Notation Used in this Course

Notation used in the course.

\(b_0\) ("b-zero"): estimated sample y-intercept in a linear regression model (more generally, estimated value of \(y\) when all the predictors equal zero)
\(\beta_0\) ("beta-zero"): population y-intercept in a regression model

\(b_1\) ("b-one"): estimated sample slope in a linear regression model (more generally, estimated sample change in \(y\) for a one-unit increase in the corresponding predictor, holding all other predictors constant)
\(\beta_1\) ("beta-one"): population slope in a linear regression model

\(e_i\): i-th (sample) prediction error (or residual error), equal to \(y_i-\hat{y}_i\)
\(\epsilon_i\) ("epsilon-i"): i-th (population) error, equal to \(y_i-\mbox{E}(Y_i)\)

\(i\): index for the i-th obeservation or experimental unit
\(n\): sample size (total number of observations)
\(p\): number of regression coefficients in a linear regression model (including the intercept), which means there are \(p-1\) predictor terms.

\(r\): (Pearson) correlation coefficient between two quantitative variables
\(r^2\) ("r-squared"): coefficient of determination in a simple linear regression model, equal to \(SSR\)/\(SSTO\)
\(R^2\) ("R-squared"): coefficient of determination in a multiple linear regression model, equal to \(SSR\)/\(SSTO\)
\(SSR\): regression sum of squares (measures deviations of \(\hat{y}\) from \(\bar{y}\))
\(SSE\): error sum of squares (measures deviations of \(y\) from \(\hat{y}\))
\(SSTO\): total sum of squares (measures deviations of \(y\) from \(\bar{y}\))

\(MSE\) ("mean square error"): (sample) mean square prediction error (or residual error)
\(S\): regression (residual) standard error (square root of MSE)
\(\sigma^2\) ("sigma-squared"): (population) common error variance in a linear regression model

\(x\): a predictor, explanatory, or independent variable in a linear regression model
\(\bar{x}\) ("x-bar"): sample mean of \(x\)

\(y\): the response, outcome, or dependent variable in a linear regression model
\(\bar{y}\) ("y-bar"): (univariate) sample mean of \(y\) (ignoring any predictors)
\(\hat{y}\) ("y-hat"): predicted or fitted value of \(y\) in a linear regression model (i.e., accounting for the predictors)
\(\mbox{E}(Y)\) or \(\mu_Y\) ("expected value of Y"): population mean of Y in a linear regression model