An art collector is studying the relationship between the selling price of a pai
ID: 3223024 • Letter: A
Question
An art collector is studying the relationship between the selling price of a painting and two independent variables. The two independent variables are the number of bidders at the particular auction and the age of the painting, in years. A sample of 25 paintings revealed the following sample information.
Develop a multiple regression equation using number of bidders and age of painting as independent variables to estimate the dependent variable auction price. (Round your answers to 2 decimal places.)
Complete the following table: (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
Discuss the equation. Does it surprise you that there is an inverse relationship between the number of bidders and the price of the painting? (Round your answers to 1 decimal place.)
The price decreases by as each additional bidder participates. Meanwhile the price increases by as the painting gets older. While one would expect (Click to select)new paintingsolder paintings to be worth more, it is unexpected that the price goes (Click to select)downup as (Click to select)moreless bidders participate!
Create an interaction variable and include it in the regression equation. (Round your answers to 2 decimal places. Negative answers should be indicated by a minus sign.)
Complete the following table: (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
What is the corresponding t value to the interaction term? (Round your answer to 2 decimal places.)
The t value corresponding to the interaction term is . This is (Click to select)significantnot significant. So
we conclude there is (Click to select)no interactioninteraction.
Use the stepwise method and the independent variables for the number of bidders, the age of the painting, and the interaction between the number of bidders and the age of the painting. Which variables would you select?
The number of (Click to select)interactionbidders enters the equation first. Then the (Click to select)interactionbidders term enters.
Variable age would (Click to select)not bebe included as it is (Click to select)not significantsignificant.
Complete the following table using stepwise method. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
An art collector is studying the relationship between the selling price of a painting and two independent variables. The two independent variables are the number of bidders at the particular auction and the age of the painting, in years. A sample of 25 paintings revealed the following sample information.
Explanation / Answer
The Multiple regression table results are when there is no interaction
Q. 1(a) Price = 3080.053 -54.19 Bidders + 16.29 * Age
Q.1 (b)
Q.1(3) Yes, equation describes negative relationship with number of bidders so it is unusual but may be there is interaction factor involved. and may be more bidders have made crowding effect.
Q.2 (1) The Multiple regression table results are when there is interaction between variables
Q.2 (a)
Price = 3971.68 - 184.99 * Bidders + 6.35 *Age + 1.46 X1X2.
(b)
(c) corresponding t value to the interaction term = 1.15 which has corresponding p - value 0.265 so we can say that there is no interaction.
Q.3 (1) p- value with regression with only no. of bidders = 0.0018
p - value with regression only with age = 0.0023
p - value with regression with age and no. of bidders interaction term = 0.033
as both p - value is less than Alpha to enter significance level, we will choose the no. of bidders first and it will be given first priority in regression model.
(2) Now we will calculate p - value with multiple regression with including no. of bidders and age = 1.03 * 10 -5
p - value with multiple regression with including no. of bidders and the interaction term = 6.71 * 10 -6
so the secodn predictor will be x1x2 orthe interaction term.
so the given table is
SUMMARY OUTPUT Regression Statistics Multiple R 0.8049 R Square 0.6478 Adjusted R Square 0.6158 Standard Error 222.0679 Observations 25 ANOVA df SS MS F Significance F Regression 2 1995489 997744.56 20.232 1.03E-05 Residual 22 1084911 49314.13 Total 24 3080400 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3080.05 343.88 8.96 0.00 2366.88 3793.23 2366.88 3793.23 Bidders -54.19 12.28 -4.41 0.00 -79.66 -28.72 -79.66 -28.72 Age 16.29 3.78 4.30 0.00 8.44 24.14 8.44 24.14Related Questions
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