Fit Definition and 347 Threads

Hello I have a doubt with the least squares fitting (linear fitting). The low-level statistics textbooks only take into account the statistical error of fitting, but not the error of the fitted points. How is the error of the fitted points taken into account, and included in the total error...

Hi, I am currently working with a histogram (with 25 bins) that looks Gaussian and am trying to fit a function to it and compute its goodness of fit. The function I am using to fit to the histogram is a Gaussian (it looks like a good fit from visual inspection) and I am treating this as my...

As a graduate student in applied mathematics (solid mechanics, elasticity) I find the process of writing difficult and I have been getting better at it progressively and very slowly. But as a hobbyist video game developer, I have opened a "work in progress" thread on my game in a game...

I'm doing an analysis where I have a set of random variables with some known uncertainties (the uncertainties are different for each random variable). The random variable is roughly Gaussian distributed. I'd like to get a meaningful characteristic value and uncertainty for the whole set. I can...

Hi, I'm trying to get how well a known function fits to a set of data. I'm not interested in the data's line of best fit or anything, I just want to know how close it is to my model. I've tried using curve_fit and linregress but neither really give me what I'm after. My data follows a...

The average annual exchange rate in Canada for the US Dollar from 1998-2007 is shown in the following table. Draw a scatter plot, without using graphing technology Year Exchange Rate 1998 .67 1999 .67 2000...

Homework Statement I'm supposed to find the first ionization energy of a gas (Argon), and to do that I used mass spectrometer. The data I plotted was amplifier voltage (acts as Ion current) vs. electron volts. The graph appears in the attachment as data2.jpeg. To find the ionization energy I'm...

Hello PhysForums! New poster here. I hope some of you will have experiences, or advice for my situation. I've searched a lot of threads here and on physicsgre or gradcafe, and haven't gotten quite the information I'd like. Here's the facts: - Senior at elite LAC in USA, Physics and Math double...

When I studied General Relativity using Misner, Thorne and Wheeler's "Gravitation", it was eye-opening to me to learn the geometric meanings of vectors, tensors, etc. The way such objects were taught in introductory physics classes were heavily dependent on coordinates: "A vector is a collection...

I'm doing some image processing of some tidal lines that I'm trying to digitize from photographs using Matlab. The digitization is heavily dependent on the indexing of the image of x-values (time) and y-values (water level). After some initial processing based on pixel contrast, line continuity...

Hello, I need to do fitting using Birch-Murnaghan equation to determine the equilibrium lattice constant. I want to use originlab, anyone can help me?

For example I have the variables x, y and a probability distribution p(x,y). I want to approximate p(x,y) as a linear function, a plane in this case, at least somewhere in the domain. However I only have samples from the distribution. In case of big amount of data the it is easy to collect them...

I like to figure things out. Creating and testing computer hardware such as circuits and processors sounds very interesting to me. Trying to figure out how to make a certain processor faster, and more efficient or trying to organize a circuit to be as small as possible. Or why this certain...

Hello, I have the following problem. I have a system of differential equations, with two parameters that satisfy certain condition. 0 < 1.5(1-a) < b < 1. So when I fix the value of a I can find values of b satisfying this and its associated equilibrium point. When I calculate (with...

Are there any elaborated theory or method how to fit parameters of a function family to data given by probability distributions of data points instead of given coordinates of points precisely without error? I think this is a very general problem, I hope it is already solved. Important: I...

Is there a formula that will give me the equation for the line of best fit of a data set, the line being a 6th degree polynomial? I know how to graph the table and add a line of best fit while showing the equation but as far as I know the equation cannot be used in the given format in excel. If...

Hi all, Firstly, hope I'm posting in the right place! I'm working with a company that works with air filters. Without going into specifics etc, I have 4 data points: | x | y | |0mm|21%| |150mm|59.6%| |300mm|83%| |550mm|90%| where x is Filter Height and y is Filtration...

I'm curious which athletes can produce the most work? I watched a decent amount of the CrossFit Games and was wondering if those guys are doing more work than an elite runner, cyclist, or rower. The crossfit slogan is "Fittest on Earth," but I'm not so sure yet. They can do crazy workouts and...

Hi there, I have a bit of a confusing question, but I'll try to be as clear as I can in asking it. I have a set of linear fits for four different sets of data. Basically, I have three sets of data, with sample sizes N1 = 5, N2 = 7, N3 = 5 respectively. I have plotted these data with...

In multiverse cosmological models, what sort of infinities are usually used? For instance, in many models is it thought that the multiverse is a continuum - an unlistable (uncountable) infinite set comparable to the real numbers, and that it contains universes of Aleph_0 listable infinities...

I am studying Applied Physics at the undergraduate level right now, and I have recently become interested in Systems and Control Engineering. I am working in a student robotics lab, and do a lot of SCE (Systems and Control Engineering) - related work there. I understand that SCE has direct...

I'm making this new post in the general math section since I don't know what field of math this question belongs to anymore. So the picture I currently have regarding the abstractions of integration and differentiation from single variable-calculus to multi-variable calculus is that the...

I have found the 2D Fourier transform of a figure and then changed it to a binary image (attached). I want to find the line of best fit through the longest "axis"? of this figure. What would be the simplest way to accomplish this?

I know that you probably get tired of weird questions like this so I apologize in advance. I was thinking about length contraction in special relativity. I was thinking if superman was moving towards a basket ball at close to the speed of light when he passed it from his frame of reference it...

Hi, I've been accepted to a couple of schools for grad school. One of them being my undergrad institution where I have a great fit with an advisor I've been working with for the past two years. The other is the most prestigious school in my country, with an international reputation and great...

If I use the un-threaded section of a 3/8th inch bolt as a pin to lock a sprocket hub to a drive shaft I would drill and ream so that the bolt would need to be lightly tapped to go through the assembly. If the fit was looser (.025 thousands clearance) would that reduce the capacity of the...

Hello. I have 2 large diameter cylindrical shells that are "rabbetted" together. I am trying to determine the approximate load required to pull them apart without much success. The parameters are as follows (all length dimensions in inches) and result in a .005" (diametric) interference...

Homework Statement Consider a set of data points: (x1, y1), (x2,y2). One seeks to find the best coefficients A and B such that the sum of squared vertical distances of the data f(x) = Ax + B is minimized. Let D = ∑[yi - f(xi]2. By requiring the derivatives of D respect to both A and B each to...

I use the least squares method in a small C-programm to fit some data points. But don't know how to get the errors of the calculated parameter.

I have a bunch of noisy data points (x,y), and I want to model the data as y = ax2 + bx + c + noise where noise can probably be assumed to be Gaussian, or perhaps uniformly distributed. My data is firmly inside of an interval and I'm only interested in modeling correctly inside of this...

I have a rainfall (mm) vs. year plot of a catch basin (see Excel file below) and I would like to get it's frequency curve. But before that, I need to fit certain distribution models (i.e. log-Pearson Type III and Gumbel Distributions) to my plot to be able to know the fittest model that I can...

Hi everyone I was hoping someone could help with a problem I’m having. I am often given large amounts of X & Y data which relate to the edges of highways. Sometimes they are just a hand full approx 20 and other times there are approx 400. I use the data to find arcs that best fit the...

Assemble "shrink fit" with a big shaft ∅203 mm? Dear all, Just a short question that is it possible to contract the shaft in liquid nitrogen and heat up the hub around 300°C so that we can assemble them together quickly? We are delivering a prototype to our customer with a tight requirement...

Hello, I have some data that I am looking into correlation factors (Pearson). Let's say I have two data sets: X and Y. I have Graph X vs. Y then graph 1/X vs. Y. The reciprocal (1/X) yields a more linear relationship. Why does this occur? Thanks in advance!

I'm getting a bit confused with the stats of a chi squared test, everyone in physics labs seems to use this as a test but I don't know why it's appropriate? My main question is how would I take a linear equation in say excel which has been fitted to a series of (x,y) data points (I do have...

Homework Statement Suppose we measure N pairs of values (xi, yi) of two variables x and y that are supposed to statisfy a linear relation y = A + Bx suppose the xi have negligible uncertainty and the yi have different uncertainties \sigma_{i}. We can define the weight of the ith measurement as...

Hello, I had a chat with a person at work and we were discussing a card shuffle and what governed its behaviour. Here's the shuffle rules. Have to use an even number of cards Take top and bottom card and make new pile the next top and bottom card go below the new pile Here's an example...

1. The problem is in the attachments 2. Basic chemistry knowledge 3. The radius of one Rb atom is 4.95/2 time 10^-8 cm, we calculate the area then divide 9 into the area of one atom, we get the number of atoms, why is 4.7 x 10^15 atoms wrong?

Hello people, I'm working on a research project involving the modelling of a black body's radiation spectrum, and near the limits of the spectrometer, the intensity goes to zero rather sharply. I cannot directly say it is error from the spectrometer, because I simply don't know. However, I...

Hello everyone, I'm new to this forum and I have a few questions to ask. First of all I'm incredibly interested in Physics, Math and anything related to Astro (Universe), but the problem comes to math. I'm currently a freshman in High school, I'm 16 years old. The problem comes to math because...

Hello, I have been interested in physics since I was 9 (i'm 15) and am going to be taking my first physics class sophomore year in this coming year. It got me thinking as to what type of physics I want to pursue. I am really interested with space and how it works and the fundamentals of...

I have the following silly problem I don't know how to get round:cry: I have a set of datapoints, each point has known variance (this is experimental data). I now want to fit this dataset using a constant, meaning I have an equation y=a, i.e. there is no independent variable. I also want...

https://www.khanacademy.org/math/probability/regression/regression-correlation/v/r-squared-or-coefficient-of-determination Homework Statement So, when determining how effectively a best-fit line describes the variance of a given set of measured data, the Coefficient of Determination is the...

Dear users I have some points with coordinate x and y forexample : x=[1 2 3 4] and y=[2 4 6 8] and then I want to fit these 4 pair of points with some function for example y=a*x+b (here I know that the answer is a=2 and b=0) what should I...

hi, this might be a stupid question. if so, bear with me. i've been using the following equation in my coursework (basic chemistry): Q = m c ΔT where, of course m = mass c = specific heat capacity ΔT = change in temperature (°C) Q, as i understand it, is simply the quantity...

Hi all. I need some advice in a project I'm into. I have some experimental (simulation) data and i need to find a function that fits to it. The experimental data behaviour change when I modify some parameters I have. My goal is, from that single function, been able to predict how the...

Homework Statement A mathematical model for temperature T as a function of depth y (in m) and time t (in days) is: (T(y,t)-T0)/(Tsurf(t)-T0)=e^(-y2/4αt) (2)where Tsurf(t) is the water temperature of the lake surface at time t, α is a property called the “eddy thermal diffusivity” and T0...

Given the data points (-1,2) (0,1) and (3,-4), you want to fit the best straight line, y=mx + b, through these points. given that m = -20/13, find the value of b that minimizes the error E = Ʃ ("N" on top, "i=1" on bottom) (MXi + B - Yi)^2. This was on a test I just took for calc 1. I did the...

Homework Statement Hello all, So I am working on my engineering project, and my professor told us to play with the graphs,and try to find something interesting about them. So what I want to do is form a better fit for the figure below. " figure 2b" , and find out why the choose not to...

Hello, Suppose, 1. I have a function f=C1 + C2/((C3-X)^C4); where Cn is a constant; I'm looking at the Havriliak-Negami equation which has some 5 constants. 2. I have a data set whose least-squares fit looks like a curve, How can I compute the values of the function's parameters C1 to...