Correlation and Regression Analysis

Study Notes

Correlation measures the degree of relatedness of variables.
The Pearson Product-Moment Correlation Coefficient is a measure of the linear relationship between two variables.

Formula for Correlation:

r =  ( x − x )( y − y ) / √( ( x − x )2  ( y − y )2)

r values range from -1 to +1:
- 0 represents no linear relationship.
- +1 represents perfect positive correlation.
- -1 represents perfect negative correlation.

Regression analysis determines the relationship between variables.
Variables are classified as:
- Independent: The variable that is thought to influence the other.
- Dependent: The variable that is being influenced.
The calculation of the slope and y-intercept of the regression line is used to determine the equation of the regression line.
Residuals are calculated to assess the fit of the model, locate outliers, and test the assumptions of the regression model.
The standard error of the estimate, calculated from the sum of squared errors, determines the model's overall fit.
The coefficient of determination, a measure of the model's fit, is related to the coefficient of correlation.
The t-test & F-test are used to test hypotheses about the slope of the regression model and the overall regression model, respectively.
Confidence intervals are used to estimate the conditional mean of the dependent variable, while prediction intervals estimate a single value of the dependent variable.
Trend lines, using alternate coding for time periods, are used to forecast outcomes for future time periods.
Computer programs are used to develop and interpret regression analysis outputs.