In this lecture we will consider the coefficients and their interpretation.
I'll take a bit of a mathematical approach but it should not be too hard to follow no matter your background.
First what was the logic model logic model for the admittance regression we created.
Is log of Pi divided by 1 minus pi equals minus sixty nine point nine one plus zero point zero for two
times as a T.
PI here refers to the probability of an event occurring while 1 minus pi to the probability of the event
not occurring.
The fraction of these two is a very popular concept odds as we explained earlier.
All right.
So from the regression summary it seems that our model is basically log of the odds equals minus sixty
nine point nine one plus zero point zero for two times S8.
Let's go through the process of interpreting this result first.
I'll take two S.A.T. scores as 81 and 82.
If we plug them in we would get two equations one for each of them log of odds two equals minus sixty
nine point nine one plus zero point zero for two times S8 to log of odds one equals minus sixty nine
point nine one plus zero point zero for two times.
Sh t 1.
Now let's create their difference log of odds.
Mine is log of odds one equals zero point zero for two times t 2 minus sh t 1 in brackets.
Looks much better doesn't it.
Now the difference between the logs is the log of the quotient of their arguments.
Therefore log of odds to divided by odds one equals zero point zero for two times as say two minus sh
t 1 in brackets OK.
Now let's make a difference in the S.A.T. score of 1.
So s 82 minus one equals one log of odds two divided by odds one equals zero point zero for two times
1 or 0.04 2.
To solve this equation we must take the exponential of the two sides as the exponential of log of X
equals x by definition.
In this way we will simplify the expression further in the end.
We get odds to divided by odds one equals e to the power of zero point zero for two or one point zero
forward to.
This can be rearranged to odds to is one four point two percent of odds one or odds two is four point
two percent higher than the odds one right.
So when the score increases by 1 The odds of admittance increases by 4.2 percent.
This formula we just arrived at.
Irrespective of the S.A.T. score it only takes into account the size of the difference.
Therefore we can derive the general rule for a unit change in a variable.
The change in the odds equals the exponential of the coefficient.
That exactly is what provides us with a way to interpret the coefficients of a logistic regression.
Good but what about a difference in S.A.T. scores of 10 points.
We can use the same approach to find that the log of odds two divided by odds one equals zero point
zero for two times 10 or 0.4 to doing the math.
We get that the odds increase by 52 percent.
What about getting 100 points or more on the S.A.T..
You are in for 66 times higher odds.
Incredible.
These are the basics of co-efficient interpretation.
They are not super intuitive but that's how it works.
Thanks for watching.