# 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)
**[notation for this is \(\hat{b}_0\) ("b-zero-hat") in the textbook]** - \(\beta_0\) ("beta-zero"): population y-intercept in a regression model
**[\(b_0\) ("b-zero") in the textbook]**

- \(b_1\) ("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)
**[\(\hat{b}_1\) ("b-one-hat") in the textbook]** - \(\beta_1\) ("beta-one"): population slope in a linear regression model
**[\(b_1\) ("b-one") in the textbook]**

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

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

- \(r\): (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 \(\hat{y}\))
**[\(RSS\) (residual sum of squares) in the textbook]** - \(SSTO\): total sum of squares (measures deviations of \(y\) from \(\bar{y}\))
**[\(TSS\) in the textbook]**

- \(MSE\) ("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