Logistic regression coefficients

Link: Logistic regression

Continuous variable §

It’s more close to the linear regression.

Transform scale to log §

1. Transform the probablitity of x to log(odds of x)
2. Get a line that looks similar to linear model
3. The line represents the fitted coefficients in terms of log

Interpret the result of logistic regression coefficients §

• Z-value
• P-value

Discrete variable §

We can use t-test from linear model and apply it to logistic regression.

1. Transform the probablitity of x to log(odds of x)

2. Get log(odds gene_nor)

3. Get log(odds gene_mut)

4. Get coefficients:

   $$log1\cdot {\beta }_1+(log2-log1)\cdot {\beta }_2$$

   log1 and (log2-log1) are the coefficients.

   Alternative form:

   $$log1\cdot {\beta }_1+log(\frac{oddsgen{e}_{mut}}{oddsgen{e}_{nor}})\cdot {\beta }_2$$

   the latter is also called log(odds ratio)