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Two Quantitative Variables

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 . Paired vs. Unpaired Variables.

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Two Quantitative Variables

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  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. Paired vs. Unpaired Variables • Paired variables come from the same data table. • Each record has one value of X and one value of Y, and they go together a pair.

  3. Paired vs. Unpaired Variables Germany • Unpaired variables come from different tables • …or from different lines of one table. • IN CHAPTER TWO WE’RE DEALING WITH PAIRED VARIABLES. France

  4. Paired vs. Unpaired Variables • Unpaired variables come from different tables • …or from different lines of one table. • IN CHAPTER TWO WE’RE DEALING WITH PAIRED VARIABLES.

  5. 80 BOATS 50 20 40 20 30 CARS Scatterplot

  6. 80 BOATS 50 20 40 20 30 CARS Scatterplot

  7. cigarettes.xls

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

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

  10. Made-up Examples IQ SHOE SIZE

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

  12. Made-up Examples LIFE EXPECTANCY GDP PER CAPITA

  13. 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 !!!!

  14. 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.

  15. 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?

  16. CORRELATION • 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.

  17. Computing correlation… • Replace each variable with its standardized version. • Multiply each pair( xi’ times yi’ ) • Take an “average” of the products

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

  19. 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

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

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