# Notation Used in this Course

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

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