Question

An auctioneer of antique grandfather clocks knows that the price received for a clock increases with the clock's age and with the number of bidders. The following model is proposed for predicting the price of an antique grandfather clock from its age and the number of bidders at an auction Pricei = β0 + β1 (Age of clocki) + β2 (Number of biddersi) where the deviations εi were assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Source Sum of squares df Model 4,277,160 2 Error 514,034 29 Variable Parameter estimate Standard error of parameter estimate Constant –1336.72 173.36 Age of clock 12.73 0.90 Number of bidders 85.82 8.71 The auctioneer also ran the multiple regression model with a term for the interaction between age of clock and number of bidders. The model is Pricei = β0 + β1 (Age of clocki) + β2 (Number of biddersi) + β3 (Age of clocki)(Number of biddersi) where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Source Sum of squares df Model 4,572,548 3 Error 218,646 28 Variable Parameter estimate Standard error of parameter estimate Constant 322.75 293.33 Age of clock 0.87 2.02 Number of bidders –93.41 29.71 (Age of clock)(Number of bidders) 1.30 0.21 Which statement is CORRECT with respect to comparing the two models above? Adding the interaction term increases R2 and decreases s, the estimate of σ. Adding the interaction term decreases R2 and increases s, the estimate of σ. Adding the interaction term decreases R2 and decreases s, the estimate of σ. None of the above

Answer 1

it is clear that the standard error for age and number of bidder are 0.90 and 8.71

and after the addition of interaction term, the standard error for age and number of bidders are 2.02 and 29.71

So, it is clear that the standard error is increased after the addition of interaction term

When standard error is increased, then this means that the R squared must be decreased after the addition of interaction term

therefore, R square is decreased and standard error is increased

option B is correct