Unit 2 Part B Vocabulary

Regression Line

a line that models how a response variable y changes as an explanatory variable x changes. Expressed in the form y=a+bx, where y hat is the predicted value of y for a given value of x

Extrapolation

the use of a regression line for prediction outside the interval of x-values used to obtain the line. The further we extrapolate, the less reliable the predictions become

Residual

the difference between the actual value of y and the value of y predicted by the regression line.

Y-Intercept

the predicted value of y when x = 0, represented by a in statistics

Slope

the amount by which the predicted value of y changes when x increases by 1 unit, represented by b in statistics

Least-Squares Regression Line

the line that makes the sum of the squared residuals as small as possible

Residual plot

a scatterplot that displays the residuals on the vertical axis and the values of the explanatory variable (or the predicted values) on the horizontal axis

Coefficient of Determination (r2)

measures the percent reduction in the sum of squared residuals when using the least-squares regression line to make predictions, rather than the mean value of y. In other words, this measures the proportion (or percentage) of the variation in the response variable that is accounted for (or explained) by the explanatory variable in the linear model.

Standard Deviation of the Residuals (s)

measures the size of a typical residual. That is, s measures the typical distance between the actual y-values and the predicted y-values.

High Leverage

points in regression with this have much larger or much smaller x-values than the other points in the data set

Outlier

a point in regression that does not follow the pattern of the data and has a large residual

Influential Point

in regression, any point that, if removed, substantially changes the slope, y-intercept, correlation, coefficient of determination, or standard deviation of the residuals