Chapter 3

Total sum of squares (TSS)

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Jan 14, 2021

Chapter 3

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Total sum of squares (TSS)

$$\sum_i (y_i - \overline{y})^2$$

measures total variance in the response \(Y\)

\(R^2\) statistic

$$\frac{\text{TSS} - \text{RSS}}{\text{TSS}} = 1 - \frac{\text{RSS}}{\text{TSS}}$$

measures the proportion of variability in \(Y\) that can be explained using \(X\)

Residual sum of squares (RSS)

$$\sum_i e_i^2$$

where \(e_i = y_i - \hat{y}_i\)

Residual standard error (RSE)

Estimate of \(\sigma\),

$$\sqrt{\frac{\text{RSS}}{n-2}}$$