STATISTICS Course
Logistic regression
If $Y \in [0,1]$, then you may use the Logistic regression. The left of the formula is changing a bit, while the right-side will not.
@ \log(\frac{P(X=n)}{1-P(X=n)}) = a + b X + c Z @
You may notice that there are no residuals anymore.
Simple logistic regression
You will use the function glm
.
# regression Y = a + b * X
# Y = quantitative variable
# X = quantitative/qualitative variable
model <- glm(Y ~ X, data=ech, family="binomial")
# or
model <- lm(ech$Y ~ ech$X, family="binomial")
# check the result table
summary(model)
Multiple logistic regression
# regression Y = a + b * X + c Z
model <- glm(Y ~ X + Z, data=ech, family="binomial")
Results
You will need to evaluate exp(b)
if you want to get b'
value. Then b'
is the same as the b
you know in linear regression.
If you want all of them, then use
exp(coefficients(model))
If you are using drop1
, then the syntax changed a bit to
drop1(model, .~., test="Chisq")
Conditions
If we are considering $|X|$ equals to
- 1: if the variable is a quantitative or binary variable
- else the number of levels minus 1
length(levels(qual))-1
Then the condition for $Z = a + bX + cT$
- $(|X|+|Z|+|T|) * 5 \le n$
- or better $(|X|+|Z|+|T|) * 10 \le n$w