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Power 16

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Projects

3

Logistics

• Put power point slide show on a high density floppy disk for a WINTEL machine.

• Email Llad@econ.ucsb.edu the slide-show as a PowerPoint attachment

4

Assignments

• 1. Project choice

• 2. Data Retrieval

• 3. Statistical Analysis

• 4. PowerPoint Presentation

• 5. Executive Summary

• 6. Technical Appendix

Power_12

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PowerPoint Presentations: Member 4• 1. Introduction: Members 1 ,2 , 3

– What– Why– How

• 2. Executive Summary: Member 5

• 3. Exploratory Data Analysis: Member 3

• 4. Descriptive Statistics: Member 3

• 5. Statistical Analysis: Member 3

• 6. Conclusions: Members 3 & 5

• 7. Technical Appendix: Table of Contents, Member 6

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Executive Summary and Technical Appendix

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I. Your report should have an executive summary of one to one

and a half pages that summarizes your findings in words for a non-

technical reader. It should explain the problem being examined

from an economic perspective, i.e. it should motivate interest in the

issue on the part of the reader. Your report should explain how you

are investigating the issue, in simple language. It should explain

why you are approaching the problem in this particular fashion.

Your executive report should explain the economic importance of

your findings.

The technical details of your findings you can attach as an

appendix.

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Technical Appendix• Table of Contents

• Spreadsheet of data used and sources or if extensive, a subsample of the data

• Descriptive Statistics and Histograms for the variables in the study

• If time series data, a plot of each variable against time

• If relevant, plot of the dependent Vs. each of the explanatory variables

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Technical Appendix (Cont.)

• Statistical Results, for example regression

• Plot of the actual, fitted and error and other diagnostics

• Brief summary of the conclusions, meanings drawn from the exploratory, descriptive, and statistical analysis.

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Slide Show

• Challenger disaster

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Challenger Disaster• Failure of O-rings that sealed grooves on

the booster rockets

• Was there any relationship between o-ring failure and temperature?

• Engineers knew that the rubber o-rings hardened and were less flexible at low temperatures

• But was ther launch dat that showed a problem

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Challenger Disaster

• What: Was ther a relationship between launch temperature and o-ring failure prior to the Challenger disaster?

• Why: Should the launch have proceeded?

• How: Analyze the relationship between launch temperature and o-ring failure

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Launches Before Challenger

• Data– number of o-rings that failed– launch temperature

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o-rings temperature3 531 571 581 630 660 670 670 670 680 691 70

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o-rings temperature1 700 700 700 720 732 750 750 760 760 780 79

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o-rings temperature

0 80

0 81

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Exploratory Analysis

• Launches where there was a problem

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1 581 571 701 631 702 753 53

Orings temperature

0.5

1.0

1.5

2.0

2.5

3.0

3.5

50 55 60 65 70 75 80

TEMP

OR

ING

S

0

1

2

3

4

50 60 70 80 90

TEMP

OR

ING

S

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Outline

• ANOVA and Regression

• Non-Parametric Statistics

• Goodman Log-Linear Model

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Anova and Regression: One-Way

• Salesaj = c(1)*convenience+c(2)*quality+c(3)*price+ e

• E[salesaj/(convenience=1, quality=0, price=0)] =c(1) = mean for city(1)– c(1) = mean for city(1) (convenience)– c(2) = mean for city(2) (quality)– c(3) = mean for city(3) (price)– Test the null hypothesis that the means are equal

using a Wald test: c(1) = c(2) = c(3)

Table 5: One-Way ANOVA Estimated Using RegressionDependent Variable: SALESAJMethod: Least Squares

Sample: 1 60Included observations: 60

Variable Coefficient Std. Error t-Statistic Prob.

CONVENIENCE 577.5500 21.08844 27.38704 0.0000QUALITY 653.0000 21.08844 30.96483 0.0000

PRICE 608.6500 21.08844 28.86178 0.0000

R-squared 0.101882 Mean dependent var 613.0667Adjusted R-squared

0.070370 S.D. dependent var 97.81474

S.E. of regression 94.31038 Akaike info criterion 11.97977Sum squaredresid

506983.5 Schwarz criterion 12.08448

Log likelihood -356.3930 F-statistic 3.233041Durbin-Watsonstat

1.525930 Prob(F-statistic) 0.046773

One-Way ANOVA and Regression

Regression Coefficients are the City Means; F statistic

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Anova and Regression: One-WayAlternative Specification

• Salesaj = c(1) + c(2)*convenience+c(3)*quality+e

• E[Salesaj/(convenience=0, quality=0)] = c(1) = mean for city(3) (price, the omitted one)

• E[Salesaj/(convenience=1, quality=0)] = c(1) + c(2) = mean for city(1) (convenience)– c(1) = mean for city(3), the omitted city– c(2) = mean for city(1) minus mean for city(3)– Test that the mean for city(1) = mean for city(3)– Using the t-statistic for c(2)

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Anova and Regression: One-WayAlternative Specification

• Salesaj = c(1) + c(2)*convenience+c(3)*price+e

• E[Salesaj/(convenience=0, price=0)] = c(1) = mean for city(2) (quality, the omitted one)

• E[Salesaj/(convenience=1, price=0)] = c(1) + c(2) = mean for city(1) (convenience)– c(1) = mean for city(2), the omitted city– c(2) = mean for city(1) minus mean for city(2)– Test that the mean for city(1) = mean for city(2)– Using the t-statistic for c(2)

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ANOVA and Regression: Two-WaySeries of Regressions; Compare to

Table 11, Lecture 15• Salesaj = c(1) + c(2)*convenience + c(3)*

quality + c(4)*television + c(5)*convenience*television + c(6)*quality*television + e, SSR=501,136.7

• Salesaj = c(1) + c(2)*convenience + c(3)* quality + c(4)*television + e, SSR=502,746.3

• Test for interaction effect: F2, 54 = [(502746.3-501136.7)/2]/(501136.7/54) = (1609.6/2)/9280.3 = 0.09

Table 11: 2-Way ANOVA of Apple Juice Sales

Source of Variation Sum of Squares Degrees of

Freedom

Mean Square

Explained(between

treatments)

ESS =

Strategy ESS(Strat) = 98838.6 (a-1) = 2 49419.3

Medium ESS(Med) = 13172.0 (b-1) = 1 13172.0

Interaction ESS(I) = 1609.6 (a-1)(b-1) = 2 804.8

Unexplained(within

treatments)

USS = 501136.7 (n-ab) = 60 – 6

= 54

9280.3

Total TSS = 614756.98 (n-1) = 59

Table of Two-Way ANOVA for Apple Juice Sales

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ANOVA and Regression: Two-WaySeries of Regressions

• Salesaj = c(1) + c(2)*convenience + c(3)* quality + e, SSR=515,918.3

• Test for media effect: F1, 54 = [(515918.3-502746.3)/1]/(501136.7/54) = 13172/9280.3 = 1.42

• Salesaj = c(1) +e, SSR = 614757

• Test for strategy effect: F2, 54 = [(614757-515918.3)/2]/(501136.7/54) = (98838.7/2)/(9280.3) = 5.32

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Nonparametric Statistics

• What to do when the sample of observations is not distributed normally

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3 Nonparametric Techniques

• Wilcoxon Rank Sum Test for independent samples– Data Analysis Plus

• Signs Test for Matched Pairs: Rated Data– Eviews, Descriptive Statistics

• Wilcoxon Signed Rank Sum Test for Matched Pairs: Quantitative Data– Eviews

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Wilcoxon Rank Sum Test for Independent Samples

• Testing the difference between the means of two populations when they are non-normal

• A New Painkiller Vs. Aspirin, Xm17-02

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Rating scheme

Score Legend

5 Extremely Effective

4 Quite Effective

3 Somewhat Effective

2 Slightly Effective

1 Not At All Effective

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New Drug Aspirin3 45 14 33 22 45 11 34 45 23 23 25 45 35 4

Ratings

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Rank the 30 Ratings

• 30 total ratings for both samples

• 3 ratings of 1

• 5 ratings of 2

• etc

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Rating Raw Rank Rank/Ties1 1 21 2 21 3 22 4 62 5 62 6 62 7 62 8 63 9 123 10 123 11 123 12 123 13 123 14 12

3 15 12

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Rating Raw Rank Rank/Ties4 16 19.54 17 19.54 18 19.54 19 19.54 20 19.54 21 19.54 22 19.54 23 19.55 24 275 25 275 26 275 27 275 28 275 29 27

5 30 27

continued

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Drug Rate Rank Asp. Rate Rank3 12 4 19.55 27 1 24 19.5 3 123 12 2 62 6 4 19.55 27 1 21 2 3 124 19.5 4 19.55 27 2 63 12 2 63 12 2 65 27 4 19.55 27 3 125 27 4 19.5

4 19.5 5 27

Rank Sum 276.5 188.5

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Rank Sum, T• E (T )= n1 (n1 + n2 + 1)/2 = 15*31/2 = 232.5

• VAR (T) = n1 * n2 (n1 + n2 + 1)/12

• VAR (T) = 15*31/12 , T = 24.1

• For sample sizes larger than 10, T is normal

• Z = [T-E(T)]/ T = (276.5 - 232.5)/24.1 = 1.83

• Null Hypothesis is that the central tendency for the two drugs is the same

• Alternative hypothesis: central tendency for the new drug is greater than for aspirin: 1-tailed test

0.0

0.1

0.2

0.3

0.4

0.5

-4 -2 0 2 4

Z

FR

EQ

UE

NC

Y

Figure 1: One-Tailed Test, 5% Level, Normal Distribution

1.645

5%