# Notation used in the course {.unnumbered}
- $b_0$ ("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