Squares Definition and 400 Threads

I'm doing a replication paper and having a bit of issues. The author uses 2 instruments and has 4 endogenous variables. Since he is under-identified, he runs 4 separate regressions, so that each equation has 1 overidentifying restrictions. I want to extend this and run the four equations as a...

I have the following problem: I have a set of m measurements $\mathbf{\phi}$ and I estimate a set of 3 variables $\mathbf{x}$ The estimated value for $\mathbf{\phi}$ depends linearly on $\mathbf{x}$ : Hx=\Tilde{\phi} The solution through weighted linear least squares is: $\mathbf{x}$ =...

Hi All, So I was just wondering if there is a formula for the number of ways a number can be written as a sum of squares?(Without including negatives, zero or repeats). For example 5=2^2+1^2. (There is only one way for 5). Second question along this line is: In how many ways can a number...

Homework Statement The diagram below shows four congruent circles whose centres are the vertices of the square DEFG and whose circumference touch the sides of an isosceles triangle. Area of triangle ABC is 10000 units square. What is the radius of the circles, to the nearest unit...

a1=22+32+62 a2=32+42+122 a3=52+52+202 Using these, gIve a general term for an such that an is always a perfect square

Homework Statement For all natural numbers, a and b, if a and b are both even, then (a^2+b^2) is not a perfect square. (prove this) Homework Equations The Attempt at a Solution I tried proving by contradiction and got (2s)^2 +(2t)^2 =k^2. which translates to 4s^2 +4t^2=k^2. I...

Homework Statement For some natural N the no of positive integers x satisfying the equation 1! + 2! + 3! + ... + x! = (N)2 is: A)one B)two C)infinite D)none The Attempt at a Solution I have no idea of how to start.. never came across such problems. By trial i have got two values...

Hallo I'm new to this (wonderful) forum, and to SR too... I've a general question about the space time interval invariance. Say we have two points A and B, at rest each other, at distance AB. Now A and B simultaneously in their reference frame emit a flash of light. The space time interval...

noope

The problem states, if c^2 = ab and (a,b) = 1, prove that a and b are perfect squares. ( the notation (a,b) means the GCD of a and b) So i have a lot of thoughts on this problem but i am getting stuck. 1) if c^2 = ab then c(c) = ab which says c divides ab. 2) the only real theorem...

Homework Statement find the limit as x tends to 3 of [sqrt(2x+3)-x] / (x-3) Homework Equations The Attempt at a Solution This is from an old Protter textbook I am working through. I started with the difference of squares which results in [2x + 3 - x^2]/ [(x-3)*sqrt(2x+3)+x]...

Homework Statement Suppose you have a set S of three points in R^2, S1 = {(1, 12), (2, 15), (3, 16)} S2 = {(1, 12), (1, 15), (3, 16)} S3 = {(1, 12), (2, 15), (2, 15)} which you seek to interpolate with the quadratic polynomial p(t) = a_0 + a_1t + a_2t^2. Problem: Least-Squares...

How would one know when to find the least squares approximation?

Need help to prove (or disprove, hope not) this result: Let Q=[q_ij] be a orthogonal matrix (Q^T*Q=Identity) and let Q2 be the matrix of the squares of the entries of Q, that is Q2=[q^2_ij]. I need to prove that Q2 is nonsingular. Been trying with some results about the Hadamard or Schur...

Homework Statement Prove only solution in integers of the equation x2 + y 2 + z2 = 2xyz is x = y = z =0 2. The attempt at a solution Well, using common sense got the idea but don't exactly know how to prove it! Can anyone please help as how to start ...? Thanks!

Homework Statement http://img683.imageshack.us/img683/4744/leastsquares.jpg [PLAIN][PLAIN]http://img149.imageshack.us/img149/4793/graphwd.jpg Homework Equations The Attempt at a Solution So would these be the points? (-41,51),(-22,62),(23,63),(44,24) I'm not too sure how...

Homework Statement for vector space C[-1,1] with L^2 inner product <f,g> = \intf(x)g(x)dx find the best least squares approximation for function x^(1/3) on [-1,1] by a quadratic function q(x) = c0 + c1x + c2x^2 Homework Equations s+r = n <t^s, t^r> = \intt^ndt = { 2/(n+1)...

I need something that I can use to draw a few simple 2D images, that don't have to look pretty. I really mean "draw" (with the mouse) and not generate from a formula, and a minimum requirement is that the program can at least let me try to draw a smooth curve with the mouse and then smooth it...

Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. ABCD*EF=GHJB*KE, and: (EH)2 + (KC)2 = (KH)2

Can you give me a "least squares" example? Assume that, I have a function to estimate like below: f(x) = a3x3 + a2x2 + a1x1 + a0x0 After several experiments I have obtained these (x, f(x)) pairs: (x1, y1) (x2, y2) (x3, y3) (x4, y4) (x5, y5) (x6, y6) How can I estimate a0, a1, a2...

Homework Statement x^2+y^2=z^2 Homework Equations The Attempt at a Solution assume to the contrary that two odd numbers squared can be perfect squares. Then, x=2j+1 y=2k+1 (2j+1)^2 +(2k+1)^2=z^2 4j^2 +4j+1+4k^2+4k+1 =4j^2+4k^2+4j+4k+2=z^2 =2[2(j^2+K^2+j+k)+1)]=2s the...

Is this possible? I've computed a multiobjective least squares solution and want to make it able to be updated recursively but I get stuck at applying the woodbury matrix identity since it's no longer a rank 1 udpate. Are there any derivations of this anywhere or is this not possible? Thanks

Homework Statement Prove that if a prime number is a sum of three squares of different primes, then one of the primes must be equal to 3. Homework Equations The Attempt at a Solution I really have no idea where to start this one.

Homework Statement Disprove or prove the statement that every positive integer is the sum of at most two squares and a cube of non-negative integers.2. The attempt at a solution I'll call the numbers that can be squares a and b. C will be the cube. The easiest way to disprove something is to...

Proving Axiom 1 of all 3 x 3 magic squares. I used summation notation to do so but it is extremely long and cumbersome. I attached the pdf file with the work. Is there a way to do this in a simpler more concise manner?

How would I generalized the set of all 3 x 3 magic squares? I don't know what to do this at all for this.

Hello, I am trying to write an algorithm to calculate the Least Squares Fit Line of a 3D data set. After doing some research and using Google, I came across this document, http://www.udel.edu/HNES/HESC427/Sphere%20Fitting/LeastSquares.pdf (section 2 in page 8) that explains the algorithm for...

Hello, I am trying to write an algorithm to calculate the Least Squares Fit Line of a 3D data set. After doing some research and using Google, I came across this document, http://www.udel.edu/HNES/HESC427/Sphere%20Fitting/LeastSquares.pdf (section 2 in page 8) that explains the algorithm for...

1. Homework Statement Suppose two variables x and y are known to satisfy a relation y=Bx. That is a graph of x vs. y is a line through the origin. Suppose further that you have N measurements (xi,yi)and that the uncertainties in x are negligible and those in y are equal. Prove the best...

I did a least squares fit project for physics and now i have to say the value of G and the slope. I know that slope is m from the equation y = mx+b but how do i determine G?

Let x = 1. Let n = Next Odd Number Let y = Previous Sum x2 = x +3 = 4 = (1+x)2 +5 = 9 = (3+x)2 +n = n+y = (n-2 + x)2 You could make a program to list all the squares without invoking the multiplication function or squaring function using a simple loop. C++ Example: #include...

I am having a problem applying the Least Squares method in the case where I have 2 fundamental solutions and therefore 2 unknown wieghts to find. I=\int_{\Gamma} |\varphi + 1/2|^2 \mathrm{d}s}_{1} + \underbrace{\int_{\Gamma_{in}} |\varphi + 1/4|^2 \mathrm{d}s (im not sure if this...

Alright let's just say (x-2)^2>12, find x can someone tell me what happens to the inequality sign when you take the square of the left hand side to the right hands side? does it swap?

I was wondering if someone could explain how to compute the Least squares fit to a straight line

I was wondering if someone could explain how to compute the Least squares fit to a straight line

Substitute each of the small letters by a different base ten digit from 1 to 9, with a<= b<=c<=d, to satisfy this equation. a2 + b2 + c2 + d2 = e2

I think that this is best suited here as it is linear algebra specific... sorry if I'm wrong. Please look at: I can do parts a,b and c. But I can't do part d. I've been trying to turn it into n independent least squares equations. Let me know if this is not the way to go or you have...

This test question is really boggling me and my math group. Any help would be appreciated. We know that AT*x=AT*b is the setup, but we're not so sure how to approach the problem most effectively. Here's the question: Use the data below to find an approximate formula for the life expectancy in...

Homework Statement For the following data, find the least squares fit of the given form x=1,2,3,4,6 y=14,10,8,6,5 h(x)=ae^x+be^(-x) Homework Equations The Attempt at a Solution So I tried to linearize the equation by taking the natural log of everything...

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=21977&stc=1&d=1258886072 I think my proof is lousy and may be wrong. Please help me with it (= Thanks in advance Homework Equations My proof is of below. The Attempt at a Solution

Homework Statement given the equality a2+b2+c2+d2+e2=f2 prove 2 out of the the 6 variables must be even.Homework Equations can use quadratic residues and primitive roots if it helps but don't think i need them. The Attempt at a Solution assume f is even. then f2 is even. and not all 5 numbers...

Homework Statement Given \epsilon > 0 , show that the unit disc contains finitely many dyadic squares whose total area exceeds \pi - \epsilon , and which intersect each other only along their boundaries. Homework Equations The Attempt at a Solution I've tried to solve this...

Homework Statement Hi, I have to do a project in Fortran based on solving a system. My professor mentioned one idea to me, I am trying to see if this idea is even feasible and some potential ways to progress through it before I submit a project proposal to do it. The problem is based on...

hi, may someone help me to clarify my doubts... in my work, i encounter diracdelta square \delta(x-x_1)\delta(x-x_2) i am not sure what it means... it seems if i integrate it \int dx \;\delta(x-x_1)\delta(x-x_2) = \delta(x_1-x_2) is either zero of infinity. is this correct? thanks

Hi, Given that the radius of a circle is X, and the side length of a square is Y, what is the maximum number of squares you can fill inside this circle, provided that the squares do not overlap? If you know of a general formula or something, can you please tell me the proof or give me a link...

Hello, I am trying to figure out how to fit a plane passing through the origin in \mathbf{R}^3, given a cloud of N points. The points are vectors of the form (x_1^{(k)}, x_2^{(k)}, x_3^{(k)}) , where k stands for the k-th point. I want to minimize the sum of squared distances point-plane. What...

So when using a perfect square I would divide the linear middle term by 2 and put the x in squared ( ) along with that term?

If you know \sqrt{(a^2+b^2)} < \epsilon, do you know a < \epsilon and b < \epsilon? If so, how?

Homework Statement 1) Find all pairs of natural numbers whose squares differ by 75. 2) Find all pairs of natural numbers whose squares differ by 79. 3) Prove that there can only be 1 pair of numbers with a prime number differenceHomework Equations none The Attempt at a Solution from...

I am trying to fit a transformation from one set of coordiantes to another. x' = R + Px + Qy y' = S - Qx + Py Where P,Q,R,S are constants, P = scale*cos(rotation). Q=scale*sin(rotation) There is a well known 'by hand' formula for fitting P,Q,R,S to a set of corresponding points. But I...