Squares Definition and 400 Threads

Homework Statement I had to make a Linear Least Squares Excel template for my first week's Physics lab to analyze linear data for the rest of the semester. All of my values come out correctly, except the standard deviation values. I was wondering if someone could take a look at my template and...

Homework Statement If a, b and c are positive integers with (a,b) = 1 and c2 = ab, show that each of a and b is the square of an integer. I've been staring at this problem for a while now and I've got not clues. I don't see the relation between a and b being relatively prime and the rest...

Please help! I'm stuck on modeling the function for the # of toothpicks in the nth figure. Thank you so much. Renee

Hello, Let me get right to my problem. I have an experimental distribution and a single-parameter theoretical distribution. I want to find the value for the best fit theoretical distribution that agrees with my experimental data for the bulk of the distributions (the tails of my...

Hi everyone given the system of equations A1Cx + B1Cy + C1Cz = D1 A2Cx + B2Cy + C2Cz = D2 A3Cx + B3Cy + C3Cz = D3 I need to solve for Cx, Cy, Cz All other variables are known and constants. However all other variables (A,b,c,d) come from experimentally measured data and thus I cannot...

I am trying to solve how an integer is simultaneously that is simultaneously a square and a cube number must be either of the form 7k or 7k+1 and I am failing when i work (7k+2)^2, even (7k+3)^2....Can i interpret 7k+1 as 7k+(-1), i think i can't but then i fail in many steps! Also i know that...

Hi I like to fit in Mathematica using NonlinearModelFit. When I look at the fitted parameters, there is an entry called "P-value". Here is what it means: "The p-value is the probability of observing a t-statistic at least as far from 0 as the one obtained.". I'm not quite sure what this...

Linear Algebra problem (Least Squares? - Distance between lines) Homework Statement We have two points R = (x,x,x) and S = (y,3y,-1). All we know is that they are on lines somewhere in 3-space and that they don't cross. Need to find an x and y that minimize || R - S ||2 Homework...

I'm doing some line fitting on experimental data. Basically I have some array of pixels, and a value measured at each pixel, and I am fitting it with several constrained Gaussians. I'm using a Levenburg-Marquadt nonlinear least squares algorithm called mpfit to fit the parameters, but the...

I took a LA course in the spring, and was interested by the least squares method for building models. I decided to practice this concept by attempting to build a model that would predict ticket sales for the Mega Millions lottery given the jackpot amount. I have 249 data pairs of jackpot and...

The main problem is that I have no idea what I am doing. But second to that I am attempting to fit a curve to some data using the equation y = ((1/A(x-B)^(C+1))+D)^-1 if that makes sense I need to get the values for A,B,C and D and so have been looking into lsqnonlin but I am having...

Homework Statement If X^2=Sqrt(x1^2+x2^2+x3^2+...)=> X? and vice versa If X=x1+x2+x3+...=> X^2? Homework Equations The Attempt at a Solution

If I see an expression like \sqrt{E^2c^2} I can just remove the square root sign right and replace it with Ec?

Suppose you consider the set of all perfect squares (the squares of all of the integers).What percent of them have an odd digit for their hundreds place?

Homework Statement (a^2+b^2)(c^2+d^2)=(ac-bd)^2 +(ad+bc)^2 prove by induction that r=a1,a2,a3...an where the a's represent the sums of 2 squares. it itself is a sum of two squares. Check it with: 2=1^2+1^2, 5=1^2+2^2, 8=2^2+2^2, for r=160, r=1600, r=1300, r=625 Homework Equations...

line integral -- confusion on squares and square root terms Homework Statement Do you see where they have sqrt(16 sin^2t etc = 5? How do they get that, the answer should be 7, the square root of 16 is 4, sin^2 + cos^2 is 1 and the square root of 9 is 3, 3 + 4 = 7. It's like they're...

Given a homogeneous linear least squares problem: A^{T}y=0 What is the difference between minimizing y^{T}AA^{T}y (the least square error) and: y^{T}AA^{+}y=y^{T}A(A^{T}A)^{-1}A^{T}y ? Thanks.

Hello all, I have a set of measurements that I want to fit to a linear model with a bunch of parameters. I do this as \theta=(H^TH)^{-1}H^Tx, where θ are the parameters and x is the set of measurements. The problem is that I'd like to reduce the number of parameters in the fit. I'd like to...

the number of ordered pairs of positive integers $x,$y such that $x^2 +3y$ and $y^2 +3x$ are both perfect squares my solution...

yi = a + bxi + ei is the simple liner regression model as per is usual "state the assumptions on the errors ei to justify a least squares fit" ? So is this just that E(ei)=0, i can't see what else is a 'must' for this? what about that they are normally distrubited? i know the properties of the...

Homework Statement The sum of two consecutive squares can be a square: for instance, 32 + 42 = 52 (a) Prove that the sum of m consecutive squares cannot be a square for the cases m = 3; 4; 5; 6. (b) Find an example of eleven consecutive squares whose sum is a square. The Attempt at a...

Homework Statement A(\vec{x}) = (F + T * x )2 F is a constant, x is a 2×1 vector T is a (constant) 1×2 matrixB(\vec{x}) = || K.Z.x ||2 k:3\times3 matrix and Z:3\times2, x the same as aboveB(x) is also R2→RC(x) = A(x) + B(x) Homework Equations 1- I am confused...

I've encountered a function like this: S(x) = [M(x) - F(x)] ^2 + || G(x) || ^ 2X being a 3*1 vector M and F: vector----->scalar G: vector------->vector and || G || meaning its norm To change S(x) into a single square, authors have described it like this: S(x) = || A + B || ^ 2 where A=(M(x) -...

Homework Statement The set of squares of rational numbers is inductive Homework Equations definition of an inductive set The Attempt at a Solution sorry i know this is probably very easy to most but I am just learning analysis. Okay, so we can see that 1 is in the set because it is...

Homework Statement http://www.math.tamu.edu/~vargo/courses/251/HW7.pdf Given a set of points (xi,yi) and assuming f(xi) is linear, the deviation measured is F(m,b)=\sum_{i}^{n}(y_i - f(x_i))^2. There are a few different questions about this from the link above. The Attempt at a...

Homework Statement Im trying to construct a function in MATLAB that models linear least squares model fitting through the use of normal equations. Homework Equations Normal equation (A'*A*c)=(A'*y) A= [column vector of all x ; column vector of all 1] y= [column vector of all y] c = [b;a]...

Dear all, I have a quantum system made up of two layers. An electric field is applied with two voltages applied at both layers. I want to calculate the electronic densities that reside at the two laters in terms of the wavefunctions obtained from solving the HamiltoniaN..Anyone knows of an...

(The usual format doesn't really fit this question, so I hope you won't mind if I set it up slightly differently) The task is to make a Fortran program that will read in a given set of data from a file, stopping when it reaches the end, and calculate the gradient and intercept of a best fit...

say we have data set {y(t sub i), t sub i} Where i=1 2 3...m. I know how to fit these into a line of the form ax+b, but how about fitting into a constant??

1. The problem: Find the value of \lambda for which the sum of squares of the roots of the equation: 2x^2 + (2\lambda +4)x^2-(1+ \lambda) = 0 has minimum value. 2. Homework Equations \alpha + \beta = -b/a \alpha\beta = c/a where a,b,c are coefficients of x^2 , x and constant...

I've noticed lots of interesting properties of the patterns of numbers in the Fibbonacci sequence that can be expressed as the sum of two squares. In fact, it's what got me into number theory in the first place. There seem to be no two adjacent entries that are not the sum of two squares- and it...

Homework Statement I'm trying to study off an old practice midterm for my upcoming statistics midterm. The midterm is attached. Part One is the following problem: The effect of a new antidepressant drug on reducing the severity of depression was studied in manic-depressive patients at...

Homework Statement number of years(x): [1,2,3,4,5,6,] number of accidents(y): [12,6,5,4,2,2] or (1,12),(2,6),(3,5),(4,4),(5,2),(6,2) Homework Equations the relation between x and y is on the form: y = a + b(1/x) by changing (1/x) to z, the model become linear instead of...

Homework Statement find ∫4cosx*sin^2 x.dx Homework Equations The Attempt at a Solution ∫4cos x * 1/2 (1 - cos2x) ∫2cosx - 4cos^2 x. Then i don't know whereto go from here??

How do I calculate least squares? The way it's described is confusing to me. \hat{β}= r* sy/sx . sx and sy is the standard deviation of x and y, correct ? So let's say I have sets of numbers such as (16,19),(18,17) etc... 16 and 18 would be x and 19 and 17 would be y. So I have to calculate the...

Hi, I'm trying to derive a result from this paper: http://www.research.yahoo.net/files/HuKorenVolinsky-ICDM08.pdf given cost function \min_{x_* , y_* } \sum_{u, i} c_{ui} (p_{ui} - x^T_u y_i)^2 + \lambda \left( \sum_u ||x_u||^2 + \sum_i ||y_||^2 \right) Where both xu and yi...

Hello there, currently I am trying to solve a least squares problem of the following form: min_{M} ||Y - M*X||^2 where M is a 3x3 matrix and Y and X are 3xN matrices. However, the matrix M is of a special form. It is a rank 1 matrix which satisfies M*M = 0_{3x3} and the trace of M is zero...

Hello, What are the error bars on the least squares fit line? recall the variables are: x ; y ; x^2 ; xy ; y^2 ; yi=mx+c ; d =(y-yi) ; d^2 --------- is it d? Thanks

Hi, I have some experimental data as a function of time t and temperature T. I have done a least squares fit of the data with a function f=f(a1,a2,t,T) (the function is non linear in a1 and a2!). Optimization of e^2 = sum((yi-f(a1,a2,ti,Ti)^2) with Matlab's fminsearch gave me a1, a2 and the...

Here is a good question for maths enthusiasts. I really find this sum very tough. Any help, advice or guidance for this question will be greatly appreciated. find the product upto n terms (1+(1/2^2)) . (1+(1/3^2)) . (1+(1/5^2)) . (1+(1/7^2)) . (1+(1/11^2))...upto n terms Where the nth...

I don't really know if this is in the right place, or what the problem is called, if its in the wrong place I'm sorry. Anyway my question is apart from intuition is there any method to solve a problem like say we have an object like a square, and we are given for instance rectangles, that in one...

If you are looking for a minimum of the sum of squares of differences of functions should it be the same as the minimum for the product of squares of differences of functions? Also assume that no difference is equal to zero.

Homework Statement Apply the formula for the distance between two points to prove the well-known theorem: In a parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. Homework Equations It gave a hint saying to put one of the...

If you were to pick two random numbers on the interval [0,1], what is the probability that the sum of their squares is less than 1? That is, if you let Y_1 ~ U(0,1) and Y_2 ~ U(0,1), find P(Y_1^2 + Y^2_2 \leq 1). There is also a hint: the substitution u = 1 - y_1 may be helpful - look for a beta...

f(x) = –3√x, 1 ≤ x ≤ 4 (a) Find the quadratic least squares approximating function g for the function f. g(x)=?

As I'm studying permutation groups I remembered that when I was in elementary school my teacher introduced Latin squares to us and asked us to find all 4 by 4 Latin squares. I never succeeded in solving the problem and I found it so challenging at that time, even later in high school when I...

I have a presentation to give on the least squares method this week, and am finding the least squares method very intuitive with the exception of one thing: why is the square of the offset used, as opposed to the absolute value? I did a bit of searching, but could not find a detailed answer...

Homework Statement A) Find an orthonormal set q1, q2, q3 for which q1,q2 span the column space A [1 1; 2, -1; -2,4] (this is a 3x2 matrix). B) Which fundamental subspace contains q3? C) What is the least-squares solution of Ax=b if b=[1 2 7]T? Homework Equations Gram-Schmidt...

Hello guys, I need your help with understanding a fitting Algorithm, so that I could make it in a C++ program. I have the following function: g(f; f0, phi0, a, b) = phi0 + a ArcTan((f-f0)/b) Which is a function of "f", frequency. I would like to fit this function with the...

Homework Statement If you have a square and can paint each side with one of three different colours, how many completely different arrays can you get? (rotated squares don't count) Homework Equations The Attempt at a Solution I was thinking 3^4 / 4 but, that is not an integer, (3^4 - 1) / 4...