It's because $a_r+b_r= \frac a {ab} + \frac b {ab} = \frac {a+b} {ab} = \frac {a+b} {(a+b)/2} = 2$. So, since $b_r = 2-a_r$, relationship between $a_r$ and $b_r$ is: linear negative fully deterministic


If by "normalization" you mean "scaling" than the idea behind this procedure is to ensure that all your variables lie in the same range and have the same importance for the model. For example, if you measure your distance in feet and the velocity in m/h - the influence that distance will have would be roughly 0.3 of the influence that the velocity will ...


Just some background first: For the probit model the estimated parameter $\beta$ and the error term $\epsilon$ within the context of $Pr(\frac{\epsilon_i}{\sigma} < x_i \frac{\beta}{\sigma})$ is assumed to have a standard deviation $\frac{\epsilon}{\sigma} = 1$, on the other hand for the logit model the same standard deviation $\frac{\epsilon}{\sigma} = \...

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