Definition: Total sum of squares
Index: The Book of Statistical Proofs ▷ Statistical Models ▷ Univariate normal data ▷ Multiple linear regression ▷ Total sum of squares
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Metadata: ID: D37 | shortcut: tss | author: JoramSoch | date: 2020-03-21, 21:44.
Definition: Let there be a multiple linear regression with independent observations using measured data $y$ and design matrix $X$:
\[\label{eq:mlr} y = X\beta + \varepsilon, \; \varepsilon_i \overset{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0, \sigma^2) \; .\]Then, the total sum of squares (TSS) is defined as the sum of squared deviations of the measured signal from the average signal:
\[\label{eq:tss} \mathrm{TSS} = \sum_{i=1}^n (y_i - \bar{y})^2 \quad \text{where} \quad \bar{y} = \frac{1}{n} \sum_{i=1}^n y_i \; .\]- Wikipedia (2020): "Total sum of squares"; in: Wikipedia, the free encyclopedia, retrieved on 2020-03-21; URL: https://en.wikipedia.org/wiki/Total_sum_of_squares.
Metadata: ID: D37 | shortcut: tss | author: JoramSoch | date: 2020-03-21, 21:44.