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AP Statistics - Chapter 3 Flashcards

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8006074398Response Variablemeasure the outcome of a study.0
8006074399Explanatory Variablemay help explain or influence changes in a response variable.1
8006074400scatterplotshows the relationship between two quantitative variables measured on the same individuals. The values of one variable may appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point in the graph. explanatory variable goes on the x-axis2
8006074401Interpreting scatterplots1) the direction 2) the form 3) the strength of the relationship - look for outliers3
8006074402Positive Associationwhen above average values of one tend to accompany above-average values of the other, and when below-average values also tend to occur together.4
8006074403Negative Associationwhen above-average values of one tend to accompany below-average values of the other.5
8006074404correlation rmeasures the direction and strength of the linear relationship between two quantitate variables.6
8006074405Facts about correlation1. correlation makes no distinction between explanatory and response variable 2. r does't change when we change the units of measurement of x, y, or both. 3. The correlation r itself has no unit of measurement. It is just a number. 4. Correlation does not imply causation. 5. Correlation requires that both variables be quantitative 6. Correlation doesn't describe curved relationships between variables, no matter how strong the relationship is. 7. Like the mean and SD, the correlation is not resistant: r is strongly affected by a few outlying observations. 8. Correlation is not a complete summary of two-variable data.7
8006074406Regression lineis a line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression time to predict the value of y given value of x.8
8006074407Regression line equationŷ = a +bx - ŷ is the *predicted value* of the response variable y for a given value of the explanatory variable x. - b is the *slope* - a is the *y-intercept*, the predicted value of y when x=09
8006074408Extrapolationis the use of a regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line. Often not accurate.10
8006074409Residualis the difference between an observed value of the response variable and the value predicted by the regression line. residual = observed y - predicted value r = y - ŷ11
8006074410least-squares regression lineof y on x is the line that makes the sum of the squared residuals as small as possible12
8006074411Residual plotis a scatterplot of the residuals against the explanatory variable. Help us assess how well a regression line fits the data.13
8006074412Standard deviation of the residualsthe value gives the approximate size of a "typical" or "average" prediction error (residual).14
8006074413Coefficient of determination r^2is the fraction of the variation in the values of y that is accounted for by the least-sqaures regression line of y on x. We can calculate r^2 using the following formula:15
8006074414Outlieris an observation that lies outside the overall pattern of the other observations.16
8006074415An observation is influential for a stat calculation..if removing it would markedly change the result of the calculation.17
8006074416Association does not imply causationAn association between an explanatory variable x and a response variable y, even if it is very strong, is not by itself good evidence that changes in x actually cause changes in y.18

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