1. Bivariate Data – Scatter Plots and Correlation Coefficient……

2. 2 Quantitative Variables……  We represent 2 variables that are quantitative by using a scatter plot.  Scatter Plot – a plot of ordered pairs (x,y) of bivariate data on a coordinate axis system. It is a visual or pictoral way to describe the nature of the relationship between 2 variables.

3. Input and Output Variables……  X: a. Input Variable b. Independent Var c. Controlled Var  Y: a. Output Variable b. Dependent Var c. Results from the Controlled variable

4. Example……  When dealing with height and weight, which variable would you use as the input variable and why?  Answer:  Height would be used as the input variable because weight is often predicted based on a person’s height.

5. Constructing a scatter plot……  Do a scatter plot of the following data: IndependentDependent Variable AgeBlood Pressure 43128 48120 56135 61143 67141 70152

6. What do we look for?......  A. Is it a positive correlation, negative correlation, or no correlation?  B. Is it a strong or weak correlation?  C. What is the shape of the graph?

7. Answer……With TI AgeBlood Pressure 43128 48120 56135 61143 67141 70152

8. Notice……  Notice the following:  A. Strong Positive – as x increases, y also increases. B. Linear - it is a graph of a line.

9. Example 2……By Hand IndependentDependent Variable # of AbsencesFinal Grade 682 286 1543 974 1258 590 878

10. Example 2……With TI IndependentDependent Variable # of AbsencesFinal Grade 682 286 1543 974 1258 590 878

11. Notice……  Notice the following: A. Strong Negative – As x increases, y decreases B. Linear – it’s the graph of a line.

12. Example 3……By Hand IndependentDependent Variable Hrs. of ExerciseAmt of Milk 348 08 232 564 810 532 1056 272 148

13. Example 3……With TI IndependentDependent Variable Hrs. of ExerciseAmt of Milk 348 08 232 564 810 532 1056 272 148

14. Notice……  Notice:  There seems to be no correlation between the hours or exercise a person performs and the amount of milk they drink.

15. Steps to see on Calculator……  Put x’s in L1 and y’s in L2  Click on “2 nd y=“  Set scatter plot to look like the screen to the right.  Press zoom 9 or set your own window and then press graph.

16. Linear Correlation Section 3.2

17. Correlation……  Definition – a statistical method used to determine whether a relationship exists between variables.  3 Types of Correlation: A. Positive B. Negative C. No Correlation

18.  Positive Correlation: as x increases, y increases or as x decreases, y decreases.  Negative Correlation: as x increases, y decreases.  No Correlation: there is no relationship between the variables.

19. Linear Correlation Analysis ……  Primary Purpose: to measure the strength of the relationship between the variables.