Which of the following are reasons for using feature scaling?

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

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

C.It speeds up gradient descent by making each iteration of gradient descent
less expensive to compute.

D.It is necessary to prevent the normal equation from getting stuck in local
optima.

1。第 1 个问题

Suppose m=4 students have taken some class, 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:

midterm exam(midterm exam)2final exam
89792196
72518474
94883687
69476178
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 hθ(x)=θ0+θ1x1+θ2x2, where x1 is the midterm score and x2 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 x(1)1? (Hint: midterm = 89, final = 96 is
enter in the text box below.

=  1268/4075 =0.32不过正确答案应该是 (89+72+94+69)/4 = 81
(89-81)/(94-69)= 8/25 = 0.32

point
2。第 2 个问题

You run gradient descent for 15 iterations

with α=0.3 and compute

J(θ) after each iteration. You find that the

value of J(θ) decreases quickly then levels

off. Based on this, which of the following conclusions seems

most plausible?

α=0.3 is an effective choice of learning rate.

Rather than use the current value of α, it'd be more promising to try a larger
value of α (say α=1.0).

Rather than use the current value of α, it'd be more promising to try a
smaller value of α (say α=0.1).

point
3。第 3 个问题

Suppose you have m=14 training examples with n=3 features (excluding the
additional all-ones feature for the intercept term, which you should add). The
normal equation is θ=(XTX)−1XTy. For the given values of m and n, what are the
dimensions of θ, X, and y in this equation?

X is 14×3, y is 14×1, θ is 3×3

X is 14×4, y is 14×1, θ is 4×1

X is 14×4, y is 14×4, θ is 4×4

X is 14×3, y is 14×1, θ is 3×1

point
4。第 4 个问题

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 θ to our data. Should you prefer gradient descent or the normal
equation?

Gradient descent, since (XTX)−1 will be very slow to compute in the normal
equation.

The normal equation, since it provides an efficient way to directly find the
solution.

Gradient descent, since it will always converge to the optimal θ.

The normal equation, since gradient descent might be unable to find the
optimal θ.

point
5。第 5 个问题

Which of the following are reasons for using feature scaling?

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

It speeds up gradient descent by making each iteration of gradient descent
less expensive to compute.

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

It is necessary to prevent the normal equation from getting stuck in local
optima.
3.B  4.A 5.A