LOS i, (Part 1): Describe the use of analysis of variance (ANOVA) in regression analysis.
1．nsider the following analysis of variance (ANOVA) table:
Source | Sum of squares | Degrees of freedom | Mean square |
Regression | 500 | 1 | 500 |
Error | 750 | 50 | 15 |
Total | 1,250 | 51 | |
The R2 and the F-statistic are, respectively:
A) R2 = 0.40 and F = 33.333.
B) R2 = 0.67 and F = 0.971.
C) R2 = 0.40 and F = 0.971.
D) R2 = 0.67 and F = 33.333.
2．nsider the following analysis of variance (ANOVA) table:
Source | Sum of squares | Degrees of freedom | Mean square |
Regression | 200 | 1 | 200 |
Error | 400 | 40 | 10 |
Total | 600 | 41 | |
The R2 and the F-statistic are, respectively:
A) R2 = 50% and F = 2.0.
B) R2 = 33% and F = 20.0.
C) R2 = 50% and F = 0.952.
D) R2 = 33% and F = 2.0.
LOS i, (Part 1): Describe the use of analysis of variance (ANOVA) in regression analysis.
1．nsider the following analysis of variance (ANOVA) table:
Source | Sum of squares | Degrees of freedom | Mean square |
Regression | 500 | 1 | 500 |
Error | 750 | 50 | 15 |
Total | 1,250 | 51 | |
The R2 and the F-statistic are, respectively:
A) R2 = 0.40 and F = 33.333.
B) R2 = 0.67 and F = 0.971.
C) R2 = 0.40 and F = 0.971.
D) R2 = 0.67 and F = 33.333.
The correct answer was A)
R2 = 500 / 1,250 = 0.40. The F-statistic is 500 / 15 = 33.33.
2．nsider the following analysis of variance (ANOVA) table:
Source | Sum of squares | Degrees of freedom | Mean square |
Regression | 200 | 1 | 200 |
Error | 400 | 40 | 10 |
Total | 600 | 41 | |
The R2 and the F-statistic are, respectively:
A) R2 = 50% and F = 2.0.
B) R2 = 33% and F = 20.0.
C) R2 = 50% and F = 0.952.
D) R2 = 33% and F = 2.0.
The correct answer was B)
R2 = 200 / 600 = 0.333. The F-statistic is 200 / 10 = 20.
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