Statistics for Economics

6.

Simple Linear Regression Analysis

6.1.

The Simple Linear Regression Model

6.1.1.

Model Specification

6.1.2.

Population Regression Function

6.1.3.

Sample Regression Function

6.1.4.

Dependent and Independent Variables

6.1.5.

Error Term and Disturbances

6.2.

Ordinary Least Squares Estimation

6.2.1.

Principle of Least Squares

6.2.2.

Derivation of OLS Estimators

6.2.3.

Normal Equations

6.2.4.

Interpretation of Coefficients

6.2.4.1.

Intercept Parameter

6.2.4.2.

Slope Parameter

6.2.5.

Fitted Values and Residuals

6.3.

Classical Linear Regression Model Assumptions

6.3.1.

Linearity in Parameters

6.3.2.

Random Sampling

6.3.3.

Sample Variation in Explanatory Variable

6.3.4.

Zero Conditional Mean

6.3.5.

Homoskedasticity

6.3.6.

No Serial Correlation

6.3.7.

Normality of Error Terms

6.4.

Properties of OLS Estimators

6.4.1.

Gauss-Markov Theorem

6.4.2.

Best Linear Unbiased Estimators

6.4.3.

6.4.4.

6.4.5.

6.5.

Goodness of Fit Measures

6.5.1.

Total Sum of Squares

6.5.2.

Explained Sum of Squares

6.5.3.

Residual Sum of Squares

6.5.4.

Coefficient of Determination

6.5.5.

Adjusted R-Squared

6.5.6.

Standard Error of Regression

6.6.

Statistical Inference in Simple Regression

6.6.1.

Sampling Distributions of OLS Estimators

6.6.2.

Standard Errors of Coefficients

6.6.3.

t-Tests for Individual Coefficients

6.6.4.

Confidence Intervals for Coefficients

6.6.5.

Testing Linear Restrictions

6.7.

Prediction and Forecasting

6.7.1.

Point Predictions

6.7.2.

Prediction Intervals

6.7.3.

Confidence Intervals for Mean Response

6.7.4.

Forecast Accuracy Measures

6.8.

Residual Analysis

6.8.1.

Properties of OLS Residuals

6.8.2.

6.8.3.

Detecting Assumption Violations

6.8.4.

Outlier Detection

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7. Multiple Linear Regression Analysis