 Module Description

Statistics II - Correlation and Linear Regression

Contents

This module is aimed at students who are taking their first course in linear regression and have taken prior statistics courses that included probability, using the normal distribution, and hypothesis testing.

The following is a list of the specific topics this module covers.

1. The bivariate (two-variable) relationship:
Scatters plots, sums of squares, covariance, correlation, coefficient of correlation, test of correlation.

2. Best fit line:
Scatter plots, dependent variable, independent variable, intercept, slope, linear component, random component.

3. Simple regression:
Formulas for intercept and slope, computation of the intercept and slope, sample regression line, interpretation of intercept and slope.

4. Simple regression statistics:
Variance of the regression (standard error), variance of the slope, coefficient of determination, F-value.

5. Hypothesis testing:
Tests of the intercept and slope, test of the regression (F-test).

6. Prediction:
Interpolation, extrapolation, individual dependent variable prediction, mean dependent variable prediction, confidence intervals.

7. Multiple regression:
Sample regression line, interpretation of intercept and slopes, dummy variables.

8. Multiple regression statistics:
Variance of the regression (standard error), variances of the slopes, adjusted coefficient of determination, F-value.

9. Hypothesis testing:
Tests of the intercept and slopes, test of the regression (F-test), multi-collinearity, variance inflation factor.

10. Prediction.

11. Model building (introduction):
Curvi-linear relationship between the dependent and independent vriables, interactions between independent variables.

12. Time series (introduction):
Definition of a time series, components, moving average, deseasonalization, definition of autocorrelation.

13. Questions: 1,000 practice questions with explained solutions.

Pre-requisites for this Module

This module requires prior knowledge of mean, variance, normal probability, and hypothesis testing such as that obtained in the Statistics I module.

This module is a pre-requisite for the Statistics III module on non-linear regression.

Sample Module.