Simple Linear Regression and the Correlation Coefficient
The following sections are included:
INTRODUCTION
POPULATION PARAMETERS AND THE REGRESSION MODELS
Data Description
Building the Population Regression Model
Sample Versus Population Regression Model
THE LEAST-SQUARES ESTIMATION OF α AND β
Scatter Diagram
The Method of Least Squares
Estimation of Intercept and Slope
STANDARD ASSUMPTIONS FOR LINEAR REGRESSION
THE STANDARD ERROR OF ESTIMATE AND THE COEFFICIENT OF DETERMINATION
Variance Decomposition
Standard Error of Residuals (Estimate)
The Coefficient of Determination
THE BIVARIATE NORMAL DISTRIBUTION AND CORRELATION ANALYSIS
The Sample Correlation Coefficient
The Relationship Between r and b
The Relationship Between r and R2
Summary
Appendix 13A Derivation of Normal Equations and Optimal Portfolio Weights
Appendix 13B The Derivation of Equation 13.16
Appendix 13C The Bivariate Normal Density Function
Using a Mathematics Aptitude Test to Predict Grade in Statistics
Appendix 13D American Call Option and the Bivariate Normal CDF
Valuating American Option
Questions and Problems
- simple regression analysis
- multiple regression analysis
- dependent variable
- response variable
- independent variable
- explanatory variable
- linear model
- regression model
- intercept
- slope
- regression coefficient
- scatter diagram
- free-hand drawing method
- method of least squares
- standard deviation of error term
- normal equations
- sum of squared deviations
- autocorrelated residuals
- best linear unbiased estimator (BLUE)
- standard error of residuals
- coefficient of determination
- total variation
- explained variation
- unexplained variation
- sample standard deviation of error term
- degrees of freedom
- correlation analysis
- bivariate normal distribution
- American call option
- portfolio weight
