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AP Statistics Ch7-9?
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Terms in this set (31)
Response Variable
measures an outcome of a study, the y-variable
Explanatory Variable
may help explain or predict changes in a response variable, the x-variable
Scatterplot
shows the relationship between two quantitative variables measured on the same individuals
Positive Association
data points that generally go upward from left to right, somewhat linear
Negative Association
data points that generally go downward from left to right, somewhat linear
Outlier
an individual value that falls outside the overall pattern of the relationship
Correlation coefficient
measures the direction and strength of the linear relationship between two quantitative variables (r)
Regression Line
a line that describes how a response variable y changes as an explanatory variable x changes
Extrapolation
the use of a regression line for prediction outside the range of values of the explanatory variable x used to obtain the line. Such predictions are often not accurate.
Least-Squares Regression Line (LSRL)
the line that makes the sum of the squared vertical distances of the data points from the line as small as possible (best-fit line on a scatter plot)
Residual
the difference between an observed value of the response variable and the value predicted by the regression line (a.k.a. prediction error) y - y-hat
Residual Plot
a scatterplot of the regression residuals plotted against the explanatory variable (x, predicted y-values). Assesses how well a regression line fits the data. No pattern = linear and LSRL appropriate to use.
Coefficient of Determination
The statistic or number determined by squaring the correlation coefficient. Represents the amount of variance accounted for by that correlation.(r^2)
Lurking (Confounding) Variable
a variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables
Residual (formula)
residual = observed y - predicted y
Least squares regression line (formula)
y-hat = a + bx OR
Coefficient of determination (symbol)
Correlation coefficient (symbol)
Predicted value (symbol)
Overall Pattern of a Scatterplot
D.O.F.S - direction, outliers, form, strength - all things that should be addressed when describing the relationship between two quantitative variables
Standard deviation of the residuals(s)
the approximate size of a typical prediction error (residual) when we use the least squares regression line to predict the value of a specific response variable
Predicted value
read as y-hat, is the value of the response variable y for a given value of the explanatory variable x.
Interpretation of slope
For every increase of x variable we predict that y variable is (increase if positive/decrease if negative) by (slope).
Interpretation of y-intercept
If the x variable were to be at zero, then the y intercept (aka A) would be at _________.
Interpretation of coefficient of determination
about % in the variation can be explained by the LSR of Y on X
Interpretation of correlation coefficient
Strength (strong, weak) and Direction (strong, moderate or weak) (for LINEAR data only)
Form of a scatterplot
linear, curved, or quadratic
Observed - predicted
residuals (y- ŷ)
Computer output
Constant= y-intercept
Variable Below=Slope
Gives you r^2 NOT r
Direction of a scatterplot
positive association, negative association (tell by r, slope, and scatterplot)
How to make a scatterplot
1.) describe which variable goes on what axis
2.) scale your axis (DON'T FORGET TO LABEL)
3.) plot points
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