Successfully reported this slideshow.
Upcoming SlideShare
×

# Quantitative Methods for Lawyers - Class #22 - Regression Analysis - Part 1

1,849 views

Published on

Quantitative Methods for Lawyers - Class #22 - Regression Analysis - Part 1

• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

### Quantitative Methods for Lawyers - Class #22 - Regression Analysis - Part 1

1. 1. Quantitative Methods for Lawyers Class #18 Regression Analysis Part 1 @ computational computationallegalstudies.com professor daniel martin katz danielmartinkatz.com lexpredict.com slideshare.net/DanielKatz
2. 2. Here is an App that Predicts the Price Per Hour of Various Lawyers City Firm Size Partner Experience Calculate Regression Analysis in Legal Procurement http://tymetrix.com/mobile_apps/
3. 3. Here is an App that Predicts the Price Per Hour of Various Lawyers City Firm Size Partner Experience Expected Hourly Rate Regression Analysis in Legal Procurement http://tymetrix.com/mobile_apps/ Our Dependent Variable (i.e. Y) Our Independent Variables (i.e. X1 ... Xn)
4. 4. Estimate a lawyer’s rate: Real Rate Report™ Regression model From the CT TyMetrix/Corporate Executive Board 2012 Real Rate Report© \$15 1 \$16 1 \$34 per 10 years\$95 +\$99 (Finance) -\$15 (Litigation) n = 15,353 Lawyers Tier 1 Market Experience Partner Status Practice Area Base + + +/- Source: 2012 Real Rate Report™ 32 \$15 Per 100 Lawyers Law Firm Size+ + \$161 \$151 \$15 per 100 lawyers \$95 \$34 per 10 years -\$15 (Litigation) +\$99 (Finance)
5. 5. Y = βo +/- β1 ( X1 ) +/- β2 ( X2 ) +/- β3 ( X3 ) +/- β4 ( X3 ) +/- β5 ( X3 ) + ε Y = \$151 + \$15 ( ) + 161 ( ) + 95 ( ) + 34 ( ) +/- β5 ( ) + ε Per 100 Lawyers If Tier 1 Market is True Partner Status is True Per 10 Years Practice Area
6. 6. Multiple Regression Example
7. 7. Multiple Regression Analysis https://s3.amazonaws.com/KatzCloud/elemapi.dta Load This Data Set from Stata into R
8. 8. Multiple Regression Analysis https://s3.amazonaws.com/KatzCloud/elemapi.dta Load This Data Set from Stata into R We Need to Understand these Variables:
9. 9. Multiple Regression Analysis Okay Lets Get the Variable Labels from Stata into R
10. 10. Here are the measures: academic performance of the school (api00), average class size in kindergarten through 3rd grade (acs_k3) percentage of students receiving free meals (meals) - which is an indicator of poverty percentage of teachers who have full teaching credentials (full) Multiple Regression Analysis regression analysis using the variables api00 as the Y Dependent Variable acs_k3, meals, full X Independent Variable
11. 11. Regression Analysis using the variables Y = α +/- β1 ( X1 ) +/- β2 ( X2 ) +/- β3 ( X3 ) + ε api00 = β0 - β1 ( acs_k3 ) - β2 ( meals ) + β3 ( full ) + ε Multiple Regression Analysis
12. 12. Regression Analysis using the variables Y = α +/- β1 ( X1 ) +/- β2 ( X2 ) +/- β3 ( X3 ) + ε api00 = β0 - β1 ( acs_k3 ) - β2 ( meals ) + β3 ( full ) + ε Multiple Regression Analysis Some Hypotheses -- We might expect that better academic performance would be associated with ( - ) higher class size ( - ) fewer students receiving free meals ( + ) higher percentage of teachers having full teaching credentials
13. 13. api00 = β0 - β1 ( acs_k3 ) - β2 ( meals ) + β3 ( full ) + ε
14. 14. api00 = 906.7 - 2.68 ( acs_k3 ) - 3.70 ( meals ) + .108 ( full ) + ε
15. 15. the three predictors - are they statistically signiﬁcant and what is the direction of the relationship? The average class size (acs_k3, b=-2.68), is not signiﬁcant (p=0.055), but only just so. The coefﬁcient is negative which would indicate that larger class size is related to lower academic performance -- which is what we would expect.
16. 16. Effect of meals (b=-3.70, p=.000) is signiﬁcant and its coefﬁcient is negative indicating that the greater the proportion students receiving free meals, the lower the academic performance.  The meals variable is highly related to income level and functions more as a proxy for poverty. Thus, higher levels of poverty are associated with lower academic performance. This result also makes sense.
17. 17. Finally, the percentage of teachers with full credentials (full, b=0.11, p=.232) seems to be unrelated to academic performance. This would seem to indicate that the percentage of teachers with full credentials is not an important factor in predicting academic performance -- this result was somewhat unexpected.
18. 18. More On Regression Analysis
19. 19. “We use regression to estimate the unknown effect of changing one variable over another regression requires making two assumptions: 1) there is a linear relationship between two variables (i.e. X and Y) 2) this relationship is additive (i.e. Y= X1 + X2 + ...+ Xn) (Note: Additivity applies across terms - as within terms there can be a square, log, etc.) Technically, linear regression estimates how much Y changes when X changes one unit.” http://dss.princeton.edu/training/ Regression Analysis
20. 20. Example: After controlling by other factors, are SAT scores higher in states that spend more money on education?* Outcome (Y) variable = SAT scores --> variable csat in dataset Predictor (X) variables • Per Pupil Expenditures Primary & Secondary (expense) • % HS of graduates taking SAT (percent) • Median Household Income (income) • % adults with HS Diploma (high) • % adults with College Degree (college) • Region (region) Regression Analysis *Source: search for dataset at http://www.duxbury.com/highered/ Use the ﬁle states.dta (educational data for the U.S.).