Question

Researchers conducted interviews with a sample of 38 people shopping on Black Friday to gauge their shopping habits. The two variables measued for each shopper were age (x) and number of years shopping on Black Friday (y).

a) The researchers wonder if there is a quadratic relationship between age and the number of years shopping on Black Friday. Pick a regression model that incorporates this relationship.
A. E[y] = ?0β0 + ?1?β1x
B. E[y] = ?0β0 + ?1?2β1x2
C. E[y] = ?0β0 + ?1?β1x + ?2?2β2x2
D. E[y] = ?0β0 + ?21β12

Use the predictor table below to answer the following questions.

Coefficients	Estimate	Std. Error	t	p-value
Intercept	-8.933	10.239	-0.872	0.389
age	0.704	0.552	1.275	0.211
age^2	-0.003	0.006	-0.507	0.615

b) Fill in the regression equation with the appropriate estimates from the table above (including any negative signs!).
?̂y^ =  +  ?x +  ?2x2

c) Test if the quadratic term is significant in the model. Perform this test with ?=0.1α=0.1.
Note: use the notation B1 = 0 to represent ?1=0β1=0 and so on. If you need ≠≠ then type B1 /= 0 for ?1≠0β1≠0!
1. ?0H0:  vs ??Ha:  
2. ?α = 0.1
3. t =  
4. Critical t=  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the quadratic term is significant.
There is not sufficient evidence to support that the quadratic term is significant.

Answer 1