Regression Analysis.pptx

Presentation skills explaining regression analysis

1. Regression Analysis…

2. Regression Analysis: the study of the relationship between variables Regression Analysis: one of the most commonly used tools for business analysis Easy to use and applies to many situations Regression Analysis

3. Regression The term regression as a statistical technique to predict one variable from another variable. It is a measure of the average relationship between two or more variables in terms of original units of data. Correlation coefficient is measure of degree of co-variability between X & Y but the objective of Regression Analysis is to study the ‘nature of relationship between variables’

4. Types of Regression Linear and Non Linear Regression- If the given points are plotted on a graph paper , the points so obtained on the scatter diagram will more/less concentrated round a curve called the curve of Regression. If the regression curve is a straight line then linear otherwise non linear/curved regression.

5. Simple & Multiple Regression It is confined with study of two variables i.e one independent and other dependent variable. It is confined with more than two variables at a time. I.e two or more independent variables and one dependent variable.

6. Types of variables Dependent variable : the single variable which we wish to estimate/ predict by the regression model (response variable) Independent variable : The explanatory variable(s) used to predict/estimate the value of dependent variable. (predictor variable) Y = A + B X dependent independent

7. Simple Linear Regression Model y = b + b 1 x + e where: b and b 1 are called parameters of the model , e is a random variable called the error term . The simple linear regression model is: The equation that describes how y is related to x and an error term is called the regression model .

8. Simple Linear Regression Equation The simple linear regression equation is: E ( y ) is the expected value of y for a given x value. b 1 is the slope of the regression line. b is the y intercept of the regression line. Graph of the regression equation is a straight line. E ( y ) =  +  1 x

9. Simple Linear Regression Equation Positive Linear Relationship E ( y ) x Slope b 1 is positive Regression line Intercept b

10. Simple Linear Regression Equation Negative Linear Relationship E ( y ) x Slope b 1 is negative Regression line Intercept b

11. Simple Linear Regression Equation No Relationship E ( y ) x Slope b 1 is 0 Regression line Intercept b

12. Estimated Simple Linear Regression Equation The estimated simple linear regression equation is the estimated value of y for a given x value. b 1 is the slope of the line. b is the y intercept of the line. The graph is called the estimated regression line.

13. Estimation Process Regression Model y = b + b 1 x + e Regression Equation E ( y ) = b + b 1 x Unknown Parameters b , b 1 Sample Data: x y x 1 y 1 . . . . x n y n b and b 1 provide estimates of b and b 1 Estimated Regression Equation Sample Statistics b , b 1

14. Method of Least Squares It states that line should be drawn through the plotted points in such manner that the sum of the squares of the deviations of the actual Y values from the computed Y values is the least. In order to obtain a line which fits the points best should be minimum. LINE OF BEST FIT

15. Least Squares Method Least Squares Criterion where: y i = observed value of the dependent variable for the i th observation ^ y i = estimated value of the dependent variable for the i th observation

16. Slope for the Estimated Regression Least Squares Method where: x i = value of independent variable for i th observation _ y = mean value for dependent variable _ x = mean value for independent variable y i = value of dependent variable for i th observation

17. y -Intercept for the Estimated Regression Equation Least Squares Method

18. Reed Auto periodically has a special week-long sale. As part of the advertising campaign Reed runs one or more television commercials during the weekend preceding the sale. Data from a sample of 5 previous sales are shown on the next slide. Simple Linear Regression Example: Reed Auto Sales

19. Simple Linear Regression Example: Reed Auto Sales Number of TV Ads ( x ) Number of Cars Sold ( y ) 1 3 2 1 3 14 24 18 17 27 S x = 10 S y = 100

20. Estimated Regression Equation Slope for the Estimated Regression Equation y -Intercept for the Estimated Regression Equation Estimated Regression Equation

21. Practice Example

22. Practice HW Pg no. 609, q1 Pg no. 610 q3, q5 Pg no. 612 q7

23. Coefficient of Determination Relationship Among SST, SSR, SSE where: SST = total sum of squares SSR = sum of squares due to regression SSE = sum of squares due to error SST = SSR + SSE

24. The coefficient of determination is: Coefficient of Determination where: SSR = sum of squares due to regression SST = total sum of squares r 2 = SSR/SST

25. Coefficient of Determination r 2 = SSR/SST = 100/114 = .8772 The regression relationship is very strong; 87.72% of the variability in the number of cars sold can be explained by the linear relationship between the number of TV ads and the number of cars sold.

26. Sample Correlation Coefficient where: b 1 = the slope of the estimated regression equation

27. The sign of b 1 in the equation is “+”. Sample Correlation Coefficient r xy = +.9366