Classical Linear Regression Model
Autor: Paul Caluban • July 12, 2015 • Study Guide • 7,410 Words (30 Pages) • 1,119 Views
(Limited Dependent Variable Models)
Classical Linear Regression Model (CLRM)
Requirement: Dependent variable is quantitative within ratio interval
Focus on drivers, regressors, right side, s, dependents[pic 1]
[pic 2]
[pic 3]
= endogenous, dependent[pic 4]
= exogenous, independent, fixed value[pic 5]
= stochastic, error term, random, sablay ng mga s[pic 6][pic 7]
Economic theory will dictate which to choose[pic 8]
Direction of causality is always towards [pic 9]
In matrix form:
[pic 10]
[pic 11]
Objectives:
Find s (problem of estimation)[pic 12]
Perform inferences on s (problem of inference)[pic 13]
Individual tests
vs [pic 14][pic 15][pic 16]
Joint test
vs at least 1 is not zero[pic 17][pic 18][pic 19]
100 % on (construction of confidence interval)[pic 20][pic 21]
[pic 22][pic 23]
Goodness of fit
if is 0.9, 90% of variation explains [pic 24][pic 25][pic 26]
[pic 27]
(population regression function (PRF))[pic 28]
(sample regression function (SRF))[pic 29]
marginal contribution independent of ceteris paribus[pic 30][pic 31]
for every unit change in , will change by ceteris paribus[pic 32][pic 33][pic 34][pic 35]
Assumptions:
is MVN (multivariant normal) error is normally distributed[pic 36]
error vanishes in the long run[pic 37]
heteroskedasticity[pic 38]
Non-correlation
exogeneity assumption[pic 39]
has full rank non-multicollinearity[pic 40][pic 41]
Gauss-Markov Theorem
If assumptions above are true, OLS is BLUE
Binary Response Models ( is dummy; 0,1 failure-success basis)[pic 42]
Linear Probability Model (LPM) (OLS)
Logit Model (Logistical link)
Probit Model (Standard normal link)
Multinomial Response Model ( is multinomial, 3 or more)[pic 43]
Multinomial Logit Model
Multinomial Probit Model
...