Starnes/Tabor, The Practice of Statistics for the AP® Course, 7e, Unit 2, English

regression line

Line that models how a response variable y changes as an explanatory variable x changes. Regression lines are expressed in the form ŷ = a + bx, where ŷ is the predicted value of y for a given value of x.

correlation r

Gives the direction and measures the strength of the linear relationship between two quantitative variables.

negative association

When values of one variable tend to decrease as the values of the other variable increase.

no association

A relationship between two variables where knowing the value of one variable does not help predict the value of the other variable.

scatterplot

Graph that shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point in the graph.

positive association

When values of one variable tend to increase as the values of the other variable increase.

association

A relationship between two variables in which knowing the value of one variable helps predict the value of the other. If knowing the value of one variable does not help predict the value of the other, there is no association between the variables.

mosaic plot

A modified segmented bar graph in which the width of each bar is proportional to the number of individuals in the corresponding category.

segmented bar graph

Graph that displays the distribution of a categorical variable as segments of a bar, with the area of each segment proportional to the number of individuals in the corresponding category.

conditional relative frequency

Gives the percentage or proportion of individuals that have a specific value for one categorical variable among a group of individuals that share the same value of another categorical variable (the condition).

joint relative frequency

Gives the percent or proportion of individuals in a two-way table that have a specific value for one categorical variable and a specific value for another categorical variable.

marginal relative frequency

Gives the percentage or proportion of individuals in a two-way table that have a specific value for one categorical variable.

two-way table

Table of counts or relative frequencies that summarizes data on the relationship between two categorical variables for some group of individuals.

explanatory variable

Variable that may help predict or explain changes in a response variable.

response variable

Variable that measures the outcome of a study.

extrapolation

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

residual

Difference between an actual value of y and the value of

y predicted by the regression line: residual = actual y − predicted y = y − ŷ.

y intercept

In the regression equation ŷ = a + bx, the y intercept a is the predicted value of y when x = 0.

slope

In the regression equation ŷ = a + bx, the slope b is the amount by which the predicted value of y changes when x increases by 1 unit.

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 explanatory variable (or the predicted values) on the horizontal axis. Residual plots help us assess whether a regression model is appropriate.

coefficient of determination r²

A measure of 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, r² measures the proportion or percentage of the variability in the response variable that is accounted for by the explanatory variable in the linear model.

standard deviation of the residuals (s)

s measures the typical distance between the actual y values and the predicted y values.

high leverage

Points that have much larger or much smaller x values than the other points in a bivariate quantitative data set.

outlier

Individual value that falls outside the overall pattern of a distribution of quantitative data.

influential point

Any point that, if removed, substantially changes the slope, y intercept, correlation, coefficient of determination, or standard deviation of the residuals.