1. Regression
Analysis, Modeling, and its
interpretation
FGS Chapter 3

2. Regression analysis and modeling
• Models are mathematical descriptions of the
crucial features of the relationships.
• We can use model for both assessing the
relationship and prediction.
• Regression analysis allows the econometrician
to fit a straight line through a set of data
points

3. Modeling

4. wage
1
Years of educ

5. Modeling
4. Obtaining the data
The goals of the econometric modeling are
 to estimate the parameters in the model
 to test the hypothesis about these parameters
from the data we have.
5. Estimation of the econometric model
by the statistical technique of regression analysis
 Methods of moments
 Maximum likelihood function
 Ordinary least squares **

6. Ordinary least squares
wage
x
x
R1
x x
x
x x x
x x
x x u
x
x x x R2
x x
x xu x x
x x
x x x
x x
x x
x
x R3
Years of educ
1. Deviations from the line must sum to zero
2. The sum of squared deviations of the actual data points from the
line is minimized

7. Modeling
6. Hypothesis testing
A suitable criteria to find out whether the estimates obtain in
from the previous step are not a chance occurrence or
peculiarity of the particular data we have used.
7. Forecasting or Prediction
6. Use of the model for control or policy
purpose

8. Interpreting Regression Coefficients
Table 3-1 Excise Taxed and Cigarette Demand
Simple Multiple
Variable Coefficient Standard t-stat Coefficient Standard t-stat
error error
Intercept 16.83 0.19 86.78 17.22 0.63 27.34
Excise Tax -3.24 0.34 -9.42 -2.28 0.33 -6.96
Income -0.0020 0.0025 -0.80
($ x 1000)
Male 2.23 0.21 10.68
African -5.05 0.34 -15.04
American(AA)
Hispanic -6.50 0.37 -17.55
Age 0.13 0.01 19.11
Education -0.67 0.05 -12.42
level
0.0092 0.1132
Elasticity -0.0989 -0.0697
N 9555 9555

9. Interpreting Regression Coefficients

10. Interpreting Regression Coefficients

11. Estimating elasticities

12. Functional forms

13. Dummy Variable

14. Example
• Helmchen, LA., Lo Sasso, AT. (2009) How sensitive is
physician performance to alternative compensation
schedules? Evidence from a large network of primary
care clinics.
• study how physicians at a network of primary care
clinics responded when their salaried compensation
plan was replaced with a lower salary plus
substantial piece rates for encounters and select
procedures