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

# ▸ Linear Regression with Multiple Variables :

- 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

- 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?

- 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?

- 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, Î¸ is 5 × 5
- X is 23 × 6, y is 23 × 6, Î¸ is 6 × 6
- X is 23 × 6, y is 23 × 1, Î¸ is 6 × 1

X has m rows and n+1 columns (+1 because of the term). y is m-vector. is an (n+1)-vector

- X is 23 × 5, y is 23 × 1, Î¸ is 5 × 1

- 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 Î¸.
- Gradient descent, since will be very slow to compute in the normal equation.

With n = 200000 features, you will have to invert a 200001 x 200001 matrix to compute the normal equation. Inverting such a large matrix is computationally expensive, so gradient descent is a good choice.

- 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 Î¸.

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- Which of the following are reasons for using feature scaling?
- It is necessary to prevent gradient descent from getting stuck in local optima.

The cost function for linear regression has no local optima.

- It speeds up solving for Î¸ using the normal equation.

The magnitute of the feature values are nsignificant in terms of computational cost.

- It prevents the matrix (used in the normal equation) from being non-invertable (singular/degenerate).

Feature scaling has nothing to do with matrix inversion.

- It speeds up gradient descent by making it require fewer iterations to get to a good solution.

Feature scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features takes on much larger values than he rest.

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