ap stats - unit 2

explanatory variable

explanatory variable

independent variable; x-axis

response variable

dependent variable; y-axis

correlation coefficient (r)

measures the strength of a linear relationship

r interpretation

There is a (strength), (direction) linear relationship between (variable) and (variable).

lurking variable

“behind the scenes” variable that affects association

LSRL

line that minimizes distance of data points to the line

LSRL equation

y^= a + bx

slope interpretation

For every increase in one (x-context), the model predicts an/a (increase/decrease) of about (slope) in (y-context).

y-int interpretation

When (x=0 context) the predicted value of (y-context) is about (y-int).

residual formula

residual = actual - predicted

residual interpretation

The actual (y-context) was (residual) (above/below) the predicted value for (x-context).

interpolation

predictions made within the range of data

extrapolation

predictions made outside of the data range (unreliable)

s

standard deviation of residuals (typical error)

s interpretation

The actual (y-context) is typically about (S) away from the number predicted by the LSRL.

R²

% improvement in error given an explanatory variable

R² interpretation

About (R²)% of the variability in (y-context) can be explained by the variability in (x-context).

outliers

do not follow linear pattern and have a large residual

high leverage points

substantially larger/smaller x-value than the rest of the data

influential points

any point that will change the LSRL substantially if removed