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APSTAT Section Two Line it up

BVD Ch. 7. Scatterplots, boo ya!. Examining Relationships. Two variablesExplanatory

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APSTAT Section Two Line it up

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    1. APSTAT Section Two Line it up!!!!!

    2. BVD Ch. 7 Scatterplots, boo ya!

    3. Examining Relationships Two variables Explanatory Explains the change (cause-ish) Response Outcome (effect-ish) ie. Amount of Time Studying Vs. GPA

    4. Scatterplot Explanatory (if there is one) variable on X-Axis Response (if there is one) variable on Y-Axis Important things to look for Direction Positive, Negative Strength of association, from weak to strong Form Linear, Curved, Groupings Outliers and any other weirdness

    5. Hedge Words Adjectives (?) that keep us out of trouble: Somewhat Fairly Moderately Roughly Rather More or less Reasonably Sort of

    6. Describe this -

    7. Correlation Coefficient- r Numerical representation of strength and direction Denoted by r Formula:

    8. Lets do it by hand-ish!!! Data: n=5, but to find other stuff, lets cheat and use the TI-83 Pop Age into L1 and HRs into L2 STAT>CALC>2VariableStats x =14, Sx=3.2, y =11, Sy=3.4

    9. Lets do it by hand-ish!!! Data: n=5, x =14, Sx=3.2, y =11, Sy=3.4 So

    10. Want an Easier Way??? STAT>CALC>LinReg r = r2 = Plus other cool stuff for later Not working? Turn Diagnostics on! Catalog>DiagnosticsOn>ENTER

    11. What is r ? Shows Direction If positive, slope of points is positive If negative, slope is negative

    12. More r Shows Strength of LINEAR Relationship

    13. Describing Strength of Linear Relationship

    14. Lets do one Data: Score on APStat Final vs Score on Alg2 Final Use TI-83 to graph, sketch it Pop into L1 and L2, StatPlot, Window Find r Describe correlation

    15. Averaged Data Using averaged data Reduces variability OK, but understand correlation will likely be higher than if you had used individuals. Example - Heights in classrooms vs individual heights

    16. Causation Correlation shows an ASSOCIATION DOES NOT show a cause and effect relationship Only with a well controlled experiment can even consider talking about cause and effect

    17. Lurking Variable Variables you cant see, but might be causative factors

    18. Common Respose Does a high GPA lead to a High SAT score? Is there something that affects both?

    19. Confounding Influence of a lurking variable on the response variable Ex. A study finds that people who drink in bars have a higher chance of developing lung cancer.

    20. BVD Ch. 8 A Linear Model

    21. Least Squares Regression Idea: Hmmm.Could a line model the data???

    22. LSRL Basics

    23. LSRL Basics

    24. LSRL Line that Minimizes the Sum of the SQUARE of the residuals

    25. LSRL Equation BOOK VS. AP EXAM

    26. TGFC! Linear Regression on TI-83 STAT>CALC>LinReg(a + bx) Gives you: LinReg y=a+bx a= -3.7 b= 1.05 r2=.9587 r=.9791

    27. Fun with our LSRL Interpret Y-intercept: Interpret Slope: Interpolation Timmy is 13, what is his predicted total of home runs? Extrapolation (not a good idea) When Timmy is 104, how many HRs?

    28. What is r2 anyway? Simple answer: Take r (correlation coefficient) and square it Not so simple, but most important answer: Coefficient of determination Fraction (or percentage) of variation in y-values that can be explained by a linear relationship with x ie. In HR/Age problem, roughly 96% of the variation in home runs can be explained by a linear relationship with age

    29. Residual Love Remember this?

    30. Residual Plot Plotting Residual Error vs. X - Value

    31. Why Residual Plot? Can Show Patterns (Bad News)

    32. Patterns Part 2 How bout this one

    33. Residual Issues, Crazy Points Check Dis

    34. Residual Issues 2 Uno mas

    35. Using TI-83 for LSRL Store LSRL from LinReg into Y1 STAT>CALC>LinReg Press enter STO>VARS>Y-VARS>Funtion> Y1 Go to STAT PLOT change options Go to Zoom>ZoomStat Beautiful!

    36. Using TI-83 to Graph Resids LSRL MUST be stored in Y1 for this to work LIST>NAMES>RESID Press ENTER STO> L3 (in LIST) and press ENTER again Now graph go to STAT PLOT and change stuff X is still the old X (L1) Y is now the residuals (L3) Graph it!!!

    37. BVD Ch. 9 Blah Blah Blah

    38. Outliers Technically, anything outside of overall pattern Usually in y direction (up/down) If in x direction (side/side), we call it an influential point.

    40. Influential Points How to find: Plot LSRL with influential point and without Compare Linear regression line and correlation coefficient If no data, just sketch and show change without influential point

    41. BVD Ch. 10 My data is curvy!

    42. CURVY DATA Sometimes data is not really linear 2 ways to deal Easy (but incomplete) way on calc Hard (correct) way using LOGs

    43. Money in the bank Put in 1 G at 10% and wait 10 years

    44. The easy way (TI83) Yr. $$$$ 0 1000 1 1100 2 1210 3 1331 4 1464 5 1600 6 1760 7 1930 8 2120 9 2330 10 2563

    45. The correct way (using logs) Yr. $$$$ LOGY 0 1000 3.00 1 1100 3.04 2 1210 3.08 3 1331 3.12 4 1464 3.17 5 1600 3.20 6 1760 3.25 7 1930 3.29 8 2120 3.33 9 2330 3.36 10 2563 3.41

    46. Predicted Value Ex: How much in bank at 5.5 years? log = 3.001+0.0407x Throw in 5.5 for x

    47. Double Log Situation Log both X and y But Why??? After logging y, resids still show curviness Power Functions!

    48. Here We Go!!! Ht WT 5 102 5.25 113 5.5 125 5.75 137 6 151 6.25 166

    49. Log y only

    50. Log x and log y

    51. MUY IMPORTANTE!!!!!! USE LSRL and R-Squared ONLY FOR LINEAR MODELS ONLY IF THERE ARE NO EXTREME OBSERVATIONS ONLY USE LSRL FOR INTERPOLATION NO EXTRAPOLATION!!!!!

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