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My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

Please click in. Set your clicker to channel 41. My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z .

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My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

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  1. Please click in Set your clicker to channel 41. My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  2. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, SOC200Lecture Section 001, Fall, 2011Room 201 Physics-Atmospheric Sciences (PAS)10:00 - 10:50 Mondays & Wednesdays + Lab Session Welcome Please double check – All cell phones other electronic devices are turned off and stowed away http://www.youtube.com/watch?v=oSQJP40PcGI

  3. Use this as your study guide By the end of lecture today11/28/11 Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple and Multiple Regression Using correlation for predictions r versus r2 Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent)Coefficient of correlation is name for “r”Coefficient of determination is name for “r2”(remember it is always positive – no direction info)Standard error of the estimate is our measure of the variability of the dots around the regression line(average deviation of each data point from the regression line – like standard deviation) Coefficient of regression will “b” for each variable (like slope)

  4. Readings for next exam Lind Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

  5. Homework due next class November 30th Assignment 14: Regression worksheet (can be found on class website) Please double check – All cell phones other electronic devices are turned off and stowed away

  6. Exam 4 Readings Lind: Chapters 1 - 15 (not 12) Plous: Chapter 17 and 18 only • Exam 4 • Study guide is online • Bring 2 pencils (with good erasers) • Bring ID • Bring Calculator We will sign up next time to take Final Wednesday • Exam 4 – Scheduling Concerns • Two options for completing Exam 4 • Monday (12/5/11) • Wednesday (12/7/11) • Must sign up to take Exam 4 on Wednesday • Only need to take one exam – these are to optional times

  7. Multiple regression equations • Can use variables to predict • behavior of stock market • probability of accident • amount of pollution in a particular well • quality of a wine for a particular year • which candidates will make best workers

  8. 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

  9. 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

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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

  16. 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?

  17. 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

  18. Multiple Linear Regression - Example

  19. 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.

  20. 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.

  21. 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.

  22. 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?

  23. Thank you! See you next time!!

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