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Questions tagged [sums-of-squares]

sum of squares plays an important role in statistical models based on the normal distribution, like ANOVA.

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ANOVA Type II vs Type II SSq for multiple factors

I have pondered type II vs type III sums of squares for some time and looked at posted examples of calculations for 2 main factors (e.g. this very nice page). That is, in the case of a model: X = A + ...
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What is the total sum of squares for these points? [closed]

y = (-2,2,3,4) and x = (3,5,8,12). Lin. Model is y = -2.5 + 0.6x Please explain how you got the answer. Thank you! I am confused on whether I should be calculating based on the x or y values, or ...
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Generalized eta squared

Partial eta-squared are very often used in psychological litterature. As underlined by some authors (e.g., Baguley, 2009; Bakeman, 2005; Olejnik & Algina, 2003), this standardized measure of ...
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Distribution of $(n-2)MSres/\sigma^2$ in simple linear regression

In simple linear regression, it was proved that $(n-2)MS_{RES}/\sigma^2$ follows a $\chi^2_{n-2}$ distribution.In order to prove this,the fact that $e_i$ or $y_i - \hat{y_i}$ follows a Normal ...
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Feature scaling getting high Error Value (sum of squared)

I got a test data set to work on in order to implement feature scaling and get better results with gradient descent. It looks like this: ...
Derivation of SSE(reduced)-SSE(full) = $(C\hat \beta - h)'(C(X'X)^{-1}C)^{-1}(C\hat \beta - h)$
When stating hypothesis in matrix formulation, as H0: $C\hat\beta=h$, $SSE(reduced)-SSE(full)$ can be expressed as: $$(C\hat \beta - h)'(C(X'X)^{-1}C)^{-1}(C\hat \beta - h)$$ How is this result ...
One definition of the Residual Sum of Squares is: $$S_r = (y-X\hat{\beta})^T(y-X\hat{\beta})$$ And I think I understand it. Now I have seen a different definition:  S_r = y^Ty- \hat{\beta}^TX^...