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Chapter 9Chapter 9 An Introduction to An Introduction to

Analysis of VarianceAnalysis of Variance

Terry Dielman Terry Dielman

Applied Regression AnalysisApplied Regression Analysisfor Business and Economicsfor Business and Economics

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POP QUIZ #12 [2.5 points]

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POP QUIZ #12

1. “ANOVA” stands for

A. A type of star in astronomy, similar to SUPERNOVA

B. A “New way” of performing Regression analysis

C. Analysis of Variance

D. Applied Novelty Analysis

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POP QUIZ #122. In the ANOVA model notation yij = µi + eij ,

µi stands for:

A. The i-th residual

B. The mean of group i

C. The i-th slope

D. The i-th predictor variable

E. The standard deviation of group i

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POP QUIZ #12

3. What is the null hypothesis in the one-way ANOVA test for the overall model effect?

A. H0: µ1 = µ2 = ... = µK

B. H0: µ1 = µ2 = ... = µK = 0

C. At least one µi is different

D. All µi are different from each other

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POP QUIZ #12

4. Refer to the car claims example. Based on the Minitab output above, what is the conclusion?A. All car models have different number of claims

B. All car models have the same number of claims

C. Some car models have different average number of claims

D. Some car models have average number of claims equal to 0

Analysis of Variance for INJURIESSource DF SS MS F PCARCLAS 8 54762 6845 22.80 0.000Error 103 30917 300Total 111 85679

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POP QUIZ #12

5. Refer to the computer sales example, where three approaches (1,2,3) were tried. Based on the (partial) Minitab output above,

A. Approach 1 works better than approach 2

B. Approach 2 works better than approach 1

C. Approach 1 works better than approach 3

D. Approach 3 works better than approach 1

Tukey 95% Simultaneous Confidence IntervalsAll Pairwise Comparisons among Levels of APPROACHIndividual confidence level = 97.94%APPROACH = 1 subtracted from:

APPROACH Lower Center Upper ----+---------+---------+---------+-----2 -2.033 6.000 14.033 (-------*-------)3 4.367 12.400 20.433 (-------*-------) ----+---------+---------+---------+----- -10 0 10 20

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Answers!√

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POP QUIZ #12

1. “ANOVA” stands for

A. A type of star in astronomy, similar to SUPERNOVA

B. A “New way” of performing Regression analysis

C. Analysis of Variance

D. Applied Novelty Analysis

√

10

POP QUIZ #122. In the ANOVA model notation yij = µi + eij ,

µi stands for:

A. The i-th residual

B. The mean of group i

C. The i-th slope

D. The i-th predictor variable

E. The standard deviation of group i

√

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POP QUIZ #12

3. What is the null hypothesis in the one-way ANOVA test for the overall model effect?

A. H0: µ1 = µ2 = ... = µK

B. H0: µ1 = µ2 = ... = µK = 0

C. At least one µi is different

D. All µi are different from each other

√

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POP QUIZ #12

4. Refer to the car claims example. Based on the Minitab output above, what is the conclusion?A. All car models have different number of claims

B. All car models have the same number of claims

C. Some car models have different average number of claims

D. Some car models have average number of claims equal to 0

Analysis of Variance for INJURIESSource DF SS MS F PCARCLAS 8 54762 6845 22.80 0.000Error 103 30917 300Total 111 85679

√

13

POP QUIZ #12

5. Refer to the computer sales example, where three approaches (1,2,3) were tried. Based on the (partial) Minitab output above,

A. Approach 1 works better than approach 2

B. Approach 2 works better than approach 1

C. Approach 1 works better than approach 3

D. Approach 3 works better than approach 1

Tukey 95% Simultaneous Confidence IntervalsAll Pairwise Comparisons among Levels of APPROACHIndividual confidence level = 97.94%APPROACH = 1 subtracted from:

APPROACH Lower Center Upper ----+---------+---------+---------+-----2 -2.033 6.000 14.033 (-------*-------)3 4.367 12.400 20.433 (-------*-------) ----+---------+---------+---------+----- -10 0 10 20

√