This document discusses different types of regression analysis. Regression analysis is used to predict the value of a dependent variable based on one or more independent variables. Simple linear regression involves one independent variable, while multiple regression involves more than one. The relationship between variables is modeled using a linear regression equation estimated with the method of least squares. This technique minimizes the sum of squared residuals to calculate coefficient values that best fit the data.

1. What is Regression? | SSE, SSR, SST | R-
squared | Errors (ε vs. e)

2. Regression Analysis
 Regression analysis is used to:
 Predict the value of a dependent variable based on the
value of at least one independent variable
 Explain the impact of changes by an independent variable
on the dependent variable.
 Dependent variable: the variable we wish to predict or explain
 Independent variable: the variable used to explainthe
dependent variable.

3. Simple Linear Regression Model
 Only one independent variable, X
 Relationship between X andY is described by a linear
function
 Changes inY are assumed to be caused by changes in X

4. Simple Linear Regression Model

5. Simple Linear Regression Model

6. Simple Linear Regression Equation (Prediction Line)
The simple linear regression equation provides an estimate
of the
population regression line

10. Rsquare = Explained variation / Total Variation
Value is between 0 and 1
Rsquare – Coefficient of Determination

14. Multiple Regression
 Multiple regression analysis
 with more than one independent variable. It is used to
quantify the influence of two or more variable. For
instance, simple (univariate) linear regression explains
the variation in Sales of the product in terms of the
variation in advertising as measured by beta.
 With multiple regression, Sales can be regressed
against beta and against additional variables, such as
Sales Promotion, brand Image, and market growth ,
that might influence Sales.

15. Multiple Regression

16. Method of least Squares

17. Coefficients by Method of Least Squares