Question 1
The screen mentions: We won't dive into the math and the steps required to fit a logistic regression model to the training data in this mission
Can you please guide me to a resource (apart from Wikipedia) which explains these concepts in a simple but detailed manner?
To be more specific something that covers:

The cost function for Logistic regression

Optimization process to find the parameters for best fit

Question 2
Also in logistic regression probability is modelled as exp(t)/(1+exp(t)
What is the relationship between t and the independent variables (function or equation)?

As show in image, you will calculate perpendicular distance from hyper plane. This distance is a t or raw score as you mention in formula.

Once you convert to probability, it will be class 0 if probability is <0.5 and class 1 if probability is >0.5
Here is sample code for perpendicular distance.

import numpy as np
# Vector multiplication
# Given a hyperplane w in augmented form ([b, w1, w2])
# a test case x in augmented form also ([1, ...])
x=[1, 0,4]
w=[-12, 3, 4]
perpendicular_distance = np.dot(x, w)
perpendicular_distance

Thanks for your response. But still need some clarity on following: Question 1
The screen mentions: We won't dive into the math and the steps required to fit a logistic regression model to the training data in this mission
Can you please guide me to a resource (apart from Wikipedia) which explains these concepts in a simple but detailed manner?
To be more specific something that covers:

The cost function for Logistic regression

Optimization process to find the parameters for best fit

Question 2
Also in logistic regression probability is modelled as exp(t)/(1+exp(t)
What is the relationship between t and the independent variables (expressed in form of a function or equation)?

If you would like to understand logistic regression in detail, then I suggest watching this playlist:

If you just want an explanation for the cost function, then I would suggest this video:

Optimization process to find the parameters for the best fit NOTE: This is a very long video

I asked this question to one of our content authors and here is the response:

The regression equation is y = f(X) where X is the independent variables and y the dependent one.

In the logistic regression (for two classes 1 and 0) we want to decide when y is equal to 1 or 0 that why we use the sigmoid function exp(y)/(1+exp(y))

For your equation t = y = f(X), so my answer to the question is t is the outcome of the combination of the independent variables through f