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# Business Quantitative - Lecture 2

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### Business Quantitative - Lecture 2

1. 1. Quantitative Analysis for Business<br />Lecture 2<br />July 5th, 2010<br />Saksarun (Jay) Mativachranon<br />
2. 2. Intro<br />Please turn your mobile phones off or switch it to silent modeand please do not pick up your calls<br />Slide will be available at<br />www.slideshow.com (soon)<br />Email: saarkman@gmail.com<br />
3. 3. Linear regression<br />
4. 4. Regression<br />Regression is used for estimating the unknown effect of changing one variable over another<br />The variable to be estimated is called “dependent variable”<br />The changing variable is called “independent variable”<br />
5. 5. Linear Regression Assumptions<br />There is NO relationship between X and Y if 1 equals to 0<br />There is ALWAYS a relationship if 1 does NOT equal to 0<br />The independent Variable (X) is not random<br />The expected value of error (e ) is 0<br />
6. 6. Linear Regression Analysis<br />Analyzing the correlation and directionality of the data<br />Estimating the model<br />Evaluating the validity and usefulness of the model<br />
7. 7. Usage of Regression<br />Causal analysis<br />Forecasting an effect (of independent variable to that of dependent variable)<br />Forecasting (trend of) future values<br />
8. 8. Simple Linear Regression<br />True value of slope and intercept are not known, so we estimate them by using sample data<br />where<br /> Y = dependent variable<br /> X = independent variable<br /> b0 = intercept (value of Y when X = 0)<br /> b1 = slope of the regression line<br />^<br />
9. 9. Scatter Diagram<br />
10. 10. example<br />Linear Regression<br />
11. 11. Situation<br />Company A wants to know the relationship between the Man Hour of their sales force and their sales number<br />They have collected their sales data and the man hour put in during the collection period<br />
12. 12. Company A Data<br />
13. 13. Company A’s Sales Scatter Diagram<br />12 –<br />10 –<br />8 –<br />6 –<br />4 –<br />2 –<br />0 –<br />Sales<br /> | | | | | | | |<br /> 0 1 2 3 4 5 6 7 8<br />Man Hour<br />
14. 14. Finding the Regression<br />Company A is trying to predict its sales from the man hour spent<br />The line in is the one that minimizes the errors<br />Y = Sales<br />X = Man Hour<br />Error = (Actual value) – (Predicted value)<br />
15. 15. Data manipulation<br />For the simple linear regression model, the values of the intercept and slope can be calculated using the formulas below<br />
16. 16. Regression Calculation<br />_<br />_<br />_<br />_<br />_<br />_<br />_<br />_<br />
17. 17. Regression Calculation (cont.)<br />Therefore<br />
18. 18. Results<br />Company A Sales model<br />Predicting sales<br />Every 1 Man-hour, Company A sells \$3.25 worth of goods<br />
19. 19. Measuring Regression Model<br />Regression model can be developed for any variable Y and X<br />But how do we know the reliability of Y from variation of X ???<br />
20. 20. Company A’s Sales Model<br />12 –<br />10 –<br />8 –<br />6 –<br />4 –<br />2 –<br />0 –<br />Sales<br /> | | | | | | | |<br /> 0 1 2 3 4 5 6 7 8<br />Man Hour<br />Error<br />Error<br />
21. 21. Measuring Regression Model (cont.)<br />How do we know the reliability of Y from variation of X ???<br />Can we find the average of the errors?<br />
22. 22. Measurement of Variability<br />SST – Total variability about the mean<br />SSE – Variability about the regression line<br />SSR – Total variability that is explained by the model <br />
23. 23. Measurement of Variability<br />Sum of the squares total<br />Sum of the squared error<br />Sum of squares due to regression<br />An important relationship<br />
24. 24. Company A example<br />_<br />_<br />^<br />^<br />^<br />_<br />_<br />^<br />^<br />_<br />
25. 25. Company A’s Variability<br />SST = 22.5<br />SSE = 6.875<br />SSR = 15.625<br />
26. 26. Company A’s Sales Model<br />12 –<br />10 –<br />8 –<br />6 –<br />4 –<br />2 –<br />0 –<br />^<br />Y = 2 + 1.25X<br />^<br />Y – Y<br />Y<br />Sales<br />Y – Y<br />Y – Y<br />^<br /> | | | | | | | |<br /> 0 1 2 3 4 5 6 7 8<br />Man Hour<br />
27. 27. Coefficient of Determination<br />The proportion of variability of Y in the regression model<br />
28. 28. Coefficient of Determination<br />The coefficient of determination is r2<br />
29. 29. Company A example<br />Explanation<br />Over 69% of Y can be predicted by variation of X<br />For Company A<br />
30. 30. Correlation Coefficient<br />The strength of linear relationship<br />Relationship of Y and X<br />It will always be between +1 and –1<br />The correlation coefficient is r<br />
31. 31. Correlation Coefficient<br />Y<br />Y<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />X<br />X<br />(a) Perfect PositiveCorrelation: r = +1<br />(b) PositiveCorrelation: 0 < r < 1<br />Y<br />Y<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />*<br />X<br />X<br />(c) No Correlation: r = 0<br />(d) Perfect Negative Correlation: r = –1<br />
32. 32. Next Week<br />Linear Regression<br />Errors in Regression model<br />Variance<br />Mean Square Error<br />Standard Deviation<br />Testing the Model<br />Multiple Regression<br />