MVDA - logistic regression analysis

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=.006

Write down the logistic regression equation

For example:

if the constant B is -4.200

the grade B is: .671

Then 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)=0

0.671(g)=4.200

g=6.259

Therefore, 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, 10

X                      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 ratio

1                   .0285           .02931          =1.958

2                   .0543            .0574            1.958

Therefore, if X increases 1 unit, the odds are going to increase by x 1.958 (times 1.958).

What is the odds ratio of X of an increase of 3 units?

In this case as our odds ratio is 1.958à 1.958³= 7.5