Coursera: Machine Learning-Andrew NG(Week 1) Quiz - Linear Regression with One Variable

These solutions are for reference only.
try to solve on your own
but if you get stuck in between than you can refer these solutions

there are different set of questions ,
we have provided the variations in particular question at the end.
read questions carefully before marking


Linear Regression with One Variable


As J(θ01)=0, y = hθ(x) = θ0 + θ1x. Using any two values in the table, solve for θ0, θ1.

explanation: Setting x = 2, we have hθ(x)=θ01x = 0 + (1.5)(2) = 3

TrueIf θ0 and θ1 are initialized at a local minimum, then one iteration will not change their values.At a local minimum, the derivative (gradient) is zero, so gradient descent will not change the parameters.
FalseSetting the learning rate to be very small is not harmful, and can only speed up the convergence of gradient descent.If the learning rate is small, gradient descent ends up taking an extremely small step on each iteration, so this would actually slow down (rather than speed up) the convergence of the algorithm.
TrueIf the first few iterations of gradient descent cause f(θ01) to increase rather than decrease, then the most likely cause is that we have set the learning rate to too large a valueif alpha were small enough, then gradient descent should always successfully take a tiny small downhill and decrease f(θ01) at least a little bit. If gradient descent instead increases the objective value, that means alpha is too large (or you have a bug in your code!).
FalseNo matter how θ0 and θ1 are initialized, so long as learning rate is sufficiently small, we can safely expect gradient descent to converge to the same solutionThis is not true, depending on the initial condition, gradient descent may end up at different local optima.

other options which can come in above question 4:
TrueIf the learning rate is too small, then gradient descent may take a very long time to converge.If the learning rate is small, gradient descent ends up taking an extremely small step on each iteration, and therefor can take a long time to converge
FalseEven if the learning rate α is very large, every iteration of gradient descent will decrease the value of f(θ01).If the learning rate is too large, one step of gradient descent can actually vastly "overshoot" and actually increase the value of f(θ01).
FalseIf θ0 and θ1 are initialized so that θ01, then by symmetry (because we do simultaneous updates to the two parameters), after one iteration of gradient descent, we will still have θ01.The updates to θ0 and θ1 are different (even though we're doing simulaneous updates), so there's no particular reason to update them to be same after one iteration of gradient descent.

FalseFor this to be true, we must have y(i)=0 for every value of i=1,2,…,m.So long as all of our training examples lie on a straight line, we will be able to find θ0 and θ1) so that J(θ01)=0. It is not necessary that y(i) for all our examples.
FalseGradient descent is likely to get stuck at a local minimum and fail to find the global minimum.-
FalseFor this to be true, we must have θ0=0 and θ1=0 so that hθ(x)=0If J(θ01)=0 that means the line defined by the equation "y = θ0 + θ1x" perfectly fits all of our data. There's no particular reason to expect that the values of θ0 and θ1 that achieve this are both 0 (unless y(i)=0 for all of our training examples).
TrueOur training set can be fit perfectly by a straight line, i.e., all of our training examples lie perfectly on some straight line.-

other options which can come in above question 5:

FalseWe can perfectly predict the value of y even for new examples that we have not yet seen. (e.g., we can perfectly predict prices of even new houses that we have not yet seen.)-
FalseThis is not possible: By the definition of J(θ01), it is not possible for there to exist θ0 and θ1 so that J(θ01)=0-
TrueFor these values of θ0 and θ1 that satisfy J(θ01)=0, we have that hθ(x(i))=y(i) for every training example (x(i),y(i))-

variations in 2nd question:

2.For this question, assume that we are using the training set from Q1.
Recall our definition of the cost function was 
What is ? In the box below,
please enter your answer (Simplify fractions to decimals when entering answer, and ‘.’ as the decimal delimiter e.g., 1.5).

variations in 3rd question:

3. Suppose we set θ0=−1,θ1=0.5. What is hθ(4)?


Setting x = 4, we have hθ(x)=θ01x = -1 + (0.5)(4) = 1

3.Suppose we set  = −2,  = 0.5 in the linear regression hypothesis from Q1. What is ?


Setting x = 6, we have hθ(x)=θ01x = -2 + (0.5)(6) = 1

variations in 4th question:

reference : coursera