Notation Used in this Course

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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