IBM 401 Lecture 2

1. Quantitative Analysis for Business Lecture 2 July 5th, 2010 Saksarun (Jay) Mativachranon

2. Intro Please turn your mobile phones off or switch it to silent modeand please do not pick up your calls Slide will be available at www.slideshow.com (soon) Email: saarkman@gmail.com

3. Linear regression

4. Regression Regression is used for estimating the unknown effect of changing one variable over another The variable to be estimated is called “dependent variable” The changing variable is called “independent variable”

5. Linear Regression Assumptions There is NO relationship between X and Y if 1 equals to 0 There is ALWAYS a relationship if 1 does NOT equal to 0 The independent Variable (X) is not random The expected value of error (e ) is 0

6. Linear Regression Analysis Analyzing the correlation and directionality of the data Estimating the model Evaluating the validity and usefulness of the model

7. Usage of Regression Causal analysis Forecasting an effect (of independent variable to that of dependent variable) Forecasting (trend of) future values

8. Simple Linear Regression True value of slope and intercept are not known, so we estimate them by using sample data where Y = dependent variable X = independent variable b0 = intercept (value of Y when X = 0) b1 = slope of the regression line ^

9. Scatter Diagram

10. example Linear Regression

11. Situation Company A wants to know the relationship between the Man Hour of their sales force and their sales number They have collected their sales data and the man hour put in during the collection period

12. Company A Data

13. Company A’s Sales Scatter Diagram 12 – 10 – 8 – 6 – 4 – 2 – 0 – Sales | | | | | | | | 0 1 2 3 4 5 6 7 8 Man Hour

14. Finding the Regression Company A is trying to predict its sales from the man hour spent The line in is the one that minimizes the errors Y = Sales X = Man Hour Error = (Actual value) – (Predicted value)

15. Data manipulation For the simple linear regression model, the values of the intercept and slope can be calculated using the formulas below

16. Regression Calculation _ _ _ _ _ _ _ _

17. Regression Calculation (cont.) Therefore

18. Results Company A Sales model Predicting sales Every 1 Man-hour, Company A sells $3.25 worth of goods

19. Measuring Regression Model Regression model can be developed for any variable Y and X But how do we know the reliability of Y from variation of X ???

20. Company A’s Sales Model 12 – 10 – 8 – 6 – 4 – 2 – 0 – Sales | | | | | | | | 0 1 2 3 4 5 6 7 8 Man Hour Error Error

21. Measuring Regression Model (cont.) How do we know the reliability of Y from variation of X ??? Can we find the average of the errors?

22. Measurement of Variability SST – Total variability about the mean SSE – Variability about the regression line SSR – Total variability that is explained by the model

23. Measurement of Variability Sum of the squares total Sum of the squared error Sum of squares due to regression An important relationship

24. Company A example _ _ ^ ^ ^ _ _ ^ ^ _

25. Company A’s Variability SST = 22.5 SSE = 6.875 SSR = 15.625

26. Company A’s Sales Model 12 – 10 – 8 – 6 – 4 – 2 – 0 – ^ Y = 2 + 1.25X ^ Y – Y Y Sales Y – Y Y – Y ^ | | | | | | | | 0 1 2 3 4 5 6 7 8 Man Hour

27. Coefficient of Determination The proportion of variability of Y in the regression model

28. Coefficient of Determination The coefficient of determination is r2

29. Company A example Explanation Over 69% of Y can be predicted by variation of X For Company A

30. Correlation Coefficient The strength of linear relationship Relationship of Y and X It will always be between +1 and –1 The correlation coefficient is r

31. Correlation Coefficient Y Y * * * * * * * * * * * * * * * * X X (a) Perfect PositiveCorrelation: r = +1 (b) PositiveCorrelation: 0 < r < 1 Y Y * * * * * * * * * * * * * * * * * * X X (c) No Correlation: r = 0 (d) Perfect Negative Correlation: r = –1

32. Next Week Linear Regression Errors in Regression model Variance Mean Square Error Standard Deviation Testing the Model Multiple Regression