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AP STATS CH3

TermDefinition
bivariate data Two- variable data set
Univariate data One-variable data set
response variable (y) measures an outcome of a study
explanatory variable (x) may help predict or explain changes in response variable
Scatter plot Shows relationship between two quantitive variable measured on the same individuals.
Direction A scatter plot can show a positive, negative, or no association
Form A scatter plot can show a linear form or nonlinear form. In a scatter plot, the form describes the general shape or pattern of the relationship between the two variables being plotted.
Strength A scatter plot can show a weak, moderate, or strong association.
Unusual features Individuals that fall outside the overall pattern
Positive assocation When values of one variable tend to increase as the values of the other variable increase
Negative association When values of one variable tend to decrease as the values of the other variable increase
No association When knowing the values of one variable doesn't help predict the values of the other variable
Outlier A point that doesn't follow the pattern of the data and has a large residual
Influential point Any point, if removed, substantially changes the slope, y-intercept, r, r^2, or standard deviation of e
Correlation For only a linear association, measures the direction and strength of association; there is a relationship between two variables (indicates a relationship between two variables)
Causation means that one variable is the direct cause of a change in the other; one variable directly causes a change in another.
r Correlation coeffient- tells you how strong the relationship is and if it's + or -
r^2 Coefficient of determination; % of variation in 'y' that can be explained by 'x'. (65% means 35% isn't due to x)
Regression line A line that models how a response variable y changes as an explanatory variable x changes. "y-hat=a+bx"
y-hat predicted value of y
Extrapolation Predicting outside of the interval of x values. The further we extrapolate, the less reliable the predictions. (ex:-10g of protein)
Residual (e for error) The vertical difference between the actual (observed) value of y and the value of y predicted by the regression line. "y minus y-hat"
a the y-intercept; predicted value of y when x=0
b the slope; amount by which the predicted value of y changes when x increases by 1 unit
Least Square Regression Line Makes the sum of the squared residuals as small as possible
Residual plot A scatter plot that displays the residuals on the vertical axis and explanatory variable on the horizontal axis
Standard deviation of the residuals (s) Measures the size of a typical residual (avg. distance between the actual y values and the predicted y values.
High leverage points An observation with an extreme value for one or more of the independent variables (x-values), influential in determining the slope of the LSRL. These points are not necessarily outliers in the y-direction; their impact comes from their position far out in
Residual plot A scatter plot that displays the residuals on the vertical axis and explanatory variable on the horizontal axis
Standard deviation of the residuals (s) Measures the size of a typical residual (avg. distance between the actual y values and the predicted y values.
High leverage points An observation that has a extreme value for the independent variable, strongly influences the slope of the regression line
Negative residual Observed values under the LSRL
Positive residual Observed values above the LSRL
Created by: avnitamia
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