Chapter 9 An Introduction to Analysis of Variance

1. Chapter 9 An Introduction to Analysis of Variance Terry Dielman Applied Regression Analysis for Business and Economics

2. POP QUIZ #12 [2.5 points]

3. POP QUIZ #12 1. “ANOVA” stands for • A type of star in astronomy, similar to SUPERNOVA • A “New way” of performing Regression analysis • Analysis of Variance • Applied Novelty Analysis

4. POP QUIZ #12 • In the ANOVA model notation yij = µi + eij , µistands for: • The i-th residual • The mean of group i • The i-th slope • The i-th predictor variable • The standard deviation of group i

5. POP QUIZ #12 3. What is the null hypothesis in the one-way ANOVA test for the overall model effect? • H0: µ1 = µ2 = ... = µK • H0: µ1 = µ2 = ... = µK = 0 • At least one µiis different • All µiare different from each other

6. POP QUIZ #12 Analysis of Variance for INJURIES Source DF SS MS F P CARCLAS 8 54762 6845 22.80 0.000 Error 103 30917 300 Total 111 85679 4. Refer to the car claims example. Based on the Minitab output above, what is the conclusion? • All car models have different number of claims • All car models have the same number of claims • Some car models have different average number of claims • Some car models have average number of claims equal to 0

7. POP QUIZ #12 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of APPROACH Individual 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 • Refer to the computer sales example, where three approaches (1,2,3) were tried. Based on the (partial) Minitab output above, • Approach 1 works better than approach 2 • Approach 2 works better than approach 1 • Approach 1 works better than approach 3 • Approach 3 works better than approach 1

8. Answers! √

9. POP QUIZ #12 1. “ANOVA” stands for • A type of star in astronomy, similar to SUPERNOVA • A “New way” of performing Regression analysis • Analysis of Variance • Applied Novelty Analysis √

10. POP QUIZ #12 • In the ANOVA model notation yij = µi + eij , µistands for: • The i-th residual • The mean of group i • The i-th slope • The i-th predictor variable • The standard deviation of group i √

11. POP QUIZ #12 3. What is the null hypothesis in the one-way ANOVA test for the overall model effect? • H0: µ1 = µ2 = ... = µK • H0: µ1 = µ2 = ... = µK = 0 • At least one µiis different • All µiare different from each other √

12. POP QUIZ #12 Analysis of Variance for INJURIES Source DF SS MS F P CARCLAS 8 54762 6845 22.80 0.000 Error 103 30917 300 Total 111 85679 4. Refer to the car claims example. Based on the Minitab output above, what is the conclusion? • All car models have different number of claims • All car models have the same number of claims • Some car models have different average number of claims • Some car models have average number of claims equal to 0 √

13. POP QUIZ #12 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of APPROACH Individual 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 • Refer to the computer sales example, where three approaches (1,2,3) were tried. Based on the (partial) Minitab output above, • Approach 1 works better than approach 2 • Approach 2 works better than approach 1 • Approach 1 works better than approach 3 • Approach 3 works better than approach 1 √