a5.R

sigmoid = function(z)
{
  return(1/(1 + exp(-z)))
}

cost = function(T)
{
  h = sigmoid(X%*%T)
  m = nrow(X)
  J = (1/m) * sum((-Y*log(h)) - (1-Y)*log(1-h))
  return(J)
}

init = rep(0,ncol(X))

#Get the optimal theta values
theta = optim(par=init,fn=cost)

#Create a test matrix and append 1 to it.
Z = as.matrix(test[,-6])
Z = cbind(1,Z)

#Predicted values
pred = sigmoid(Z %*% theta$par)

#From the graph, for all predictions greater than 0.7 ==> 1 else 0
pred[pred>=0.7] = 1
pred[pred<0.7] = 0
pred = factor(pred)
plot(pred)

#Predict R-sqaured
perf(pred,test$Occupancy)

#Output
#[1] 0.9426025