# squares

1. ### squares

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. ### 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 bâ€™s. (b) Find e = b - a \hat{x} and the variance ||e||^2...
3. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### Sum of two squares

Hi, somehow I just cant get this right... (a + R/2)Â² All I get is.. aÂ² + 2aR/2 + RÂ²/4 And its not correct, whats going on?
11. ### 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. ### 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. ### Two squares between near primes?

Are there ever two natural numbers whose squares lie between successive primes?
14. ### The Difference of Two Squares and Perfect Square Trinomials

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