Hi,
I'm interested in this question primarily in how it relates to what is usually called classic or frequentist statistics (p-values, etc). I'm fully aware of how stepwise and other automated techniques can negatively impact analyses and render inference based upon parameter estimates...
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
i need to calculate the closest distance of the point that lies closest to the regression
line for my programing but i am not sure what is the formula. maybe someone can help me out here?
thanks in advance
Hi,
I have a regular OLS regression that includes a variable both by itself and squared (i.e. y=b0+b1*x+b2*x^2). I am interested in the marginal effect of the variable at the mean. I know how to get the point estimate, but does anyone know how to get standard errors for the marginal effect...
Hello everybody,
I have two questions on conditional expectation w.r.t (Polynomial) OLS:
Let X_t be a random variable and F_t the associated filtration, Vect_n{X_t} the vector space spanned by the polynomials of order {i, i<=n }, f(.) one function with enough regularity. I am wondering how...
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...
Hi,
My question is about a common procedure used to find minimum and maximum values of a function. In many problems we find the first derivative of a function and then equate it to zero. I understand the use of this method when one is trying to find the minimum or maximum value of 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...
Does anyone know how to do a regression analysis on excel? I need to find the correlation coefficient and the coefficient of determination and I only know how to do that with a graphing calculator TI 83+
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...
We did a lab that involved using sound probes that gave us a bunch of data points which we were able to plot into a waveform using excel. However, we have to determine the equation of the waveform and it is expected that we include the uncertainty of the coefficients (much like using the LINEST...
Least squares regression of Y on A-D based on sample size of 506
[FONT="Courier New"]
Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D
s.errs (0.32) (0.117) (0.043) (0.019) (0.006)
R^2 = 0.581
problem A. Test null that coefficient on D is equal to 0
d = coefficient on...
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...
Hi,
In many statistics textbooks I read the following text: “A models based on ordinary linear regression equation models Y, the dependent variable, as a normal random variable, whose mean is linear function of the predictors, b0 + b1*X1 + ... , and whose variance is constant. While...
Hi,
I have a large data set (2D Coordinates with errors) and i am using the Levenberg-Marquardt method to estimate the best polynomial function.
That part is working fine.
Now in my data set are exactly two KNOWN data points that are 100% correct. Therefore I want my function to go...
Hello,
I am a first year undergraduate university student majoring in Engineering and Computing Sc. One of my courses is Linear Algebra. We have been given an assignment in which question no. 2 is out of syllabus. It is on Least Squares Regression Analysis. This has not been taught to us. We...
determining the "best fit" regression for a set of data
Is there a test one can perform to quickly determine what type of regression (linear vs. non-linear) will best fit the relationship between two variables?
i.e. How can one quickly determine the most probably relationship between two...
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
I want to know how to find equation for the interpolated function of any degree. On Mathematica, for example.
The Attempt at a Solution
Unfortunately, on Excel, the plots are deceiving because the points on the plot are actually out of range.
For example, this...
What are some of the elementary remedial procedures to multicollinearity (VIF >= 10) in linear regression? We were told to simply just drop that particular independent variable, but someone else suggested we could center the predictor variables (ie., xi = Xi - Xbar). Can somebody explain why...
I have two data sets and want to do a regression so that the equation that relates them is of the form y = C(x^n), where C and n are constants.
How do I do this in Excel?
I have a regression project where I have to pick a real life situation data and answer questions.
here is my data:
18 data points were entered:
4.00 4.20 4.50 4.60 4.60 4.70 4.90 5.10 5.40 5.50 5.60 5.60 5.80 6.00 6.10 6.80 6.90 7.50
Mean = 5.43
95% confidence interval for actual...
Hi
Sorry this may be an obvious one...can anyone help me with getting from the first to the second equation below? I'm particularly stuck with manipulating the terms inside the summations formulas.
I can derive to here:
\sum_{i=1}^{N}x_iy_i - N\bar{x}\bar{y} - \left(...
Hi, I had made an inquiry about regression last week and am still working on understanding the whole concept.This week my question is different. How would I use the a and b values of the regression to indicate how something is growing. Like I'm having problems interpreting data because I do not...
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...
Hello, I've just started learning about regression. While working on some problems I noticed that one problem set had exactly the x,y values swapped. And as you know when you switch the points that's normally an inverse, but the regression doesn't show that pattern as the regression values are...
What are the most sophisticated methods of performing regression analysis and how does least squares rank among them? Additionally which category would the least squares method fit into below (if any):
Simple, Multiple, Non-linear, Robust, Ridge, Logistic
Thanks,
-Diffy
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...
Ok, so I am trying to find an equation to match a 2D data-set (x,y) positions. I have X and I want to use an equation to predict Y to a rather accurate degree.
As far as I can understand, I need to use some form of regression (non-linear, since the data is awfully curved).
Now, I have no...
Currently I am studying about mechanics of satellite orbits, however I cannot seem to understand in the regression of nodes, why the line of nodes would rotate in a direction contrary to that of the actual satellite orbit (irrespective if it is prograde or retrograde orbit) ?
Ive tried...
Homework Statement
Determine the inverse of the exponential regression equation that you foun in the first bullet.
Homework Equations
y=ab^x
The Attempt at a Solution
in the first bullet i got the equation
y= (8.7166)(0.93240)^x
then i found using logs that x = -5...
Dear everybody,
I wave an equation with datas and want to regress in non linear form with plot.
Would you help me to solve the equation bellow by any softwares, please?
The data, the equation and parameters are given bellow. I want to fit the data to non-linear equation to find Df and k...
Hello, all. I know what I want, but I just don't know what it's called.
This has to do with regression (polynomial fits). Given a set of N (x,y) points, we can compute a regression of degree K. For example, we could have a hundred (x,y) points and compute a linear regression (degree 1). Of...
You must have used it couple of times while solving an engineering problem. For example in line fitting, why do we have to square?
Can't we just pass the line thru the max number of points. Can someone explain.
Thanks in advance.
Just went against the tide of the school and bought an Hp 50g Calculator(love RPN!) however to my dismay the calculator does not appear to do quadratic regression. Now my teacher is pressuring me into using a ti and I can't stand them now that I've gotten used to RPN.
Does anyone know how to...
[SOLVED] Multivariate Linear Regression With Coefficient Constraint
I'm attempting a multivariate linear regression (mvlr) by method of least squares. Basically, I'm solving a matrix of the following form for \beta_p,
$ \begin{bmatrix} \sum y \\ \sum x_1 y \\ \sum x_2 y \\ \sum x_3 y...
[SOLVED] Regression Analysis for a Gamma function
My regression analysis program that I developed in BASICS back in the 1980's applies for half a dozen linear equations some of which are transormed into log forms. I would like to modify my program to include this Gamma function...
For my chemistry lab, in order to computer change in temperature for a calorimetry experiment we're suggested to take the line of best fit from the peak temperature onwards (excluding the initial data) and extrapolate to y = 0. For example, here's some of the data I gathered:
A, Trial 2...
My google search just turns up results telling me that one of the assumptions I have to make is that each Y is normal. My question is why do I have to assume its normal. Why does it follow that it has to be normal as opposed to some other distribution? Hope that makes sense.
Edit: I thought...
OK, I have a question I have no idea how to answer (and all my awful undergrad stats books are useless on the matter). Say I make a number of pairs of measurements (x,y). I plot the data, and it looks strongly positively correlated. I do a linear regression and get an equation for a line of best...
1) To test the quality of a tennis ball you drop it onto the floor from a hieght of 4 m. it rebounds to a hieght of 2 m. if the ball is in contact with the floor for 12 ms, what is the magnitude of its average acceleration during contact and is the average acceleration up or down.
What i did...
"Sports Illustrated Jinx": Regression to the Mean
GENERAL BACKGROUND
A few weeks ago, my uncles and others were discussing the so-called "Sports Illustrated Jinx", "Sophomore Jinx", and "Heisman Jinx".
Statisticians have said that the Sports Illustrated Jinx, in particular, is not a jinx at...
First of all, I'm not sure if this is the best place to ask this question so if it isn't...sorry.
I'm doing a piece of coursework on cox regression, but I'm having trouble finding any data to use. Most of the data I've seen just gives percentages of people in certain groups, which isn't...