Starnes, UPDATED The Practice of Statistics, 6e, Chapter 3

Response variable

Measures an outcome of a study.

Explanatory variable

May help predict or explain changes in a response variable.

Scatterplot

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 set appears as a point in the graph.

positive association

Two variables have a positive association when values of one variable tend to increase as the values of the other variable increase.

negative association

Two variables have a negative association when values of one variable tend to decrease as the values of the other variable increase.

no association

There is no association between two variables if knowing the value of one variable does not help us predict the value of the other variable.

Correlation 𝓇

For a linear association between two quantitative variables, the correlation 𝓇 measures the direction and strength of the association.

Regression line

A 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 (pronounced “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.

Residual

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

y intercept, Slope

In the regression equation ŷ = a + bx — a is the "y intercept", the predicted value of y when x = 0; b is the "slope", 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 on the horizontal axis.

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.

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, r² measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.

high leverage

Points with high leverage in regression have much larger or much smaller x values than the other points in the data set.

outlier

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

influential point

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