Welcome to clinical data management program using SAS In this video we'll be discussing about the concepts of logistic regression what is logistic regression? logistic regression? my dependent variable parenting developed dependent variable using number of independent variables, but unlike linear regression, where in linear regression I had dependent independent variables both were continuous in nature in logistic regression my dependent variable stack promising nature an independent variable can be categorical in nature or continuous in nature and basically in logistic regression, my dependent variable is y is basically calculating the probability of phi equal to even lie state region we are calculating the probability for occurrence of an event and why culty event denotes that is y equals to one and y equals to non event denotes the Y equals to zero and since we are calculating the probability for y equal to event the value of our dependent variable lies between zero and one as it is a probability right.

So, in logistic regression is to predicting the value of the dependent variable y from database Once we calculate the probability of y equal to event, given know why this is the predicate is unlikely deviation the dependent variable is to enrich this dichotomous in nature, that is, it calculates the probability for y equal to event, since probability value lies between zero and one therefore, the value of the dependent variable lies between zero and one where zero denotes the impossible event I want the notes and so when why was one minister shirt even when y equals to zero means is an impossibility. Now let's discuss the standard formalize the regression equation, the standard form guys to revision equation is provided by equals to one is equal to one by one plus exponential exponential means e to the power minus b naught plus b one x one plus EA and y equals to primary device equals to zero is one minus y equals to one that is one by one plus exponential that is e to the power V naught plus b one x one plus E. So, this is the curve which fits regression model this is called an sigmoid curve where any well since we are calculating the probability of gravity of gravity lies between zero and VA to any value below zero does not exist in about one also does not exist.

So, therefore, the Cova sigmoidal nature because gravity is between zero and one. So, here probability equal to one means probability of an event and probability by equal to zero its probability of unknown event here we have considered one independent variable that is X Factor cost that fits illustrate which model is called a sigmoid curve which is the line of best fit or the best fit for a price to decrease. Now, there are different applications of luxury readmission rate risk analytics like where we decide basically whether loans will be given to a person or not if the loan should be given to a person that means an event loan should not be given to a person instead non even sales, whether a particular product will be sold or not, or whether a potential consumer will buy that particular product or not to the potential consumer by then it is an event others synonymous next similarly, technician communication analytics, we also use it in clinical data management and then actually analytics that is measuring the admission rate and many more now, what are the different assumptions of rusty regression what are the different assumptions of this model as follows First is the dependent variable should be dichotomous in nature, there are terms should not be normally distributed, they should they need not be normally distributed, there should be minimal multicollinearity for the independent variables homoscedasticity is not required for logistic regression that is variance narratives may not be constant.

Logistic regression assumes linearity between independent variables is a log of odds. So, there should be a relation a linear relationship between the law or the independent variables. Plus a ration typically requires an adequate sample size. These are the different assumptions. Next, let's discuss about the goodness of fit Felicity regression in order to measure the goodness of fit for ice equation that is to check whether the model is a good fit or not. We do our test called hosmer limb show Goodness of Fit Test where the null hypothesis for this test is the model is a good fit adulterating hypothesis the model is not a good fit.

So, if my P value is greater than my level of significance, which is high percent that is 0.05 then my model is a good fit, that is I will accept null hypothesis or reject. So, the hospital Goodness of Fit Test is a is a Goodness of Fit Test for logistic regression especially for risk prediction models. A Goodness of Fit Test tells us how well your data fits the model pacifically. The historical cost test calculated the observed event rates match the expected event rates in population subgroups. So my nanobot is arranged notice in the model is good fit and alternative hypothesis h1 is the model is not a good fit. Next, let's come to the concept of odds.

What is all odds is the ratio of probability of an event by probability of unknown event according to a standard logistic regression equation probability of an event formula is equal to one by one plus exponential or we can see the expression for probability by equal to one is equal to one by one plus exponential e to the power minus P naught plus b one x one plus EA operability by equal to zero which is one minus probability by equals to one is equal to one by one plus exponential e to the power V naught plus b one x one plus EA. So, all this is if we divide these two expressions distributed by equal to one the probability value to zero, we get after simplifying our expressions we get this that is e to the power V naught plus v one extra. Now, if you take a natural logarithmic transformation on both sides, then ln of all the log of Oz will give you P naught plus the one that is the linear model it will take you along with me transmission our odds then we get back to a linear model and here the assumption that we have discussed before that there should be linearity between the log of parts and independent variables.

This is proved that assumption is proved over here that there should be a linear relationship between the log of auth and independent variables for us to address Next, let's come to the concept of changing offs. So, before it's Can you change the norms. Let me ask you one question. Suppose if I increase in order to explain the concept of engineering You need to first understand this question and solve this question basically, suppose if you increase the value of x x is the independent variable, suppose if I increase the value of my x by one unit, that is my x value becomes x plus one, then how will they all exchange So, all for the variable x is e to the bar d naught plus b one x, if you increase the value of x by one, then the odds value becomes e to the D naught plus d one into x plus one.

So, the new Hots value will be e to the power d one times the original odds value. So, if you increase the value of x by n types that is x becomes n plus n that means, when you odds value will change by the by N D or E to the power n v one k So, that is the concept of change in us. Next comes the concept of odds ratio odds ratio is the ratio of two odds to suppose in order to explain you all the concept of odds ratio we'll be taking an example. Suppose an accident is awkward now the probability for Y equals two One nice accident has occurred and for every device, accident has not occurred and better two types of vision person one is poor vision personalities good vision. Same for the poor budget person the probability of occurrence of accident will be obviously maximum probability by equal to one for this concept I'm traveling to vehicle to zero for a poor wish possibly to obviously, responsible that is a country similarly privately by equal to one that is, for good vision present will be obviously less because the occurrence of accident for a good vision present for everything will be as it is called for and privately by equal to zero for a good mission person is one minus point four 6.6 now all Scala proficient person getting hit by a car is 1.7 5.3.

This would be point seven by point three so that is seven by three is 2.33. And also for a good fishing person getting hit by a car will be point Kobe point six that is two by three that is 0.67. Now what is the odds ratio odds ratio either we can take 2.33 by 0.67. There is an issue towards Either we do ask for a good or we can do a good way of score. Here we are doing our score way or good, which is 24330467 that is 3.48. So the implication of this author issue is that as we move from a good vision person to a poor vision person, the odds of getting hit by increasing by three per query times 3.5 ticks.

Similarly, if you take the reciprocal offered, if you do all good by your score, then you will you can see that it will be point six seven by 2.33. So in that case, we will see that as we move from a poor vision person to a good vision person, the odds of getting hit by a car is increasing by point two eight here just because we are doing poor or poor way as good. So we are it's implied that as you're moving from a good vision person, to a furbishing person, the odds of getting hit by a car is increasing by cheaper Puritans. 3.5 This is a concept of odds ratio. Next, let's discuss the concept of concurrent players discarded Taipei Hong Kong passive face on cases where the probability of an event is greater the probability of an event than discordant pairs discordant pairs of cases where probability of an event is less than probability of unknown even cases where probability of an event is less the probability of a non event and type of cases, the probability of an event is equal to probability of one known event, you should always remember that for all good model, a good logistic regression model, the more of the amount of the concurrent press better is the code.

So in this video, we'll be doing the cure. In my upcoming video, we'll be discussing some of the further concepts or icy regression. We'll be discussing few further concepts and concurrent pairs also. So for now, I'll end this video over here. Thank you, goodbye. see you for the next video.