Correlation is a measure of the linear association between two variables, but there is no differentiation between x and y so correlation may not be used for prediction.
Notes from class
Types of Regression Analyses
There are two major types of regression analysis—simple and multiple regression analysis. Both types consist of dependent and independent variables. Simple linear regression has two variables—dependent and independent. Multiple regression consists of dependent variable and two or more independent variables.
1. How does a multiple regression compare with a simple linear regression?
Multiple and simple linear differ in the fact that simple only will contain one dependent variable and one independent variable. For instance, I could predict how much I will spend on gas from how many miles I have driven in the past month. In comparison, multiple regression has one dependent variable and two or more independent variables. An example would be to predict GPA based on test scores in math and reading. I also want to point out that there are several different kinds of regression, including multivariate where there is more than one dependent variable.
2. What are the various ways to determine what variables should be included in a multiple regression equation?
Four Criteria for Regression Assessment
1 Logic Is there an a priori reason to expect a causal relationship between the predictors and the response variable?
2 Fit Does the overall regression show a significant relationship between the predictors and the response variable?
3 Parsimony Does each predictor contribute significantly to the explanation? Are some predictors not worth the trouble?
4 Stability Are the predictors related to one another so strongly that regression estimates become erratic?
3 Compare and contrast the following processes: forward selection, backward elimination, and stepwise selection.
Forward selection is part of stepwise regression. This method starts with no variables and systematically tests variables using model comparison criteria. Variables are added to the model until the model does improve anymore.
Backward elimination is also part of step regression. This method starts with all variables and whittles them down via the chosen criteria. The variables that improve the model the most are eliminated until the model is at peak position.
Bidirectional elimination is a combination of forward selection and backward elimination. Each step is tested for variables to include and exclude.
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