1. Two Quantitative Variables Scatterplots examples how to draw them Association what to look for in a scatterplot Correlation strength of a linear relationship how to calculate good news and bad news

2. Scatterplot CARSBOATS 4030 2025 3065 20 30 40 20 50 80 CARS BOATS

3. Scatterplot CARSBOATS 4030 2025 3065 20 30 40 20 50 80 CARS BOATS

4. Made-up Examples PERCENT TAKING SAT STATE AVE SCORE

5. Made-up Examples SHOE SIZE IQ

6. Made-up Examples BAKING TEMP JUDGE’S IMPRESSION 250 350 450

7. Made-up Examples GDP PER CAPITA LIFE EXPECTANCY

8. Scatterplots: Which variable goes where? RESPONSE VARIABLE goes on Y axis (“Y”)(“dependent variable”) EXPLANATORY VARIABLE goes on X axis (“X”)(“independent variable”) If neither is really a response variable, it doesn’t matter which variable goes where.

9. Scatterplots: Drawing Considerations Don’t show the axes without a good reason Don’t show gridlines without a good reason Scales should cover the ranges of the variables-- —outliers? —no need to include 0 —what if same units?

10. What to look for in a scatterplot… Do the cases break up into separate clusters? Are there outliers? Is there an ASSOCIATION between the variables? OR are they INDEPENDENT? ALWAYS DRAW THE PICTURE !!!!

11. Kinds of Association… Positive vs. Negative Strong vs. Weak Linear vs. Non-linear

12. CORRELATION (or, the CORRELATION COEFFICIENT) measures the strength of a linear relationship. If the relationship is non-linear, it measures the strength of the linear part of the relationship. But then it doesn’t tell the whole story. Correlation can be positive or negative.

13. Computing correlation… 1.Replace each variable with its standardized version. 2.Take an “average” of ( x i ’ times y i ’ ):

14. Computing correlation r, or R, or greek  (rho) n-1, not n sum of all the products

15. Good things about correlation It’s symmetric ( correlation of x and y means same as correlation of y and x ) It doesn’t depend on scale or units — adding or multiplying either variable by a constant doesn’t change r — of course not; r depend only on the standardized versions r is always in the range from -1 to +1 +1 means perfect positive correlation; dots on line -1 means perfect negative correlation; dots on line 0 means no relationship, OR no linear relationship

16. Bad things about correlation Sensitive to outliers Misses non-linear relationships Doesn’t imply causality