1. K


    i.e. square of 26 n.n = (n-a).(n-a)+(n-a).(2a)+a.a n = square of which we have to find {eg. 26} a = any mnumber before the number whose square...
  2. Z

    Least Squares Problem

    This problem projects b = (b_1,b_2....,b_m) onto the line through a = (1, 1, 1, ....1). We solve m equations ax = b in 1 unknown (by least squares). (a) Solve a_T~a~\hat{x} = a_T~b to show that \hat{x} is the mean (the average) of the b’s. (b) Find e = b - a \hat{x} and the variance ||e||^2...
  3. L

    Algebra Help - Perfect squares

    The quadratic equation: px^2 +15p + 4 = (20 + 3p)x is a perfect square. Find the value(s) of p. Any help would be appreciated :confused:
  4. K

    Least Squares

    Hi, I got this question but I don't know how to solve it: Consider the following optimization problem: sqrt((x1-1)^2+(2*x2+3)^2+x1^2+x2^2-x1*x2) Write down the above problem as the least squares problem and solve it.
  5. agentredlum

    Writing Natural numbers as the sum of 4 squares

    Greetings MMF members and guests. It is a well known result that every Natural number can be written as the sum of $4$ squares. $3$ squares are not enough. (For example , $7$ cannot be written as the sum of $3$ squares) Euler did work on the problem and then Lagrange provided a proof...
  6. C

    Method of Least Squares

    Hi, I've attached the question and my worked solution. I am confident I have the correct least squares straight line of best fit to the data to 2 d.p., but I'm unsure what is being asked in the next part. Am I to sub the xi values into the least squares straight line of best fit to...
  7. N

    Help with least squares estimator

    Hi, I need help with least squares estimator, particularly with how to arrive at the solution show in the image. Thanks!
  8. M

    Least Squares Regression

    If you were to use Least Squares when you have a solution for Ax=b, what would happen? I've tried two examples, but I didn't get an answer I liked, so I assumed I messed them up.
  9. M

    divisors of sum of two squares

    Hi Again, In this thread, I am attempting a proof for the following theorem: every divisor of two squares of coprimes is a sum of two squares. 1. For this, I will start by proving the following: (C1) if n is a sum of two squares and p is a prime divisor who is sum of two squares than n/p is...
  10. M

    Sum of two squares

    Hi, somehow I just cant get this right... (a + R/2)² All I get is.. a² + 2aR/2 + R²/4 And its not correct, whats going on?
  11. M

    Between 2 consecutive squares

    Let A=x^2 B=(x+1)^2 Can you find the first A such as between A and B there 2 numbers powered to 3 (2 cubes)? Keep in mind that y^6 = (y^2)^3 so it is a cube. If it is not possible can you prove it?
  12. I

    How to minimize sum of squares?

    Here is the picture: Imgur: The most awesome images on the Internet What would be the steps for solving this problem? I don't understand which parts I am supposed to differentiate and which parts I am supposed to substitute.
  13. L

    Two squares between near primes?

    Are there ever two natural numbers whose squares lie between successive primes?
  14. G

    The Difference of Two Squares and Perfect Square Trinomials

    36a^3-16a Don't know the steps to solve this. Thanks.
  15. C

    Least squares

    This is the first three steps of matrix steps for least square estimation 1. L = y-Xb)'(y-Xb) 2. L = y'y - b'X'y - y'Xb + b'X'Xb 3. L = y'y - 2b'X'y + b'X'Xb I am struggling to see how you move from step 2 to step 3. It means that b'X'y = y'Xb. How do they equal each other, am I missing...
  16. D

    Squares and Triangles

    A square ABCD has sides of length 2. E and F are the midpoints of the sides AB and AD respectively. G is a point on CF such that 3CG=2GF. What is the area of triangle BEG? Thank You!
  17. G

    log linear weighted least squares application

    Hi, I am trying to fit a curve to a set of data using a weighted least squares approach. The reason I am using the weighted approach is to bias my solution to my more reliable data. I am however having a problem trying to derive the analytical solution to the problem. T curve I am trying...
  18. A

    How to calculate the eq of least squares regression.

    Hello all:)..can someone help me with the following..please?? calculate y on x and x on y using (i).using normal equation (ii).using regression coefficients what are the formula and difference between these two methods..??
  19. X

    Factorising cubics and 2 squares?

    Question: 2(x-y)^3 - 54(2x+y)^3 I got it down to --> -2(215x^3+327x^2y+159xy^2+28y^3) --> -2[(215x^3+28y^3)+(327x^2y+159xy^2)] Maybe there is a better way? I don't know what I got myself into but the answer for this is: -2(5x+4y)(43x^2+31xy+7y^2)
  20. V

    Linearizing a nonlinear least squares model

    I have a nonlinear least squares problem with a set of parameters $\bf{g}$, where I need to minimize the function: $$ \chi^2 = \sum_i \left( y_i - M(t_i ; {\bf g}) \right)^2 $$ The $t_i$ are some independent parameters associated with the observations $y_i$ and the model function has the...