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MULTIPLE CLASSICAL LINEAR REGRESSION MODEL: SPECIFICATION
I. MCLRM as an extension of the SCLRM
II. Advantages
a. Control confounding variables
b. Analyze effect of two or more explanatory variables
c. Make better predictions
III. Variables
a. Variables of interest
b. Control variables
IV. Functional form
a. Functional form is linear
b. Interpretation of parameters
c. Elasticity measures
d. Prediction
V. Error term
a. Assumptions
1. Error term has mean zero
2. Error term is not correlated with the explanatory variables
3. Error term has constant variance
4. Errors are independent
5. Error term has a normal distribution
MULTIPLE CLASSICAL LINEAR REGRESSION MODEL: ESTIMATION
I. Ordinary least squares (OLS) estimator for regression coefficients
a. Rule
b. Residual sum of squares function
c. Deriving the OLS estimator
d. Properties of the OLS estimator
1. Sampling distribution
a. Form
b. Mean
c. Variance
d. Standard deviation (error)
e. Variance-covariance matrix
2. Small sample properties
3. Large sample property
4. Conclusions
II. Other estimators
a. Estimator for elasticity
b. Estimator for error variance
c. Estimator for standard error of estimate of marginal effect
d. Estimator for standard error of estimate of elasticity
III. Interval estimate
MULTIPLE CLASSICAL LINEAR REGRESSION MODEL: HYPOTHESIS TESTING
I. Different types of hypotheses
a. Hypothesis about the value of an individual parameter (fixed value restriction)
b. Joint hypothesis about the values of two or more individual parameters
(joint fixed value restriction)
c. One or more linear hypotheses (linear restriction)
d. One or more nonlinear hypotheses (nonlinear restriction)
II. Hypothesis about the value of an individual parameter
a. t-test
III. Joint and linear hypotheses
a. F-test
b. F-statistic
1. Unrestricted model
2. Restricted model
c. Calculating the F-statistic
1. Manual approach
2. Restrict command approach
3. Test command approach
d. Examples
1. Education and experience have no joint effect on the wage
2. Education, experience, and gender have no joint effect on the wage
3. Marginal effects of education is equal to the marginal effect of experience
4. Sum of marginal effect of education and experience is 2
MULTIPLE CLASSICAL LINEAR REGRESSION MODEL: HYPOTHESIS PREDICTION AND
GOODNESS OF FIT
I. Prediction
II. Measures of goodness of fit
a. Standard error of the regression
b. R2 statistic
c. Adjusted R2 statistic
1. Relationship between adjusted R2 statistic and t-statistic