Question

Consider the following ANOVA table, and do the necessary calculations:

Factor	SS	DF	MS	F-value	p-value
A	20.167	1		9.8108	0.005758
B		2	100.167		0.000000
AxB			8.167		0.037224
Error		18
Total	273.833	23

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1)The Residual Mean Squares is:
Select one:

a. It cannot be calculated

b. 2.056

c. 11.906

d. 128.500

2)

What is the approximate r² value of this ANOVA?

Select one:

a. It cannot be calculated

b. 86.5%

c. 13.5%

d. 98.4%

3)

Which of the following is true for the ANOVA table below:

Select one:

a. Factor A and Factor B have a high probability of a Type I error

b. The main effects are significant and act independently

c. The relatively high Total SS indicates that there is much unexplained variance in the model

d. Factor A and Factor B may produce a synergistic effect on the response variable

4)the F-value of the Interaction Term is:

Select one:

a. 3.973

b. 4.8

c. 0.037

5)

One factor accounts for most of the treatment effect in the model. What proportion of the model variance does it account for?

Select one:

a. 0.767

b. It cannot be determined

c. 0.178

d. 0.732

d. 48.730

Answer 1

ANOVA
Source of Variation	SS	df	MS	F	P-value
Factor A	20.167	1	20.167	9.8108	0.0058
Factor B	100.167*2 = 200.334	2	100.167	48.7194	0.0000
Interaction	8.167*2 = 16.334	23-18-1-2 = 2	8.167	3.9723	0.0372
Error	36.998	18	2.056
Total	273.833	23

1)

SSE = SST-SSA-SSB-SSAB = 36.998

Residual Mean Squares = 2.056

Answer b.

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2) r^2 = 1-SSE/SST = 1-36.998/273.833 = 86.5%

Answer b.

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3. Answer: a. Factor A and Factor B have a high probability of a Type I error

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4) F-value of the Interaction Term:

F = 3.973

Answer a. 3.973