1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Caclulus III problem involving mean.

  1. Apr 27, 2014 #1
    http://i.imgur.com/DkYMylb.png, probably easier to understand than me trying to type it out.



    so far I tried exapanding the (y_i - y(x_i))^2 and and then subbing in y_i = ax + b. This gives me part of the answer but i'm not sure if it's legal. I'm generally struggling to find a workable relationship between yi, y and y(bar), same for x.

    If nothing else, I could use some clarification as to what the y is (y_i - y(x_i))^2. I thought maybe it was like f(x) but if that's not the case, what would it be if not y_i?

    Thanks for your help.
     
    Last edited: Apr 27, 2014
  2. jcsd
  3. Apr 27, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The problem is to find the equation of the straight line, y= ax+ b, that is "closest" (in the "least squares" sense) to the given point. That is what "[itex]y(x_i)[/itex]" is: the value of that function at [itex]x_i[/itex]. [itex]y(x_i)= ax_i+ b[/itex].

    No, you do not substitute [itex]ax+ b[/itex] for [itex]y_i[/itex]. "[itex]y_i[/itex]" is the given y value of the ith point.
     
  4. Apr 27, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It is saying that ##E(a,b) = \sum_{i=1}^n ( y_i - a - b x_i)^2.##
     
  5. Apr 27, 2014 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is not asking you to find the line of best fit. Just expand ##E(a,b)## out, use the definition of ##\bar z## (for ##z## whatever variable you need) and see if you don't get the answer. (Also note that Ray inadvertently left off the ##\frac 1 n## in his formula above in post #3 ##E(a,b) =\color{red}{\frac 1 n} \sum_{i=1}^n ( y_i - a - b x_i)^2##).
     
    Last edited: Apr 27, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Caclulus III problem involving mean.
  1. Calc III problem (Replies: 4)

Loading...