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The dispersion formula for Fisher's kriterium is: $D_{\tilde y}=\frac {1}{n-k} \sum\limits_{1}^{n} \left[\frac {y_{mi}-y(x_{mi})}{y(x_{mi})}\right]^2$ depending on type of regression model used. $y(x_{mi})$ is the value got from the regression model, all values with "m" subscript are observed values. Then, it is divided by $\sigma^2$ which is a square of a measurement error (with number of degrees of freedom equal to infinity (because is reliable and close to a population dispersion). n - is number of observations, k - degrees of freedom of a regression. What would be degrees of freedom for a linear regression, polynomial regression and what is the common law that defines a degree of freedom of a regression model?

I understand, that a degree of freedom in common is equal to a number of independent elements and k seem to be equal to a number of parameters of a regression model, but I don't have any clear image in my head.

Nikolay Yasinskiy
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Well, I caught it finally. In this case, ad far as we are talking about regression residuals $y_{m_i}−y(x_{m_i})$, number of degrees of freedom is literally the number of variables, so from calculation example I have, if we have a polynome regression like $y = a_1x^2 + a_2x + b$, regression residuals dispersion depends on $3$ variables: $y$, $x^2$, $x$. So, the number of degrees of freedom is $3$. For linear regression it's always $2$ of course. Still one question stays: why $x^2$ is also assumed as a variable, independent from others...

Dominique
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Nikolay Yasinskiy
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