Linear regression Definition and 109 Threads

I really like the derivations here http://en.wikipedia.org/wiki/Proofs_involving_ordinary_least_squares Could some one recommend a good book for them. I'm tired of googling these equations every time I want to use them. Thanks!

Homework Statement We want to determine the coefficients of a polynomial of the form: ##p(x)=c_{1}x^2 +c_{2}x+c_{3}##The polynomial ##p(x)## must satisfy the constraint ##p(1)=1##. We would also like ##p(x)## to satisfy the following 4 constraints: ##p(−1)=5## ##p(0)=−1## ##p(2)=6##...

This is for an experimental physics homework,I am using the latest version of MS Excel. I have a set of data, I perform linear regression on them and it gives me a line y=ax + b. Given that both a and b have physical significance I would like to know how could I know the uncertainty...

I am using linear regression to predict 'y' based on 8 variables. With my example, most the Betas that I got are negative. So, y, the value to predict, is negative. To my data, y is a time in seconds, so I think it shouldn't be negative. I my example in python, and I want to know if y...

Homework Statement I'm looking through some example problems that my professor posted and this bit doesn't make sense How do you come up with the values underlined? Homework Equations The Attempt at a Solution Upon researching it, I find that you should use α/2 for both...

Sorry if I'm in the wrong subforum. This is a rather simple and straightforward question, I hope. I'm doing a measurement that requires me to do a linear regression on data points to get a value of the slope. The slope is the value of the actual property that I am measuring. Assuming...

In a linear regression with 1 independent variable, if X is always the same (let's call I am unlucky), but Y present different values for the same X, I still can find the coefficient of the straight line equation?

Hi, I am trying to understand how I find the error in linear regression, and what to do with it. I am using linear regression to predict the time of execution based on the size of the input and the number of tasks used in the computer to get the result. 1 - In a linear regression, I calculate...

I am trying to understand how linear regression and R-squared differ. 1 - Can anyone give me an example of use of linear regression and R-squared? 2 - They have some relation between them? E.g., they are useful for each other? 3 - What are the dangers when analysing the linear regression...

Homework Statement Why does excel give me this: http://postimg.org/image/68b9z1lqt/ And various online calulators (for example http://www.alcula.com/calculators/statistics/linear-regression/), and my own calulations give me this: http://postimg.org/image/kpljm4awx/ Homework...

I have posted this question before but I don't think I was clear on what i was trying to do exactly. I am trying to simulate a set of muon detecting drift tubes in 2d space. I have 2 sets of detector tubes (shown as black circles in the image), a particle trajectory goes through all tubes...

Hi, I am trying to simulate muon paths through drift tubes and I have ran into a problem performing a linear regression. I have generated simulated muon trajectories in 2 dimensions and they passes through my simulated drift tubes represented as black circles with a '+' in the center. As the...

I wasn't sure where to put this question. Can anyone tell me what method LineFit uses to perform linear regression with error in both coordinates? Thank you.

I read about "Linear regression" and I want to make sure that what I read is right Just tell if these equations are right- Slope of line of regression for y on x is given by m=\frac{E(XY)-E(X)E(Y)}{E(X^{2})-[E(X)]^{2}} \\ m=\frac{Cov(XY)}{Var(X)} \\ m=\frac{ρσ_{x}σ_{y}}{σ_{x}^{2}} \\...

A text says that if you calculate the linear regression of data points and you get the equation y=mx+b with an r2 value, the error in the slope is given by: δm/m=2(1-r) No explanation was given. Could someone please explain this formula? Thanks!

Hello! how I linearize this function? y(x)= a(1-e-bx) a and b are constants

βHomework Statement Data y1,y2...yn are modeled as observations of random variables Y1,..Yn given by Yi = α + β(xi-xbar) + σεi Where α , β and σ are unknown parameters x1,x2...xn are known constants and xbar is (1/n)Ʃxi and εi's are independent random variables each with the...

Homework Statement Hello, I have done a laboratorial experiment (electron diffraction) and I've been doing the analysis of the obtained data. I have plotted the data obtained experimentally, and the slope of the obtained linear regression should give a certain value. What's happening...

I have couple questions about this and I was hoping someone with some stats knowledge could clarify. First, when people report numbers such as 10 plus or minus 5, what does the 5 mean? Is it the standard deviation or the confidence interval or the variance? What is the relationship between...

Homework Statement "You are asked to do an experiment where you will need to use a rotating blade to measure the wind speed. You measure the number of rotations of the blade at 10 different wind speeds, 10 times each and will make a linear fit to determine the wind speed as a function of...

I'm currently looking at a linear regression handout from Uni and there are two methods to calculate the equation. The Normal one is to find a and b for y=a+bx, the equations for a and b are given in the handout but I'll assume you're familiar with them. The simplified one is using y = Bx +...

Hi all, I would like to understand the theory for determining outliers in the following scenario. Let's say I am to fit a linear model to the data of house size v. sale price for a particular location. And let's say I have a fairly good linear relationship, as house size increases, so does...

Hi everyone, This is not a homework question. I just want to understand an aspect of linear regression better. The book "Applied Linear Models" by Kutchner et al, states that a linear regression model is of the form Y_i = B_0 + B_1 X_i + \epsilon_i where Y_i is the value of the...

I've been told that their exists no perfect mathematical method of obtaining a line of best fit from a population of data. This doesn't make a whole lot of sense to me, so I have made an attempt at doing such (see google docs link)...

Dear all, let's say I want to know the elasticity constant of a spring (k), so I measure several times different values for the force applied to the spring, F, and the displacement of the spring, x. So, for N measures, I have xi and Fi and their uncertainties. Now, I'm really not an expert of...

Hi y'all, wondering if you could help me with this. I have a data set with a linear relationship between the independent and dependent variables. Both the depended and independent variables have error due to measurement and this error is not constant. For example, {x1, x2, x3, x4, x5}...

I've been trying to figure out how to do a linear regression on data with asymmetric x and y error bars (different for each data point). Any help would be much appreciated.

Homework Statement [PLAIN]http://img822.imageshack.us/img822/4421/statsii.jpg The Attempt at a Solution Done parts (a) and (b). How do I do parts (c) and (d)? Is the simple linear regression model just Y_i=\beta_0+\beta_1 X_i + \varepsilon_i where \varepsilon_i \stackrel...

In the least square linear regression, say we have y=Xb+e (y,b,e are vector and X is matrix, y is observations, b is coefficient, e is error term) so we need to minimize e'e=(y-Xb)'(y-Xb)=y'y-y'Xb-b'X'y+b'X'Xb we can take the derivative of e'e to b, and we can get the answer is 0-2X'y+2X'Xb...

I want to do multiple linear regression, but one of the requirements is the residuals to be normally distributed, and I can check that with QQplots but then the QQ plot shows it is about 95% of data fit into the normal line, but 5% is way off! can I still proceed ?*or do I have to find a way...

Hello all; I'm doing work for my job, and I've forgotten my statistics =(. I first want to know if what I'm trying to do is possible. I want to create a linear regression of the form Y = a * x1 + b * x2 + c. http://imgur.com/Q4vGP" As you can see, there is space that is grayed...

Homework Statement Where can I find Y(subscript: 1) on the TI-83 plus calculator? I was working on Linear Regressions in the book and I came across a question that requires me to input Y1 on the screen but I can't find the 'y'.. how can I find it? Homework Equations The Attempt at...

Hi guys, I have data of 20 peoples height, weight, calorie intake and skinfold thickness. I have carried out a regression of calorie on height, on weight and on height and weight. I have done the same thing for skinfold thickness. I then used R to work out the summary of results. each...

I have a model y= beta0 + beta1 x1 + beta2 x2 + eps, eps~N(0,1). How to test hypothesis beta1=0 ? Is the same test for beta2=0?

Hello, In simple linear regression (or even in multiple linear regression) how does one prove that the coefficient of determination, given by R^2 = \frac{SS_{Reg}}{SS_{Total}} = 1-\frac{SS_{Res}}{SS_{Total}}= 1-\frac{\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}{\sum_{i=1}^{n}(y_i-\overline{y})^2} is...

I am trying to figure out how to combine uncertainty (in x and y) into the standard error of the best fit line from the linear regression for that dataset. I am plotting units of concentration (x) versus del t/height (y) to get a value for the flux (which is the slope) I understand how...

Hi: This is my first post and I'm not sure if this is the right forum. Please redirect if necessary. I'm new to nonlinear regression, but from what I've read I realize that making "good" initial guesses for the model parameters is very important, otherwise a "best fit" may not result...

Hi Guys, Can anyone recommend a code, preferably in fortran 90/77, or possibly in C, which provides a weighted linear regression of a 3 column file? Natski

In my textbook, the following results are proved in the context of SIMPLE linear regression: ∑e_i = 0 ∑(e_i)(Y_i hat)= 0 I tried to modify the proofs to mutliple linear regression, but I am unable to do so, so I am puzzled... Are these results also true in MULTIPLE linear regression...

In MULTIPLE linear regression, is it still true that the regression sum of squares is equal to ∑ (Y_i hat -Y bar)^2 ? My textbook defines regression SS in the chapters for simple linear regression as ∑ (Y_i hat -Y bar)^2, and then in the chapters for multiple linear regression, the...

"Suppose that in a MULTIPLE linear regression analysis, it is of interest to compare a model with 3 independent variables to a model with the same response varaible and these same 3 independent variables plus 2 additional independent variables. As more predictors are added to the model, the...

Consider this situation. There is an exam designed in such a way that it appears that the pass/failure rate of the exam has a linear relationship to the age of the exam taker. The older the test taker, the higher the pass rate. I'm not interested in the exact scores of the exam, only pass or...

Simple linear regression: Y = β0 + β1 *X + ε , where ε is random error Fitted (predicted) value of Y for each X is: ^ Y = b0 + b1 *X (e.g. Y hat = 7.2 + 2.6 X) Consider ^ X = b0' + b1' *Y [the b0,b1,b0', and b1' are least-square estimates of the β's] Prove whether or not...

1) "Simple linear regression model: Y = β0 + β1X + ε E(Y) = β0 + β1X A linear model means that it is linear in β's, and not necessarily a linear function of X. The independent variable X could be W2 or ln(W), and so on, for some other independent variable W." I have some trouble...

1) "Simple linear regression model: Yi = β0 + β1Xi + εi , i=1,...,n where n is the number of data points, εi is random error We want to estimate β0 and β1 based on our observed data. The estimates of β0 and β1 are denoted by b0 and b1, respectively." I don't understand the difference...

1) "In regression models, there are two types of variables: X = independent variable Y = dependent variable Y is modeled as random. X is sometimes modeled as random and sometimes it has fixed value for each observation." I don't understand the meaning of the last line. When is X random...

Homework Statement I've been given a set of data x 0 0.5 0.7 1.5 1.75 y 0.5 0.72 0.51 1.5 1.63 Given y=ax+b for this data points of linear model, I have to 1. minimize the sum of the absolute values of deviations between experimental value of Y and value predicted by the...

Homework Statement Consider model of linear regression: Y_i = \beta_0 + x_i \beta_1 + \epsilon_i i = 1, ..., 5, where \epsilon_i \sim \mathcal{N}(0, \sigma^2) are independent. Find expected value and variance of predicted values \widehat{Y}_i considering that observations are...

I'm interested in fitting a line to some data. There is a built-in function in R lm() that gives me both the best-fit slope and intercept, however, I would like to determine the best fit intercept GIVEN a specified value of the slope. Is there an easy way to do this? I apologize if this is in...

AFAIK, there are two basic type of linear regression: y=ax+b and y=a2 + bx + c But I have to do the same with the function y = asin(x)+bcos(x). Here is what I have done: We have: \begin{array}{l} \frac{{\partial L}}{{\partial a}} = 0 \frac{{\partial L}}{{\partial b}} = 0Continue...