How to interpret the coefficients for logistic regression

Logistic regression coefficient interpretation. The logistic regression is given by. [math]\pi_i=Pr(Y_i=1|X_i=x_i)=\dfrac (\beta_0+\beta_1 x_i)> (\beta_0+\beta_1 x_i)> \tag [/math] By algebraic manipulation, the logistic regression equation can be written in terms of an odds ratio for success. [math]\begin \text (\pi_i)&=\text \left(\dfrac \right)\\ &= \beta_0+\beta_1 x_i\\ &= \beta_0+\beta_1 x_ + \ldots + \beta_k x_ \\ \end \tag [/math] We can interpret the logistic regression in three ways. Based on the coefficient sign : The equation 1 shows the relation between the probabilities of class i and the logistic regression coefficient. If the coefficient is positive then increasing X will be associated with increasing p(X). If the coefficient is negative then increasing X will be associated with increasing p(X). Odd : The odd of success is defined as ratio of probability of success to probability of failure. If p is equal to 0.8, then the above equation becomes. The odd is 4 which means that odd of success is 4 to 1. We knew that logistic regression gives log odd. If the [math]\beta_ [/math] value is 1.6, it means that 1 unit change in [math]X_ [/math] while others independent variables are at same level, produces 1.6 unit change in log of the odd. If we take exponential for log odd , we will get odd value. Odd ratio: Odd ratio is defined as ratio of one odd divided by another. We usually use odd ratio to study the effect of treatment on outcomes. The Odd ratio represents the odds that an outcome will occur given a particular treatment, compared to the odds of the outcome occurring in the absence of that treatment. Odd Ratio = 1 Treatment doesn’t affect the odds of outcome Odd Ratio [math]\geq [/math] 1 Treatment increases the odd of outcome Odd Ratio [math]\leq [/math] 1 Treatment decreases the odd of outcome.