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AP Statistics Chapter 3 and 4 Test Review Scatterplots Display bivariate data: Explanatory variable on x axis, response of y axis. Describing associations: direction, form, strength in context Outlier: individual data point that falls far outside overall pattern of graph Influential Point: data point that markedly change LSRL if removed Least Squares Regression Line Correlation Coefficient ŷ = a + bx -1 r 1 r tells you two things a) slope: +r = + slope -r = - slope a = - b b) dispersion of data around line of best fit. Use 2-var stats to The closer to 1 or –1 the less get these numbers variation from LSRL Interpreting the LSRL ŷ=a+bx The slope of a regression line is usually important for interpreting the data. The regression equation relating number of cavities to dental office visits gives ŷ=6.7+.5x Interpretation: For each additional trip to the dentist (x) the LSRL predicts an increase of .5 cavities. Can you read computer output? Relating the range of motion and age for 12 patients recovering from knee surgery Predictor Coef Stdev T-ratio P-value Constant 107.58 11.12 9.67 0.000 Age -.8710 .4146 2.10 0.062 N = 12 S = 10.42 R-Sq: 30.6% R-Sq(adj): 23.7% 1. What is the equation of the LSRL? 2. What is the predicted range of motion for a 25 year old patient? 3. What is the value of the correlation coefficient? Correlation Tidbits Every regression line passes through the point (,) Correlation ( r ) is a unitless measurement r measures the direction & strength only of a linear relationship between two variables. Like the mean and standard deviation r is strongly affected by influential points. It is not resistant Coefficient of Determination r2 The percent of variation in the response variable (y) that is explained by the least squares regression of y on x Remember to interpret in context: 68% of the variation in airfare can be explained by change in the length of a flight (distance). Residuals The difference between an observed value of the response variable and the value predicted by the regression line More Simply: actual – predicted = residual if the point is above the line + residual if the point is below the line - residual Modeling Nonlinear Data A variable grows exponentially if an (x,log y) transformation linearizes the data. y = a(bx) If a (log x, log y) transformation is linear, then the data is best modeled by a power model y = a(xb) A residual plot of the transformed data should show a random scatter of points. Make sure you understand how to answer the free response question from Quiz 4.1. You will probably see another question like it tomorrow Interpreting Correlation and Regression Extrapolation: using a regression line for prediction outside the domain of values of the explanatory variable Lurking variables: a variable that has an important effect on the relationship among the two variables, but is not directly included in the study Interpreting Association 1. Association Causation one variable causes changes in a second variable Ex: a drop in outdoor temperature causes an increase in natural gas consumption 2. Common response: both variables are commonly responding to a third lurking variable. Ex. Both SAT verbal and SAT math scores respond to a students ability and level of knowledge. 3. Confounding: The effect on y of the explanatory variable is hopelessly mixed up with the effects on y of other variables Ex: Minority students have lower average test scores on college exams than white students, but minorities (on average) grew up in poorer neighborhoods and attended poorer schools than the average white. The effect of social and economic differences mess up our ability to say race explains test scores. Final Tips for success Review past quizzes and worksheets Read your textbook looking at the examples and definitions again Get a good nights sleep Take a deep breath and smile. YOU ALL RULE!!
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