1. UNIT 8 Regression and Correlation

2. Correlation Correlation describes the relationship between two variables. EX: How much you study verse how well you do on a test. We can say that these two variables have a relationship, therefore they are correlated.

3. Positive Correlation POSITIVE Correlation: as one variable increases, the other variable increases. Ex: The more you study, the higher your grade on a test

4. Negative Correlation Negative Correlation: as one variable increases, the other variable decreases. Ex: The more you sleep in class, the lower your grade is.

5. No Correlation No Correlation: When two variables are not related at all. Ex: How tall you are, and how high your grade is in English class.

6. Correlation Describe the following as POSITIVE, NEGATIVE or NO Correlation. 1. Hours you work, how much you get paid 2. Money you spend, Money in your bank account 3. Amount of Music you listen to, How much you eat.

7. RECALL: Linear Regression To enter the data: STAT  EDIT L 1 is independent variable; L 2 is dependent variable Calculator Steps: STAT  CALC 4: LinReg  VARS  Y-VARS ENTER 3 Times

8. Find the Linear Model for the Following. \

9. Turning on Correlation Coefficient Calculator commands: 2 nd  Zero  DiagnosticOn  Enter

10. Correlation Coefficient Correlation Coefficient: (r) is a number that tells how well a line of best fit, fits the data. - Closer to 1 or -1, the stronger the relationship - If r is close to 1, then positive correlation -If r is close to -1, then negative correlation -If r is closer to 0, then no correlation R only applies for LINEAR MODELS!!!!

11. Find the Linear Model for the Following. \ Look at the r value, what does it say about the data?

12. Find the Linear Model for the Following. Theater tickets sales on successive nights.

13. Choosing a Model

14. We are going to analyze graphs and tables to make an informed decision as to which function would best model a given set of data.

15. Decision Making When given a data set and asked to find a model, it helps to first know what model is best. The three most common are…. Linear Exponential Quadratic

16. Exponential Model Quadratic Model Linear Model

17. Graphing Calculator It is often easiest to determine the best model by the shape of the graph. Then find the regression. To do this: 1. Turn the scatter plot on using 2. Enter the data into 1: Edit 3. Press 9: Stat. 4. Analyze the shape of the graph. 5. Use CALC and choose LinReg, QuadREg or ExpReg. STAT 2ndY = ZOOM STAT

18. Let’s Try Some!!!! xy 20 08 13.2 21.28 30.512 xy 00 11.5 26 313.5 424