An antiques dealer is interested in factors that might influence the final selli
ID: 3369533 • Letter: A
Question
An antiques dealer is interested in factors that might influence the final selling price of grandfather clocks at auction. Her data (from 32 previously auctioned clocks) includes the age of the clock (Age), the number of bidders (Bidders) at the auction, and the final selling price (Y) of the clocks.
What would the conclusion be, in the context of the problem, of the full model F test at the 0.05 level of significance?
Fail to reject the null hypothesis. We conclude that Age, Bidders, and sale price are independent.
Fail to reject the null hypothesis. We cannot conclude that any of the coefficients are not equal to 0.
Reject the null hypothesis and conclude that the coefficients for Age, Bidders, and the intercept term are not equal to 0 (i.e., all beta terms are not equal to 0).
Reject the null hypothesis and conclude that the beta coefficients for either Age, or Bidders, or both are not equal to 0 (i.e., at least one coefficient is not equal to 0).
Fail to reject the alternative hypothesis. We conclude that Age = Bidders.
Reject the null hypothesis and conclude that the beta coefficients for both Age and Bidders are not equal to 0.
Fail to reject the null hypothesis. We conclude that Age, Bidders, and sale price are independent.
Fail to reject the null hypothesis. We cannot conclude that any of the coefficients are not equal to 0.
Reject the null hypothesis and conclude that the coefficients for Age, Bidders, and the intercept term are not equal to 0 (i.e., all beta terms are not equal to 0).
Reject the null hypothesis and conclude that the beta coefficients for either Age, or Bidders, or both are not equal to 0 (i.e., at least one coefficient is not equal to 0).
Fail to reject the alternative hypothesis. We conclude that Age = Bidders.
Reject the null hypothesis and conclude that the beta coefficients for both Age and Bidders are not equal to 0.
Explanation / Answer
Solution
Reject the null hypothesis. Conclude that both beta terms are not equal to 0, implying that both Age and Bidders are potentially useful for predicting price.