Probability and Odds Taking the natural logarithm of each side of the odds equation yields the following A probability is the likelihood that a given event will occur. It is the frequency of a given outcome divided by the total number of all possible outcomes +bx a definition of "odds"is the likelihood of a en event occurring, compared to the likelihood of the same event not occurring The above equation has the logit o on the left-side bo+b The logit is a linear Probabi bility p=1 bo+bx hn bo+br function of the X bother The probability is Odds a non -inear 1+eo+x function of the X ariables9 17 Probability and Odds • A probability is the likelihood that a given event will occur. It is the frequency of a given outcome divided by the total number of all possible outcomes. • A definition of “odds” is the likelihood of a given event occurring, compared to the likelihood of the same event not occurring. 18 Probability Odds 10 19 Taking the natural logarithm of each side of the odds equation yields the following: The above equation has the logit on the left-side 20 The logit is a linear function of the X variables The probability is a non-linear function of the X variables