Changes

:<math>Y = X \beta + \varepsilon</math>

:<math>Y = X \beta + \varepsilon</math>

In the comparison two different models will be matched to the data, <math>\varepsilon</math> contains the size of the error for how well the model and data match. The larger the <math>\varepsilon</math> the worse the match. However, models must be penalized for the number of free parameters (<math>\beta</math>) that they posses. A theoretical linear model with an infinite number of parameters can perfectly explain any data set, but this is not a valuable model. Usually the liner model a statistician is interested in is compared against the [[null hypothesis]] linear model which has fewer free parameters, as such the more complicated model must have a smaller <math>\varepsilon</math> in proportion to the number of free parameters to be [[statistically significant]]. The measurement of free parameters is referred to as the [[degrees of freedom]].

In the comparison two different models will be matched to the data, <math>\varepsilon</math> contains the size of the error for how well the model and data match. The larger the <math>\varepsilon</math> the worse the match. However, models must be penalized for the number of free parameters (<math>\beta</math>) that they posses. A theoretical linear model with an infinite number of parameters can perfectly explain any data set, but this is not a valuable model. Usually the linear model a statistician is interested in is compared against the [[null hypothesis]] linear model which has fewer free parameters, as such the more complicated model must have a smaller <math>\varepsilon</math> in proportion to the number of free parameters to be [[statistically significant]]. The measurement of free parameters is referred to as the [[degrees of freedom]].

[[category:Probability and Statistics]]

[[category:Probability and Statistics]]