Regression analysis is used to predict the value of a dependent variable based on the value of one or more independent variables. The dependent variable is what we want to predict, while the independent variables are what we use to explain the dependent variable. Simple linear regression uses one independent variable to describe the linear relationship between it and the dependent variable, assuming changes in the dependent variable are caused by changes in the independent variable. Multiple regression extends this to use two or more independent variables.

1. 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.

2. 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

3. Simple Linear Regression Model

4. Simple Linear Regression Model

6. Multiple Regression

8. R , Rsquare & Adj R Square
• R is same as Coeff of Corr for Regression
• Is R=0.7 twice more than R =0.5?
• R Square = SSR/SST= 1-(SSE/SST)
• Adj R Square = 1-(1-Rsq)(n-1/n-k-1)
where k = number of independent variables
RSq > Adj RSq as k increases
Significance of normality of residuals (error)

9. Evaluating Regression

10. Evaluating Regression

11. Evaluating Regression

12. Evaluating Regression

13. Evaluating Regression

14. Evaluating Regression

15. Evaluating Regression

16. Evaluating Regression

17. Coefficient of Determination, r2
 The coefficient of determination is the portion of the
total variation in the dependent variable that is
explained by variation in the independent variable
 The coefficient of determination is also called r-squared and
is denoted as r2