Regression and correlation
Two-variable vocabulary: fitting a line, reading residuals, and what r and r-squared report.
8 terms
Coefficient of determination (r²)The coefficient of determination, r-squared, is the fraction of the variation in the response variable that the regression line explains, from 0 to 1.Correlation coefficientThe correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables, always between -1 and 1.ExtrapolationExtrapolation is using a regression line to predict outside the range of x-values the data covered, where the pattern may no longer hold.Influential pointAn influential point is an observation that, if removed, would markedly change the regression line's slope, intercept, or correlation.Least-squares regression lineThe least-squares regression line is the straight line through a scatterplot that makes the sum of the squared residuals as small as possible.ResidualA residual is the difference between an observed y-value and the value the regression line predicts for it: observed minus predicted.Residual plotA residual plot graphs the residuals against the explanatory variable or predicted values, used to check whether a line fits the data well.Slope of a regression lineThe slope of a regression line is the predicted change in the response variable for each one-unit increase in the explanatory variable.