AP Statistics: Regression, Interpreting a Regression Line, Residuals

Regression Line

A line that describes how a response variable y changes as an explanatory variable x changes.

Interpreting Regression line (template)

Often used to predict the value of y for a given value of x.

Regression Line Equation

ŷ = a+bx OR ŷ = mx+b

Ŷ

The predicted value of the response variable y for a given value of the explanatory variable x.

Interpreting Ŷ given x

The predicted value of (response/dependent variable) when the (explanatory/indpendent variable) is (x-value) is (calculated y value)

b/m

Slope, the amount by which y is predicted to change when x increases by one unit.

Interpreting slope (template)

As x increases/decrease by n, y is predicted to increase/decrease by (slope).

a/b

y-intercept, the predicted value of y when x = 0.

Interpreting y-intercept (template)

It is predicted that when (response/dependent variable) is zero, (explanatory/independent variable) is (y-int).

Extrapolation

Using the regression equation to predict the response y-hat for a specific value or x that is outside the data range

Extrapolation interpretation (template)

___ should not be used to find a prediction because x-value + what x represents is a value larger/smaller than the given data set

Extrapolation description example

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Residual

The difference between an observed value of the response variable and the value predicted by the regression line

Residual Equation

Residual = actual y - predicted y

Interpreting Residuals (template)

Actual y (in context) for x value was residual value more/less than predicted y.