A logistic regression model is a model with a binary response variable (like 'agree' or 'don't agree'). It's also possible for logistic regression models to have ordinal or nominal response variables. The mean is the proportion of responses that are 1. The linear probability model is P(y=1) = α + βx. This model often is too simple, a more extended version is:The logarithm can be calculated using software. The odds are:: P(y=1)/[1-P(y=1)]. The log of the odds, or logistic transformation (abbreviated as logit) is the logistic regression model: logit[P(y=1)] = α + βx.To find the outcome for a certain value of a predictor, the following formula is used:The e to a certain power is the antilog of that number.A straight line is drawn next to the curve of a logistic graph to analyze it. β is maximal where P(y=1) = ½. For logistic regression the maximal likelihood method is used instead of the least squares method. The model expressed in odds is:The estimate is:With this the odds ratio can be calculated.There are two possibilities to present the data. For ungrouped data a normal contingency table suffices. For grouped data a row contains data for every count in a cel, like just one row with the number of subjects that agreed, followed by...

Week 4: Logistic Regression Analysis (LRA)LRA can be used when the dependent variable (Y) is binary and the predictors (X1, X2) interval level (or binary). The research question is: Can Y be predicted fromX1and/orX2?Example: Can the passing (1) or failing (0) the MVDA exam (Y) be predicted from the student’s grade on the psychometrics exam (X)?Is there a significant association between grade and passing/failing the exam? (report test statistic, df, and p value)?Here, we look at the Variables in the Equation table at the Wald of the grade. If it’s significant, then yes there is a significant association. An example of how this can be reported: Yes, Wald χ2(1) = 7.090,p=.006Write down the logistic regression equationFor example:if the constant B is -4.200the grade B is: .671Then the equation looks like this:(From now on, sorry for the weird format of the formulas)For what grade is the probability of passing the MVDA exam equal to the probability of failing the MVDA exam?Passing= 50%Failing=50%P=1/2 = In order for to be 1, -4.200+ .671(Grade) has to be equal to 0. This is because e to the power of 0 is 1. So, -4.200 + 0.671(g)=00.671(g)=4.200g=6.259Therefore, the grade where there is an equal chance for passing and failing is 6.259.Calculate the probabilities and odds of passing for X= 0,5, 10X P Odds (rounded up) 0 =0.0148 = = 0.015 5 = 0.3005 = 0.429 10 = 0.9248 =11.5 How to calculate the odds ratio?Example: X P Odds Odds ratio1 .0285 .02931 =1.958 2 .0543 .0574 1.958Therefore, if X increases 1 unit, the odds are...