unit 3 AP stats

Slope

"The predicted y goes up/down by about b for each increase of 1 unit in X."

Y-intercept

"The predicted y is __ when __ is 0."

Residual

"The actual __ is __ more/less than the value predicted by the regression line using x=__."

Residual = Actual - predicted

"Residual is the prediction error of the equation of the least Squared Regression Line."

Describing scatterplot

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"Is a line an appropriate model?"

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"Positive or negative trend (to the right)."

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"Correlation is useful for linear models."

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"Clusters, points far away from others."

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Correlation

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General form of a regression equation

"ŷ = a + bx"

Extrapolation

"Using a model to make predictions outside the range of observed inputs."

Best-fit regression line for a set of data

"Minimizes the sum of the squared residuals."

Equation of the least squares regression line

"b = r Sy/Sx, a = ybar - b(xbar)"

Residual plot

"Plots the x list vs the residual (error) for each input. Helps determine if a line is the best model to use."

Linear model appropriateness

"No pattern - linear model is good. Pattern - line might not be the best fit."

S

"Prediction made using this linear model typically vary by about S units from the actual y."

Compare sum of squared residuals

"Sum of squared error from the line that just uses the mean."

"Sum of squared errors from the least squared regression equation line."

r²

"Measures how much better the sum of squared errors from the least squared regression equation line is than the sum of squared errors from the line that uses mean."

Interpret r²

"__% of the variability in __ is accounted for by the least squared regression line with x=__."

r = √R²

"r² and s both measure how well a line fits the data, just in different ways."