Multiple Linear Regressionnnnnnnnnnn.pptx

Multiple Linear Regressionnnnnnnnnnn.pptx

1. MULTIPLE LINEAR REGRESSION

2. SLR VS MLR SIMPLE LINEAR REGRESSION 🡪 ONE INDEPENDENT VARIABLE MULTIPLE LINEAR REGRESSION 🡪 MULTIPLE INDEPENDENT VARIABLE

3. USES OF MULTIPLE REGRESSION: First, it might be used to identify the strength of the effect that the independent variables have on a dependent variable. Multiple linear regression analysis helps us to understand how much will the dependent variable change when we change the independent variables.  Multiple linear regression analysis predicts trends and future values.

4. MULTIPLE LINEAR REGRESSION

5. MULTIPLE LINEAR REGRESSION

6. MULTIPLE LINEAR REGRESSION

7. DUMMY VARIABLE TRAP

8. P-VALUE

9. BUILDING A MODEL PART OF MODEL TRAINING AND VARIABLE SELECTION DON’T INCLUDE THE IRRELEVANT DATA OR THE DATA WHICH HAVE NO LINEARITY WITH THE DEPENDENT VARIABLE WHY BECAUSE

10. BUILDING A MODEL

11. METHODS-BUILDING MODEL

12. ALL-IN

13. BACKWARD ELIMINATION

14. FORWARD SELECTION

15. BIDIRECTIONAL ELIMINATION

16. Consider the following dataset with one response variable  y  and two predictor variables X 1  and X 2 :

17. Calculate X 1 2 , X 2 2 , X 1 y, X 2 y and X 1 X 2 .

18. Calculate b , b 1 , and b 2 . b 1  = [(194.875)(1162.5)  – (-200.375)(-953.5)]  / [(263.875) (194.875) – (-200.375) 2 ] =  3.148   b 2  = [(263.875)(-953.5)  – (-200.375)(1152.5)]  / [(263.875) (194.875) – (-200.375) 2 ] =  -1.656 b0= b 0  = 181.5 – 3.148(69.375) – (-1.656)(18.125) =  -6.867

19. Multiple Linear Regression Equation   ŷ = b  + b 1 *x 1  + b 2 *x 2 ŷ = -6.867 + 3.148x 1  – 1.656x 2 b  = -6.867 . When both predictor variables are equal to zero, the mean value for y is -6.867. b 1  = 3.148 . A one unit increase in x 1  is associated with a 3.148 unit increase in y, on average, assuming x 2  is held constant. b 2  = -1.656 . A one unit increase in x 2  is associated with a 1.656 unit decrease in y, on average, assuming x 1  is held constant.