auctions
better, serve his steady customers better and make a higher profit overall for
himself. Part of the data are shown in the table at right. Use the Excel
package to estimate the model,

      y = _0 + _1x1
+ _2x2 + _3x3 + _

a Do the signs of the coefficients conform
to what you expected?

b Do the results allow us to conclude at
the 5% significance level that price is linearly related to each of age,
audience size and previous attendance?

c What proportion of the variation in y is
explained by the independent variables?

d Test the utility of the overall
regression model, with _ = 0.05.

e What price would you forecast for a
100-year-old rug, given an audience size of 120 that had on average attended
three of the auctioneer’s auctions before?

f The correlation matrix is

What (if anything) do the correlations tell
you about your original answers in (a)–(e)?

g Check to determine whether the error
variable is normally distributed.

h Check to determine whether 2 _
_ is fixed.

i Check whether the errors are independent.

j How do your answers in (g)–(i) affect
your answers in (a)–(e)?

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