The following table lists a number of properties in a location popular as a vaca

Question

The following table lists a number of properties in a location popular as a vacation spot that have sold at auction.

1.What factors affect the winning bid?

2.Build a model to predict the winning bid.

3.What is the point prediction for the winning bid for a residential property coming up for auction on July 20, 2011, with an estimated value of $1,500,000?

4.Does this prediction change if there is a lot of interest in the property (that is, many bids are expected)?

5.Does the prediction change if the buyer is expected to be a non-resident?

6.What is the 95% prediction interval for the same property auction?

Date of Sale Winning Estimate d Number of Type of Buyer Bid Value Bids receivedProperty Commercial Nonresident Residential Residential Residential Residential Commercial Nonresident 22-May-10 1,028,885 1,176,800 372,455 427,100 940,0161,090,200 288,703336,700 14u-10 2,166,426 2,445,300 848,100 13-Aug-101,305,550 1,553,500 28-Sep-10 211,412 278,300 385,900 28-Oct-10 2,749,662 3,074,100 12-Nov-10 1,156,4431,284,900 28-Nov-10 1,956,165 2,203,100 -10 348,470 431,300 20-Dec-10 1,530,358 1,735,600 5-n-11 1,883,154 2,105,300 393,344446,100 695,400 27-Feb-11 4,920,658 5,806,700 377,600 472,200 13-Apr 466,776 593,000 892,5311,032,900 14-May-11 1,025,087 1,146,000 629,500 6-jun-10 13-Jun-10 29-Jun-10 Resident Resident ntia Resident Nonresident 6-Aug-10 751,420 ntial Resident ntia Resident Residential Commercia Resident Commercia Nonresident Commercial Nonresident Commercia Rident Residential Commercia Nonresident Residential Commercia Nonresident Commercial Resident Residential Commecia Resident Residential Commercial Resident Commercia Nonresident Commercial Resident 5-Oct-10 331,677 5-Dec-10 ntia Resident Nonresident 20-Jan-11 12-Feb-11 609,573 Resident 6-Mar-11 ntia Resident 29-Apr-11 22-May-11 517,964

Explanation / Answer

Dependent variable is winning bid.

Independent variables are estimated value, number of bids received, type of property and buyer.

Here we have to fit multiple regression.

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : winning bid --> Predictors : estimated value, number of bids received, type of property and buyer --> Results : select second option --> ok --> ok

1.What factors affect the winning bid?

Here we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not=0

where B is population slope for independent variable.

Assume alpha = level of significance = 0.05

Here the test statistic follows t-distribution.

Decision rule :

If P-value < alpha then corresponding variable is significant otherwise the variable is insignificant.

Here we see that estimated value and buyer are significant variables while number of bids received and type of property is insignificant variable.

2.Build a model to predict the winning bid.

Here we have to write regression equation.

The regression equation is
winning bid = 21585 + 0.863 estimated value - 5522 number of bids received
- 6083 type of property + 56231 buyer

Overall significance :

Here we have to test the hypothesis that,

H0 : Bj = 0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Here test statistic follows F-distribution.

F = 6139.73

P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

R-sq = 99.9%

It expresses the proportion of variation in response variable which is explained by variation in independent variables.

3.What is the point prediction for the winning bid for a residential property coming up for auction on July 20, 2011, with an estimated value of $1,500,000?

We have to find winning bid when,

estimated value= 1500000

Type of property = 1

buyer = 0

number of bids received = 0

winning bid = 21585 + 0.863*1500000 - 5522*0 - 6083*1 + 56231*0

= 1310002

5.Does the prediction change if the buyer is expected to be a non-resident?

Buyer = 1

estimated value= 1500000

Type of property = 1

winning bid = 21585 + 0.863*1500000 - 5522*0 - 6083*1 + 56231*1 = 1366233

The prediction will be changed.

6.What is the 95% prediction interval for the same property auction?

Predicted Values for New Observations

New Obs Fit SE Fit 95.0% CI 95.0% PI
1 1365976 39154 ( 1283716, 1448236) ( 1259600, 1472352) XX
X denotes a row with X values away from the center
XX denotes a row with very extreme X values

Values of Predictors for New Observations

New Obs estimate number o type of buyer
1 1500000 0.000000 1.00 1.00

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