The odds are definend as the probability of success of a certain event over the probability
of failure for istances hypotise that we want to know the odds using a dice with 6 faces the
results is 4 this the odds will be 1/5 as there will be only one Probability of success over 5
of failure
The odds Ratio is the odds of a certain events over the odds of another one
θ the value of theta for which two Variables are considered to be dependent are the closer
dependent on the likelihood function, in general the highest the likelihood function is the
higher will be the correlation
Logit is the quantile of a logistic regression and it’s define at ln(p/1-p) where p is the
success probability
The formula for a logistic regression is esp(B0+B1X)/(1+esp(B0+B1x), where B0 is the
intercept while B1 is the parameter of correlation, the highest is B1, the highest will be the
probability of a certain thing to happen, in this case B1> 0 the two variables will be positive
correlated B1< they will be negatively correlated
The relative change in odds is the change in how much the odds change, using a logistic
regression, following a change in X it’s evaluated in the following ways:
1) (esp(b1Δx)-1)%
2) B1(Esp(B0+B1X)* Δx
We can derive the predictor value in so that there is an equal of both success and failure
probability imposing: esp(B0+B1X)/(1+esp(B0+B1x) = 0.5, which leads to B0+B1x = 0;
x =-B0/B1
We can derive the confidence interval for the relative odds using the second expression
and building a confidence interval for both X and B1