Coursera: Machine Learning (Week 2) Quiz - Linear Regression with Multiple Variables | Andrew NG

 

 Recommended Courses:

1. Coursera: Machine Learning
2. Google Data Analytics Professional Certificate.

1.Linear Regression with Multiple Variables.

Don't just copy & paste for the sake of completion. The solutions uploaded here are only for reference.They are meant to unblock you if you get stuck somewhere.Make sure you understand first.

1. Suppose m=4 students have taken some classes, and the class had a midterm exam and a final exam. You have collected a dataset of their scores on the two exams, which is as follows:
   
   You’d like to use polynomial regression to predict a student’s final exam score from their midterm exam score. Concretely, suppose you want to fit a model of the form , where  is the midterm score and x_2 is (midterm score)^2. Further, you plan to use both feature scaling (dividing by the “max-min”, or range, of a feature) and mean normalization.
   What is the normalized feature  ? (Hint: midterm = 69, final = 78 is training example 4.) Please round off your answer to two decimal places and enter in the text box below.
   

-0.47

2. You run gradient descent for 15 iterations with  and compute after each iteration. You find that the value of  decreases slowly and is still decreasing after 15 iterations. Based on this, which of the following conclusions seems most plausible?
   •  Rather than use the current value of α, it’d be more promising to try a larger value of α (say  = 1.0).
   •  Rather than use the current value of α, it’d be more promising to try a smaller value of α (say  = 0.1).
   •   = 0.3 is an effective choice of learning rate.

2. You run gradient descent for 15 iterations with  and compute after each iteration. You find that the value of  decreases quickly then levels off. Based on this, which of the following conclusions seems most plausible?
   •  Rather than use the current value of α, it’d be more promising to try a larger value of α (say  = 1.0).
   •  Rather than use the current value of α, it’d be more promising to try a smaller value of α (say  = 0.1).
   •   = 0.3 is an effective choice of learning rate.
   • 
     

3. Suppose you have m = 23 training examples with n = 5 features (excluding the additional all-ones feature for the intercept term, which you should add). The normal equation is . For the given values of m and n, what are the dimensions of , X, and y in this equation?
   •  X is 23 × 5, y is 23 × 1, θ is 5 × 5
   •  X is 23 × 6, y is 23 × 6, θ is 6 × 6
   •  X is 23 × 6, y is 23 × 1, θ is 6 × 1
   •  X is 23 × 5, y is 23 × 1, θ is 5 × 1

4. Suppose you have a dataset with m = 1000000 examples and n = 200000 features for each example. You want to use multivariate linear regression to fit the parameters  to our data. Should you prefer gradient descent or the normal equation?
   •  Gradient descent, since it will always converge to the optimal θ.
   •  Gradient descent, since  will be very slow to compute in the normal equation.
•  The normal equation, since it provides an efficient way to directly find the solution.
•  The normal equation, since gradient descent might be unable to find the optimal θ.

5. Which of the following are reasons for using feature scaling?
   •  It is necessary to prevent gradient descent from getting stuck in local optima.
   •  It speeds up solving for θ using the normal equation.
   •  It prevents the matrix  (used in the normal equation) from being non-invertable (singular/degenerate).
•  It speeds up gradient descent by making it require fewer iterations to get to a good solution.

• 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一

                         Machine Learning Coursera-All weeks solutions [Assignment + Quiz]   click here

                                                                                &

                         Coursera Google Data Analytics Professional Quiz Answers   click here

Have no concerns to ask doubts in the comment section. I will give my best to answer it.

If you find this helpful kindly comment and share the post.

This is the simplest way to encourage me to keep doing such work.

Thanks & Regards,

- Wolf