An antiques dealer is interested in factors that might influence the final selli
ID: 3369423 • 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.
SUMMARY OUTPUT
ANOVA
What would the conclusion be, in the context of the problem, of the full model F test at the 0.05 level of significance?
a) Fail to reject the alternative hypothesis. We conclude that Age = Bidders.
b) Reject the null hypothesis and conclude that the beta coefficients for both Age and Bidders are not equal to 0.
c) Fail to reject the null hypothesis. We conclude that Age, Bidders, and sale price are independent.
d) 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).
e) Fail to reject the null hypothesis. We cannot conclude that any of the coefficients are not equal to 0.
f) 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).
Regression Statistics Multiple R 0.944834723 R Square 0.892712653 Adjusted R Square 0.885313526 Standard Error 133.1365018 Observations 32Explanation / Answer
We know that t-statistics and their associated 2 tailed p values is used in testing whether a given coefficient is significantly different from zero.
If p value is smaller than alpha level(i.e. 0.05),then we reject the null Hypothesis and conclude that the coefficient for predictor variable is significantly different from zero.
Here, p value for intercept, age and bidders are smaller than alpha level 0.05. So we reject the null hypothesis and conclude that the coefficients for age, biddersand the intercept term are not equal to 0(i.e. All beta terms are not equal to 0)
Hence f) is correct.