I'm in the beginning of my machine learning course and I'm stuck at a quiz. A set of questions are setup like the following...
Linear Regression Graph (Quadratic)
Possible answers are (Select all that apply):
w0
w1
w2
None of the above
It won't let me embed images yet so you have to click the link to see it. I'm faced with a set of the same question, each using a differently positioned line in the graph. I've received the following advice...
Let's say f(x) = x, if you plot a graph with x as horizontal line and f(x) as vertical line, what you get is 45º line start at (0,0). The result is because when x=1, f(x)=1. so all the points will be (0,0),(1,1),(2,2)...
Let's say f(x)= 2+x, you still get the same 45º line except the position of the line move up by 2 unit[(0,2),(1,3),(2,4),...], because if x=0, f(x)= 2+0, and so on. Now if we swap '2' with variable, like this f(x) = a +x, a will be the factor to decide on the position of the line(the video say something about the position at around 1:50˜ish).
Lat's say f(x)=2x, if you plot it into graph you will get [(0,0),(1,2),(2,4),(3,6),...]. It is still a straight line but the degree of the slanting line is different now. So same case, if swap '2' with variable into f(x)=bx, b will be the factor of the slant.
Let's say f(x)=xˆ2(square), you will get curve line(google quadratic). simply plot the graph you will get [(0,0),(1,1),(2,4),(3,9),(4,16),...]. So when there is s curve line, that means there must be some ˆ2 somewhere in the formula. Additionally f(x)= xˆ2 can also be f(x)= 1*(xˆ2), and again if we swap '1' with variable, we will get f(x)= c*(xˆ2).
The last critical point is 0. so anything multiply 0 will be 0.
This is as far as I can explain. Now, try to put everything together and you will see what how the formula related to the graph.
Here's another tip I received...
First off, completely ignore the blue dots, they're just noise. Concentrate on the green line.
Basically it's asking you how to produce that green line/curve.
So the green line is plotted with an x and y values. The x value is always the value going along the vertical axis (0, 1, 2, 3, etc). And the y is the answer to the equation f(x) = etc.
Looking at the equation we need to figure out whether to set w0 and/or w1 and/or w2 to 0. As each one controls how the green line is drawn.
I worked something like this if x = 0, which of the w values would I need to set to 0 to get the starting point. Then I asked the question, which w value would I need to set to 0 to draw either a straight line, or curved line.
But I'm still having trouble understanding how 0 is fitted to w0, w1,or w2. The tips I've gotten don't seem to explain it to the level of detail that makes it intuitive enough for me. I have to get past this though. If I could just get past this initial point I shouldn't have a problem with the rest of my regression work.
Any help in clarifying every aspect of this problem (In simplified terms) would be greatly appreciated.