Question

Please answer Question 17-20 based on the following ANOVA table of Linear Regression (α=0.05):

Source	SS	DF	MS	F	P
A	a	1	9.999	0.504	0.498
B	180.378	b	60.1	3.029	0.093
Interaction	8.479	3		0.142	0.932
Error	158.797	8

17. How many factor levels of factor B are evaluated?

A. 1

B. 2

C. 3

D. 4

E. 16

18. What is the sample size?

A. 1

B. 2

C. 3

D. 4

E. 16

19. what is the missing value of a in the ANOVA table?

A. 4.995

B. 9.999

C. 19.839

D. 20.078

E. None of the above.

20. Given the above results, what is your conclusion?

A. Factor A and B significantly affect the response.

B. Only factor A significantly affects the response.

C. Only factor B significantly affects the response.

D. Future experiment is needed due to the interaction.

E. Neither the interaction nor the factors significantly affect the response.

Answer 1

17) If k and l are the number of levels of factors and b respectively then DF(SSA) = k-1, DF(SSB)=l-1, DF(interaction)=(k-1)(l-1). Given DF(SSA) = 1, thus (k-1)=1 and DF(interaction)=3. Thus (k-1)(l-1)=3 implies than (l-1)=3. Thus the number of levels of B is l=4. Hence answer is (D) 4

18) Sample size = DF(total)+1, here DF(Total)=DF(SSA)+DF(SSB)+DF(interaction)+DF(Error) = 1+3+3+8=15. Thus the sample size 16. Hence answers is E. 16

19) MSA = SSA/DF(SSA) = 9.999, thus SSA= MSA =9.999 as DF(SSA). Hence answer is B. 9.999

20) None of the factors and interaction is significant as the p-value are not significant. Hence the answer is E. Neither the interaction nor the factors significantly affect the response.