# ▸ Logistic Regression :

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1. Suppose that you have trained a logistic regression classifier, and it outputs on a new example a prediction $\inline&space;h_\theta(x)$ = 0.2. This means (check all that apply):
• Our estimate for P(y = 1|x; Î¸) is 0.8.
h(x) gives P(y=1|x; Î¸), not 1 - P(y=1|x; Î¸)
• Our estimate for P(y = 0|x; Î¸) is 0.8.
Since we must have P(y=0|x;Î¸) = 1 - P(y=1|x; Î¸), the former is
1 - 0.2 = 0.8.
• Our estimate for P(y = 1|x; Î¸) is 0.2.
h(x) is precisely P(y=1|x; Î¸), so each is 0.2.
• Our estimate for P(y = 0|x; Î¸) is 0.2.
h(x) is P(y=1|x; Î¸), not P(y=0|x; Î¸)

1. Suppose you have the following training set, and fit a logistic regression classifier $\inline&space;h_\theta(x)&space;=&space;g(\theta_0&space;+&space;\theta_1x_1&space;+&space;\theta_2x_2)$.

Which of the following are true? Check all that apply.

1. For logistic regression, the gradient is given by $\inline&space;\frac{\partial&space;}{\partial&space;\theta_j&space;}&space;J(\theta)&space;=&space;\frac{1}{m}&space;\sum_{i=1}^{m}(h_\theta(x^{(i)})-y^{i})x^{(i)}_j$. Which of these is a correct gradient descent update for logistic regression with a learning rate of $\inline&space;\alpha$ ? Check all that apply.

1. Which of the following statements are true? Check all that apply.

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1. Suppose you train a logistic classifier $\inline&space;h_\theta(x)&space;=&space;g(\theta_0&space;+&space;\theta_1x_1&space;+&space;\theta_2x_2)$. Suppose $\inline&space;\theta_0&space;=&space;6$, $\inline&space;\theta_1&space;=&space;-1$, $\inline&space;\theta_2&space;=&space;0$. Which of the following figures represents the decision boundary found by your classifier?
• Figure:

In this figure, we transition from negative to positive when x1 goes from left of 6 to right of 6 which is true for the given values of Î¸.
• Figure:

• Figure:

• Figure:

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Feel free to ask doubts in the comment section. I will try my best to answer it.
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1. Fifth question is wrong

1. Ok. What do you think the correct answer is??

3. Thanks for the response.But simply Not possible.
If you substitute to value of theta1 & theta2 in the equation given in the question, you will get x1=6. If you plot the graph x1=6 line, that line will always be parallel to x2 axis.

4. no ur answer is wrong ..it will be D..THANK ME LATER

6. Hi @Akshay, your answer is correct. I took the rest, and the reason why shivam and ravi say its D is because the question is different. (I got the same question that they got and the answer is D). The question reverses theta 1 = 0 and theta 2 = 1, in which case D is correct. They read the question wrong

7. Thank you Sneha.
This will help many others.

8. is there a discord server for discussion?? or asking questions

2. 2nd question has stupid options which dont make much sense without knowing formula

3. theta =
6
-1
0

y = 1 if 6 + (-1(x1) + (0*x2) => GE(greaterThanEqualTo) 0
6 - x1 => = 0
-x1 => -6
x1 <= (lessThanEqualto) <= 6
therefore the decision boundary is a vertical line where x1=6 and everything to the left
of that denotes y = 1 , while everything to the right denotes y = 0

you don't have to copy somebody's answer it is in the course notes.

1. Thanks for the detailed explanation.

So For other viewers, to avoid the confusion, The correct answer for Que 5 is "A" only.