SU3: Linear and Multiple Regression Analyses and Correlation
Chapter 1: Linear Regression and Correlation
Correlation Analysis
Dependent variable (Y axis): the variable being predicted or estimated
Independent variable (X axis): variable that provides bases for estimation
Coefficient of Correlation
Coefficient of Determination, r2
Simple Linear Regression Analysis
Equation: Y^=a+bX
Assumptions underlying Linear Regression
The standard deviations of the normal deviations are the same
The Y values are statistically independent
The means of normal dist of Y values all lie on the line of regression
For each value of X, there is a group of Y values. Y values follow normal dist
Chapter 2: Multiple Regression Analysis
Extension of Simple Linear Regression
Multiple Regression Equation: Y^=a+b1x1+b2x2+b3x3...
Global test: Whether Mulitple Regression Model is valid
H0: beta1=beta2=beta3=0
H1: Not all beta=0
Assumptions about Multiple Regression
There is a linear relationship between dependent variable and each independent variable
The variation in the residuals is the same for all fitted values of Y
The residuals are normally distributed with a mean of 0
Multicollinearity does not exist
Successive residuals should be independent