logi.R

## linear regression
ols <- lm(speed ~ dist, data = cars)
olsCoef <- ols$coefficients

# prediction is made by X * beta or beta_0 + beta_1*x_1+ ... + beta_k*x_k
olsX <- model.matrix(speed ~ dist, data = cars)
olsPred <- olsX %*% olsCoef

as.vector(head(olsPred))
[1]  8.615041  9.939581  8.946176 11.926392 10.932987  9.939581

head(predict(ols, newdata = cars))
1         2         3         4         5         6 
8.615041  9.939581  8.946176 11.926392 10.932987  9.939581 

## logistic regression
library(logistf)
data(sex2)
lg <- logistf(case ~ age+oc+vic+vicl+vis+dia, data = sex2)
lgCoef <- lg$coefficients

# prediction is made by g(X * beta) or g(beta_0 + beta_1*x_1+ ... + beta_k*x_k) - g() is a link function, search canonical link function of logistic regression
lgX <- model.matrix(case ~ age+oc+vic+vicl+vis+dia, data = sex2)
lgPred <- 1/(1+exp(-lgX %*% lgCoef))

as.vector(head(lgPred))
[1] 0.3389307 0.9159945 0.9159945 0.9159945 0.9159945 0.9159945

head(lg$predict)
[1] 0.3389307 0.9159945 0.9159945 0.9159945 0.9159945 0.9159945

# prediction on new data - different prediction if different data is added
newSex <- sex2[3:4,]
lgXNew <- model.matrix(case ~ age+oc+vic+vicl+vis+dia, data = newSex)
lgPredNew <- 1/(1+exp(-lgXNew %*% lgCoef))
as.vector(lgPredNew)
[1] 0.9159945 0.9159945