Hello fellow learners,
Could someone please explain the following? In the video, we are given the value of w, 0.5, but I’m struggling to understand why it is then divided by 1 in both cases, the plot in the middle and the one on the right-hand side.
I have attached a screenshot from the video lecture for reference.
Additionally, see the link to the video here: https://www.coursera.org/learn/machine-learning/lecture/1Z0TT/cost-function-formula
Thanks!
I do not se a division there the yellow 1 means if variable x changes by 1 unit, we need to find how much does the output f(x) change, which actually equals to the slope. So another way to say is:
slope = (f(x+1)-f(x))/(x+1-x) = (f(x+1)-f(x))/1
Thanks gent.spah. Here’s an excerpt of that part of the video in case you couldn’t watch it. I bolded the part where 0.5 is divided by 1 for convenience.
“As a second example, if w is 0.5 and b is equal 0, then f of x is 0.5 times x. When x is 0, the prediction is also 0, and when x is 2, then the prediction is 0.5 times 2, which is 1. You get a line that looks like this and notice that the slope is 0.5 divided by 1. The value of w gives you the slope of the line, which is 0.5. Finally, if w equals 0.5 and b equals 1, then f of x is 0.5 times x plus 1 and when x is 0, then f of x equals b, which is 1 so the line intersects the vertical axis at b, the y intercept. Also when x is 2, then f of x is 2, so the line looks like this. Again, this slope is 0.5 divided by 1 so the value of w gives you the slope which is 0.5.”
To me it seems uncessary to make that division, given that we already know the value of w.
It’s just in that specific example where the slope happens to already be known, so division by 1 doesn’t change anything.
In general, the slope isn’t going to be known in advance. So the horizontal delta isn’t going to necessarily be 1. In fact, the whole purpose of machine learning is to learn what the best ‘w’ values are.
Thank you!
