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MGMT 276: Statistical Inference in Management McClelland Hall, Room 132 8:30 – 10:45 Monday - Thursday Summer II , 2012. Welcome. Please start portfolios. Please read: Chapters 10 – 12 in Lind book and Chapters 2 – 4 in Plous book : (Before the next exam) Lind

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  1. MGMT 276: Statistical Inference in ManagementMcClelland Hall, Room 1328:30 – 10:45 Monday - ThursdaySummer II, 2012. Welcome

  2. Please start portfolios

  3. Please read: Chapters 10 – 12 in Lind book and Chapters 2 – 4 in Plous book: (Before the next exam) Lind Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Chapter 12: Analysis of Variance Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

  4. Use this as your study guide By the end of lecture today8/7/12 Simple and Multiple Regression Review for Exam 3

  5. Homework: No more homework!!

  6. Evaluations

  7. Regression Example The manager of copier company wants to determine whether there is a relationship between the number of sales calls made in a month and the number of copiers sold that month. The manager selects a random sample of 10 representatives and determines the number of sales calls each representative made last month and the number of copiers sold.

  8. Scatter Diagram What are we predicting?

  9. Correlation Coefficient– Excel Example

  10. Correlation Coefficient– Excel Example • Interpret r = 0.759 • Positive relationship between the number of sales calls and the number of copiers sold. • Strong relationship • Remember, we have not demonstrated cause and effect here, only that the two variables—sales calls and copiers sold—are related. 0.759014

  11. Correlation Coefficient– Excel Example • Interpret r = 0.759 • Does this correlation reach significance? • n = 10, df = 8 • alpha = .05 • Observed r is larger than critical r (0.759 > 0.632) therefore we reject the null hypothesis. • r (8) = 0.759; p < 0.05 0.759014

  12. Coefficient of Determination– Excel Example • Interpret r2 = 0.576(.7592 = .576) • we can say that 57.6 percent of the variation in the number of copiers sold is explained, or accounted for, by the variation in the number of sales calls. • Remember, we lose the directionality of the relationship with the r2 0.759014

  13. Regression Equation- Example If you probably sell this much If make this many calls Step 3 – State the regression equation Y’ = a + bX Y’ = 18.9476 + 1.1842 X What is the expected number of copiers sold by a representative who made 20 calls? Step 4 – Solve for some value of Z Y’ = 18.9476 + 1.1842 (20) Y’ = 42.63

  14. Regression Equation- Example If you probably sell this much If make this many calls Step 3 – State the regression equation Y’ = a + bX Y’ = 18.9476 + 1.1842 X What is the expected number of copiers sold by a representative who made 40 calls? Step 4 – Solve for some value of Z Y’ = 18.9476 + 1.1842 (40) Y’ = 66.3156

  15. Can use variables to predict which candidates will make best workers • Measured current workers – the best workers tend to have highest “success scores”. (Success scores range from 1 – 1,000) • Try to predict which applicants will have the highest success score. • We have found that these variables predict success: • Age (X1) • Niceness (X2) • Harshness (X3) Both 10 point scales Niceness (10 = really nice) Harshness (10 = really harsh) According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Y’ = b1X 1+ b2X 2+ b3X 3 + a Y’ = b1 X1 + b2 X2 + b3 X 3 + a Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

  16. According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Y’ = b1 X1 + b2 X2 + b3 X 3 + a Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

  17. According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Y’ = b1 X1 + b2 X2 + b3 X 3 + a Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 • Y’ is the dependent variable • “Success score” is your dependent variable. • X1 X2 and X3are the independent variables • “Age”, “Niceness” and “Harshness” are the independent variables. • Each “b” is called a regression coefficient. • Each “b” shows the change in Y for each unit change in its own X (holding the other independent variables constant). • a is the Y-intercept

  18. Y’ = b1X 1 + b2X 2 + b3X 3+ a The Multiple Regression Equation – Interpreting the Regression Coefficients Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 b1 = The regression coefficient for age (X1) is “1” The coefficient is positive and suggests a positive correlation between age and success. As the age increases the success score increases. The numeric value of the regression coefficient provides more information. If age increases by 1 year and hold the other two independent variables constant, we can predict a 1 point increase in the success score.

  19. Y’ = b1X 1 + b2X 2 + b3X 3+ a The Multiple Regression Equation – Interpreting the Regression Coefficients Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 b2 = The regression coefficient for age (X2) is “20” The coefficient is positive and suggests a positive correlation between niceness and success. As the niceness increases the success score increases. The numeric value of the regression coefficient provides more information. If the “niceness score” increases by one, and hold the other two independent variables constant, we can predict a 20 point increase in the success score.

  20. Y’ = b1X 1 + b2X 2 + b3X 3+ a The Multiple Regression Equation – Interpreting the Regression Coefficients Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 b3 = The regression coefficient for age (X3) is “-75” The coefficient is negative and suggests a negative correlation between harshness and success. As the harshness increases the success score decreases. The numeric value of the regression coefficient provides more information. If the “harshness score” increases by one, and hold the other two independent variables constant, we can predict a 75 point decrease in the success score.

  21. Here comes Victoria, her scores are as follows: Prediction line: Y’ = b1X 1+ b2X 2+ b3X 3+ a Y’ = 1X 1+ 20X 2- 75X 3+ 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 • Age = 30 • Niceness = 8 • Harshness= 2 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 What would we predict her “success index” to be? Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 We predict Victoria will have a Success Index of 740 (1)(30) - 75(2) + (20)(8) + 700 Y’ = = 3.812 Y’ = 740 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

  22. Here comes Victoria, her scores are as follows: Prediction line: Y’ = b1X 1+ b2X 2+ b3X 3+ a Y’ = 1X 1+ 20X 2- 75X 3+ 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 • Age = 30 • Niceness = 8 • Harshness= 2 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 What would we predict her “success index” to be? Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 We predict Victoria will have a Success Index of 740 (1)(30) - 75(2) Y’ = + (20)(8) + 700 = 3.812 Y’ = 740 Here comes Victor, his scores are as follows: We predict Victor will have a Success Index of 175 • Age = 35 • Niceness = 2 • Harshness= 8 What would we predict his “success index” to be? Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 (1)(35) - 75(8) + (20)(2) + 700 Y’ = Y’ = 175

  23. Can use variables to predict which candidates will make best workers We predict Victor will have a Success Index of 175 We predict Victoria will have a Success Index of 740 Who will we hire?

  24. Multiple Linear Regression - Example Can we predict heating cost? Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature, (2) the number of inches of insulation in the attic, and (3) the age in years of the furnace. To investigate, Salisbury's research department selected a random sample of 20 recently sold homes. It determined the cost to heat each home last January

  25. Multiple Linear Regression - Example

  26. The Multiple Regression Equation – Interpreting the Regression Coefficients b1 = The regression coefficient for mean outside temperature (X1) is -4.583. The coefficient is negative and shows a negative correlation between heating cost and temperature. As the outside temperature increases, the cost to heat the home decreases. The numeric value of the regression coefficient provides more information. If we increase temperature by 1 degree and hold the other two independent variables constant, we can estimate a decrease of $4.583 in monthly heating cost.

  27. The Multiple Regression Equation – Interpreting the Regression Coefficients b2 = The regression coefficient for mean attic insulation (X2) is -14.831. The coefficient is negative and shows a negative correlation between heating cost and insulation. The more insulation in the attic, the less the cost to heat the home. So the negative sign for this coefficient is logical. For each additional inch of insulation, we expect the cost to heat the home to decline $14.83 per month, regardless of the outside temperature or the age of the furnace.

  28. The Multiple Regression Equation – Interpreting the Regression Coefficients b3 = The regression coefficient for mean attic insulation (X3) is 6.101 The coefficient is positive and shows a negative correlation between heating cost and insulation. As the age of the furnace goes up, the cost to heat the home increases. Specifically, for each additional year older the furnace is, we expect the cost to increase $6.10 per month.

  29. Applying the Model for Estimation What is the estimated heating cost for a home if: • the mean outside temperature is 30 degrees, • there are 5 inches of insulation in the attic, and • the furnace is 10 years old?

  30. Multiple regression equations Predict success in a paralegal program from: • High School GPA (X1) • SAT - Verbal (X2) • SAT - Mathematical (X3)

  31. Y’ = -.411 +1.20X1 + .0016X2 - .0019X3

  32. Y’ = -.411 +1.20X1 + .0016X2 - .0019X3

  33. Y’ = -.411 +1.20X1 + .0016X2 - .0019X3

  34. Y’ = -.411 +1.20X1 + .0016X2 - .0019X3

  35. Multiple regression equations Predict success in a paralegal program from: • High School GPA (X1) • SAT - Verbal (X2) • SAT - Mathematical (X3) Andy completes a multiple regression analysis and comes up with this regression equation: Prediction line Y’ = b1X 1+ b2X 2+ b3X 3+ a Y’ = 1.20X 1+ .0016X 2- .00194X 3 - .411 Y’ = 1.20 gpa + .0016satverb - .00194satmath - .411

  36. Here comes Alice, her scores are as follows: Prediction line: Y’ = b1X 1+ b2X 2+ b3X 3+ a Y’ = 1.2X 1+ .00163X 2-.00194X 3 - .411 • High School GPA = 2.80 • SATVerbal = 430 • SATMathematical= 460 What would we predict her GPA to be in the paralegal program? Y’ = 1.2 gpa + .00163satverb - .00194satmath - .411 Y’ = 1.2 (2.80)+ .00163(430)- .00194 (460)- .411 We predict Alice will have a GPA of 2.7575 Y’ = 3.36 + .7009 - .8924 - .411 = 2.7575 Predict Alberta’s GPA, his scores are as follows: We predict Alberta will have a GPA of 3.9575 • High School GPA = 3.80 • SAT - Verbal = 430 • SAT - Mathematical = 460 Y’ = 1.2 gpa + .00163satverb - .00194 satmath - .411 Y’ = 1.2 (3.80)+ .00163(430)- .00194 (460)- .411 Y’ = 4.56 + .7009 - .8924 - .411 = 3.9575

  37. Prediction line: Y’ = b1X 1+ b2X 2+ b3X 3+ a Y’ = 1.2X 1+ .00163X 2-.00194X 3 - .411 Here comes Alice, her scores are as follows: • High School GPA = 2.80 • SATVerbal = 430 • SATMathematical= 460 We predict Alice will have a GPA of 2.7575 Predict Alberta’s GPA, his scores are as follows: We predict Alberta will have a GPA of 3.9575 • High School GPA = 3.80 • SAT - Verbal = 430 • SAT - Mathematical = 460 Y’ = 1.2 gpa + .00163satverb - .00194 satmath - .411 Alberta scored exactly one point higher on her High School GPA. How did this affect her overall score? It went up by 1.2….why?

  38. Exam 3 Review

  39. Thank you! See you next time!!

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