UCSB ECON 240a - Analysis of Variance (50 pages)

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Analysis of Variance



Previewing pages 1, 2, 3, 24, 25, 26, 27, 48, 49, 50 of actual document.

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Analysis of Variance

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Pages:
50
School:
University of California, Santa Barbara
Course:
Econ 240a - Intro Econometrics
Intro Econometrics Documents

Unformatted text preview:

1 Power Fifteen Analysis of Variance ANOVA Analysis of Variance One Way ANOVA Tabular Regression Two Way ANOVA Tabular Regression 2 One Way ANOVA Apple Juice Concentrate Example Data File xm 15 01 New product Try 3 different advertising strategies one in each of three cities City 1 convenience of use City 2 quality of product City 3 price Record Weekly Sales 3 Advertising Strategies Weekly Sales for 20 Weeks Convenience Quality Price 529 804 672 658 630 531 793 774 443 614 624 532 Mean 577 5 Mean 653 0 Mean 608 65 4 Is There a Significant Difference in Average Sales Figure 1 Mean Apple Juice Sales By Advertising Strategy 660 640 620 600 580 560 540 520 convenience quality price A dvertising Strategy Null Hypothesis H0 2 Alternative Hypothesis 1 2 1 3 2 3 5 Table Way ANOVA of Apple Juice Sales By Advertising Strategy Source of Variation Sum of Squares k Explained between ESS n j x j 1 Degrees of Mean Freedom Square x 2 k ESS k xij x j 2 n k USS n k xij x 2 n j treatments k Unexplained withi n USS j n j i treatments k Total TSS j n j i Fk 1 n k ESS k 1 USS n k 6 Apple Juice Concentrate ANOVA Source of Variation Explained Between Treatments Unexplained Within Treatments Total Sum of Degrees of Squares Freedom ESS k 1 2 57 512 23 Mean Square ESS k 1 28 756 12 USS 506 984 n k 57 USS n k 8894 45 TSS 564 496 n 1 59 F2 57 28 756 12 8894 45 3 23 7 F Distribution Test of the Null Hypothesis of No Difference in Mean Sales with Advertising Strategy Figure 2 F D istribution Density For 2 DOF 57 DOF 1 0 DENSITY 0 8 0 6 F2 60 critical 5 3 15 0 4 0 2 0 0 0 2 4 6 8 10 F Variable 8 One Way ANOVA and Regression 9 Regression Set Up y 1 is column of 20 sales observations For city 1 1 is a column of 20 ones 0 is a column of 20 Zeros Regression of a quantitative variable on three dummies y 1 1 y 2 0 y 3 0 0 0 1 0 0 1 Y C 1 Dummy city 1 C 2 Dummy city 2 C 3 Dummy city 3 e 10 11 One Way ANOVA and Regression Table 5 One Way ANOVA Estimated Using Regression Dependent Variable SALESAJ Method



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