Statistics and Risk Management Regression

Statistics and Risk Management Regression Performance Objective: After completing this lesson, the student will understand the concepts of defining relationship between two variables and use that information to predict outcomes. Approximate Time: When taught as written, this lesson should take 4-5 days to complete. Specific Objectives: The student will discuss the important relationship between variables. The student will understand some basic terms and concepts of correlational values. The student will understand some basic terms and concepts of regression values. This lesson corresponds with Unit 7 of the Statistics and Risk Management Scope and Sequence. 1

TEKS Correlations: This lesson, as published, correlates to the following TEKS for Regression. Any changes/alterations to the activities may result in the elimination of any or all of the TEKS listed. 130.169(g)(6)(M) analyze two variable problems using linear regression and correlation 130.169(g)(6)(N) interpret the results of a computer-generated regression model InterdisciplinaryTEKS: English: 110.31 (C) (21) (B) organize information gathered from multiple sources to create a variety of graphics and forms (e.g., notes, learning logs) 110.31 (C) (22) (B) evaluate the relevance of information to the topic and determine the reliability, validity, and accuracy of sources (including Internet sources) by examining their authority and objectivity 110.31 (C) (23) (C) use graphics and illustrations to help explain concepts where appropriate 2

110.31 (C) (23) (D) use a variety of evaluative tools (e.g., self-made rubrics, peer reviews, teacher and expert evaluations) to examine the quality of the research Math: 111.36 (C) (4) (A) compare theoretical and empirical probability; 111.37. (C) (3) (B) use probabilities to make and justify decisions about risks in everyday life Occupational Correlation (O*Net - http://www.onetonline.org/) Biostatisticians 15-2041.01 Similar Job Titles: Associate Professor of Biostatistics, Biostatistician, Professor of Biostatistics, Biostatistics Director Tasks: Design research studies in collaboration with physicians, life scientists, or other professionals. Draw conclusions or make predictions based on data summaries or statistical analyses. Provide biostatistical consultation to clients or colleagues. (Soft) Skills: Critical Thinking; Complex Problem Solving; Writing; Active Listening 3

Instructional Aids: 1. Display for presentation, websites for assignments and class discussion 2. Assignment Worksheets 3. Supporting Spreadsheets Materials Needed: 1. Printer paper 2. Assignments and website information ready to distribute to students. Student projects will be displayed to increase interest in Statistics Equipment Needed: 1. Computer with presentation and Internet Access 2. Computers for Students to Conduct Research and Collect Data for Projects 4

References: Introduction to Linear Regression and Correlation Analysis Use this link to: calculate and interpret the simple correlation between two variables, determine whether the correlation is significant, calculate and interpret the simple linear regression equation for a set of data, and understand the assumptions behind regression analysis. www.fordham.edu/economics/vinod/correl-regr.ppt Regression and Correlation Analysis This site analyzes the concepts of regression and correlation, discusses the regression model, explains the least squares method, and defines the relationship between correlation and regression analysis. http://abyss.uoregon.edu/~js/glossary/correlation.html Regression Through this interactive Regression lesson, instructors can set up an online lesson that correlates with their textbooks. The learner tab explains regression, the activity tab contains the actual activity, the help tab provides assistance on using the activity, and the instructor tab allows teachers to set up the activity to fit with their lecture concepts. http://www.shodor.org/interactivate/activities/regression/ Regression Line Example This video from Khan Academy provides a detailed example of how to calculate and for a regression line. This interactive lesson provides supplemental instruction to accompany a teacher s lecture on regression. http://www.khanacademy.org/math/statistics/v/regression-line-example 5

Teacher Preparation: Teacher will: 1. Review terms in outline, presentation, and handouts. 2. Locate and evaluate various resources and websites. 3. Have assignments and websites ready. Learner Preparation: Break the boring barrier. Probability can be fun and definitely interesting. Find examples the student might find interesting; understanding gaming, designing games, evaluating decision on an ongoing basis. Introduction: STUDENTS will watch the Unit video found here: jukebox.esc13.net/untdeveloper/videos/regression.mov STUDENTS will take the practice test and review using the Key, found in Common/Student Documents. EXHIBIT: Excitement about the relationship between correlation and regression anaylsis. INTRODUCE: The following article to read. http://www.easternct.edu/~adams/resources/grannies.pdf ASK: Are there flaws in the argument? How are statistics misused? 6

I. Linear Correlation A. Statistics & Risk Management B. Relationships C. Would you like to know. 1. Is there a correlation between your paycheck and your education? 2. Are what you eat and your health correlated? 3. Does your age make a difference in your car insurance rates? 4. Does the number of tickets affect your car insurance rates. D. Causal? 1. If there is a correlation. do we know if one causes the other? E. Correlation 1. Is a calculated value (1.0 to -1.0) that demonstrates a relationship (or lack of) between two sets of data. F. Spreadsheet Formula 1. CORREL(C1:C5,D1:D5) 2. This function uses two lists: Factor One (Column C) and Factor Two (Column D) G. Spreadsheet Charting 1. Create Two Columns 2. Use a Scatter Chart 3. Stress vs. Blood Pressure 4. Age vs. Weight Use LinearCorrelation.pptx. Provide Assignment sheets and discuss and answer any questions about assignment (In class or take home- Instructor s Option) Provided.docx files 7.1a_LinearCorrelation.docx 7

II. Linear Regression A. Statistics & Risk Management B. Beyond Correlation 1. If you have a strong correlation, you may be able to predict outcomes. 2. Collect Data 3. Charted 4. Establish Line 5. Analysis 6. 60 inches of rain? 7. 90 inches of rain? 8. 120 inches of rain? 9. Could we plateau out? 10. Could we eventually have too much rain? Use LinerarRegression.pptx. Provide Assignment sheets and discuss and answer any questions about assignment (In class or take home- Instructor s Option) Provided.docx files 7.2a_LinearRegression.docx 8

Guided Practice: See assignments. Independent Practice: Review document Spreadsheets for Statistical Purposes in Common Documents. See assignments. Review: Question: Describe what is meant by a normal distribution? Question: What are some main uses of confidence intervals? Informal Assessment: Instructor should observe student discussion and monitor interaction. Formal Assessment: Completion of provided assignments using included keys for grading. 9

Student Assignment 7.1a Linear Regression - Linear Correlation Key Name: You noticed that the average points scored in your high school football conference games seem to correlate with the average night time temperature for the football season for the last 10 years. Temp Score Temp Score #1 67.5 12.6 #6 66.6 13.6 #2 55.0 9.8 #7 60.4 11.3 #3 58 10.1 #8 55.8 11.4 #4 60 10.0 #9 59.6 9.8 #5 59 9.8 #10 62.5 10.1 Is that a correlation or an inverse correlation? Do you think it is a strong correlation? Why? ANSWER: Using the 7ss_Regression_Correlation.xlsx spreadsheet and Correlation tab we find the correlation at.713 1.0 is a maximum positive correlation so.713 is strong positive correlation. Statistically, the score goes up the warmer it gets. 10

Student Assignment 7.1a Regression Linear Regression Key Name: You are examining the safety record at a plant for an insurance company. You have looked at the accidents per ten thousand hours figure and are trying to identify a correlation with the overtime worked per ten thousand hours. OtHr Accidents OtHr Accidents #1 1000 2.5 #6 500 1.5 #2 900 2.6 #7 400 1.4 #3 800 1.9 #8 300 1.5 #4 700 1.95 #9 200 1.2 #5 600 1.85 #10 100.9 They have a new government contract and expect 1500 of overtime for several periods during the years. Will there be a significant increased risk of more accidents during those periods? Answers will vary per student, but look that they have made an effort to fulfill the requirements of this assignment any various levels. You may ask yourself does this student demonstrate to apply correlational or regression techniques to understanding the relationship of overtime hours and the number of accidents. If the used the provide spreadsheet they would find a r of.7355 which represent a strong correlation. Thus at using the formula of Y=0.002x+.06 x=.002 x 1500 +.06 =3.06 or 3.6 accidents per 1000 hour worked. That is almost four times the number of accidents as when little (100 hours) or no overtime is worked. 11

Name: Date: Class: TRUE and FALSE: Regression Test 1. The correlation demonstrating the relationship between 2 sets of data is a calculated value. A. True B. False 2. If you have a strong correlation, you may be able to predict outcomes. A. True B. False 3. The correlation coefficient is a measure of linear association with 2 variables. A. True B. False 4. Regression and correlation analysis should be interpreted as establishing a cause and effect relationship. A. True B. False 5. A correlation coefficient of +1 indicates 2 variables are related in a negative linear sense. A. True B. False 6. Linear regression consists of finding the best fitting straight line through the points. A. True B. False MATCHING: A. Linear Regression B. Dependent Variable C. Regression D. Variable E. Independent Variable 7. An attribute or characteristic of a statistical unit that differs among a population of units. 8. The technique of fitting a straight line to the data points on a scatter chart to determine the relationship between 2 variables. 9. The variable that is measured to determine the effect of an independent variable. 10. The technique of predictive relationships based upon correlational data. 11. The variable that changes or can be controlled. MULTIPLE CHOICE: 12. is the technique of predictive relationships based upon correlational data. A. Regression B. Variance C. Correlation D. Deviation 13. is the measurement of a relationship between two variables. A. Regression B. Variance C. Deviation D. Correlation 14. A correlation coefficient of indicates 2 variables are related in a positive linear sense. A. 1 B. 0 C. +1 D. +2 15. A correlation coefficient of indicates that there is no linear relationship between the 2 variables. A. 1 B. 0 C. +1 D. +2 12

Name: Date: Class: 16. Values of the correlation coefficient are always between and. A. 1 and 1 B. 2 and 2 C. 3 and 3 D. 4 and 4 17. The best fitting line in a linear regression is called the. A. Line of Correlation B. Line of Best Fit C. Regression Line D. None of the above 18. If a point is much higher than the regression line, it will have a error of prediction. A. Small B. Positive C. Large D. Negative 19. are simply deviations from the mean. A. Outliers B. Raw Scores C. Deviation Scores D. None of the Above 20. A graph representing data points charted along the x and y axes are a. A. Histogram B. Pie Chart C. Scatter Chart D. Bar Chart 21. The following is a picture of which type of linear regression? A. Negative B. Positive C. Flat D. No linear regression 22. The greater the absolute value of a correlation coefficient, the stronger the relationship. A. Linear B. Positive C. Cubic D. Negative 23. A positive correlation means that if one variable gets the other variable gets. A. Bigger, Smaller B. Smaller, Bigger C. Smaller, Smaller D. Bigger, Bigger 24. A negative correlation means that if one variable gets the other variable gets. A. Bigger, Smaller B. Smaller, Bigger C. Smaller, Smaller D. Bigger, Bigger 25. The weakest linear relationship is indicated by a correlation coefficient equal to. A. 1 B. 0 C. +1 D. +2 13

Regression Test Key 1. A 2. A 3. A 4. B 5. B 6. A 7. D 8. A 9. B 10. C 11. E 12. A 13. D 14. C 15. B 16. A 17. B 18. C 19. C 20. C 21. B 22. A 23. D 24. A 25. B 14