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AP Statistics Chapter 3 Notecards

AP Statistics Chapter 3 Notecards. Interpreting Correlation. Direction Positively associated – above average explanatory results in above average response Negatively associated – above average explanatory results in below average response 2) Form – (linear, exponential, quadratic)

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AP Statistics Chapter 3 Notecards

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  1. AP Statistics Chapter 3 Notecards

  2. Interpreting Correlation • Direction • Positively associated – above average explanatory results in above average response • Negatively associated – above average explanatory results in below average response 2) Form – (linear, exponential, quadratic) 3) Strength – how sure are you of the relationship (strong, moderate, weak) 4) Outliers – individual observations outside pattern (difference between outlier and influential point) 5) IN CONTEXT!

  3. Linear Regression/Residuals a = average change in y for every change in x b = predicted y – intercept = predicted y for given x is a point on the regression line r – correlation coefficient ( -1 ≤ r ≤ 1) - r +r - The closer r is to 1 or negative 1, the stronger the linear correlation. An r of 0 implies no correlation between x and y -Remember, correlation does NOT imply causation r2 – coefficient of determination percentage of change in y that is due to the change in x

  4. An r near one is not enough to assure correlation is linear – you must look at the residual plot. If the residual plot shows a pattern, linear correlation is not a good assumption. Residuals are scattered – no apparent pattern - LINEAR Residuals show a definite pattern - NONLINEAR • Every x has two y’s associated with it; the y the equation predicts and the observed value. The residual is the observed – expected

  5. Linear equation without data We can find the equation of the regression line if we know; x, Sx, y, Sy, and r

  6. log y x Exponential/Power Transformations • Look at scatterplot – if linear, run regression and check residual plot If linear is not appropriate; try: 2) log y vs x If log y vs x is linear Exponential relationship logy = ax + b

  7. log y log x 3) log y vs log x If log y vs log x is linear Power relationship logy = a logx + b 4) Run appropriate regression 5) Plot y = on original data to check

  8. Limitations of regression • Describe only linear relationships resulting in need to transform data • Strongly influenced by extreme observations (non-resistant) • Extrapolation – prediction outside the domain of values (can yield incorrect predictions) • Lurking variables variables that have an important effect on the relationship but are not included in the study

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