1. AP Stat Day 14 64 Days until AP Exam Introduction to Bivariate Data Describing Patterns Correlation and Causation Introduction to Bivariate Data Describing Patterns Correlation and Causation

2. Bivariate Data Up until now, we have been working with univariate (one variable) data. Today we start working with bivariate (two variable) data. So, we will be working with x and y. X is (generally) our explanatory variable. Y is our response variable

3. Changing Stats Vocab to Algebra So, x, the explanatory variable is also called the independent variable. And y, the response variable, is also called the response variable. Sometimes there is not an explanatory/response relationship between x and y.

4. Making a scatterplot You must make sure that your data table is set up so that the explanatory and response variables for a given subject are an ordered pair (x,y) You must label the axes and title the graph. Then plot the points carefully and describe the relationship. (more on this Thursday)

5. EXAMPLE- sketch a scatterplot Following are the mean heights of Kalama children: Age in MonthsHeight in Centimeters 1876.1 1977.0 2078.1 2178.2 2278.8 2379.7 2479.9 2581.1 2681.2 2781.8 2882.8 2983.5

6. ACTIVITY- Make a Scatterplot On p. 6 copy down the data we collect. Use the data to create a scatterplot. Be sure to label appropriately. Does there seem to be a relationship between our two variables?

7. Scatterplots on your Calculator Put your class data into L 1 and L 2. Now, 2 nd, y=, turn on Stat Plot 1, and choose the 1 st graph. Make sure x is L 1 and y is L 2. Hit graph and zoom 9. Does your hand-sketched scatterplot look like the calculator screen? Is there something you need to work on?

8. Describing Bivariate Distributions When we describe bivariate distributions we do not CUSS and BS. We talk about form, direction, and strength, AND we BS. Form- Linear or Non-linear Direction- Positive or Negative Strength- Strong, Moderate, Weak or No association.

9. EXAMPLES

10. Categorical Variables on a Scatterplot You can display categorical data on a scatterplot by assigning each category its own symbol or color and providing a key.

11. Correlation and Causation Correlation means that there is a relationship between your two variables that can be modeled by an equation. The strength of the correlation can be calculated- it is a number. Causation is another thing entirely. Just because your data has a relationship, that does not mean that x caused y.

12. EXAMPLE A ski resort in New Mexico did a study and found that on days where they sold more ski tickets, they sold more hot chocolate. It may seem that the purchase of a ski ticket caused the purchase of hot chocolate, or alternatively, the purchase of hot chocolate caused the purchase of the ski ticket. But, can you think of something else that could have caused both? (LURKING VARIABLE)

13. Calculating Correlations Luckily, you will NOT have to calculate this by hand. (Unless your calculator dies…) Hey! We SHOULD recognize r!

14. Summary p.7 What do we focus on when describing a bivariate distribution? What is the difference between correlation and causation? What MUST you include when making a scatterplot?

15. Prep Questions p.8 Have you ever run a linear regression function on your calculator? How would you interpret a slope of ¾? What would a y-intercept of 21 mean? What is a line of best fit?