1 Multiple Variables Regression
Definition
How a response variable changes as the predictor (explanatory) variables , , … change
In a variable regression,
- There is 1 response variable
- And predictor variables , , , … , Goal is to find the values of , , , …
Regression Strategy
Same strategy used in the 2-variable regression: The least-squares regression line of y and x is the line that makes
- the sum of the squares of the vertical distances of the data points from the line as small as possible
2 Correlation between Multiple Variables
2.1 Correlation Matrix
Definition: Correlation
A correlation matrix shows the linear correlation between each pair of variables under consideration in a multiple regression model
Predictor Variables Selection Criteria in Multi Regression
- Predictor variables should have a high linear correlation with the response variable
- But do not include variables that are highly correlated among themselves
Multi-collinearity
Multi-collinearity exists between 2 explanatory (predictor) variables if they have a high linear correlation
3 Normality of Residuals
4 Test Individual Regression Coefficients for Significance
4.1 Coefficient: p-value
Since both p-values are sufficiently small
- We reject both the NULL hypothesis
- There is a linear relationship between both the predictor variables and the response variable
If the p-value for the slope coefficient is large
- We should consider removing it from the model