Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.
-1
votes
1answer
25 views
Can someone help me to decode these functions? [closed]
I need to use the following functions, however, I don't manage to read them... Can someone help me?
Cedergreen hormesis model:
f(x) = c + \frac{d-c+f \exp(-1/x^{α})}{1+\exp(b(\log(x)-\log(e)))}
...
2
votes
2answers
28 views
Linear Regression: Expectation Proof
I found the following proof in my notes:
$E(Y_i) = E[\beta_0 + \beta X_i + \varepsilon_i] =\cdots= \beta_0 + \beta X_i$. This does not seem right to me, however. Why would $E(\beta_1 X_i) = \beta_1 ...
0
votes
2answers
23 views
Is a Relationship Quadratic?
I have a relationship $y=f(x)$ for which I can obtain data through simulation.
I have good reason to suspect that this relationship is quadratic (rather than, say, exponential), and would like to ...
0
votes
0answers
16 views
Calculate the tendency of a set of samples
I develop an application in which I constantly get samples of heart pulse.
I defined an interval of $t$ seconds.
In each $t$ seconds I have $n$ samples.
In every interval, I want to calculate the ...
1
vote
0answers
62 views
How to calculate probability with sigmoid output in feedforward neural network?
first of all I'm sorry for my not very skilled English, but I will do my best to explain my problem.
I'm trying to create a feedforward neural network with one hidden layer (with probably arctan ...
0
votes
0answers
16 views
Stata: “Between and fixed effect estimates” in a linear regression?
I'm working on a paper by B. H. Baltagi and I am trying to replicate the results. It can be found here, the data is here. I'm supposed to do a linear regression - sounds simple. The author uses Stata, ...
0
votes
1answer
16 views
Interpretation of regression formula returned by computer software
I have a dataset consisting of 744 records. Data exploring software generated an equation I don't know how to interpret in simple words. I really appreciate if you could help me about this matter. ...
0
votes
0answers
27 views
Multiple regression using excel [closed]
I'm having a project that requires forecasting using multiple regression given an excel sheet.
Using the standard formula for multiple regression
First, I tried to get accurate values for predictors, ...
0
votes
0answers
18 views
-1
votes
0answers
20 views
Which Regression methods are suitable for binary valued features and continuous output?
I want to build a machine learning model to regression on continuous output given binary valued features(0,1). the dimension of my problem is around 200. which of the flowing methods seems suitable ...
0
votes
1answer
21 views
Multiple regression problems (restricted regression, dummy variables)
Q1.
Model 1: $Y=X_1\beta_1+\varepsilon$
Model 2: $Y=X_1\beta_1+X_2\beta_2+\varepsilon$
(a) Suppose that Model 1 is true. If we estimates OLS estrimator $b_1$ for $\beta_1$ in Model 2, what will happen ...
1
vote
0answers
20 views
regression coefficient
Consider observations on three variables X1;X2 and X3: Suppose that
X1 is regressed on X2: When the residual of the above regression is
regressed on X3; the regression coefficient of X3 is b3: When X1 ...
1
vote
0answers
21 views
Nesterovs third method - implementation in python [migrated]
I am looking at implementing Nesterov's method for my algorithm being written in python. Can anyone please point me to docs which can help me get started in terms of implementation of this method? I ...
0
votes
0answers
46 views
Generating an equation from an image I have
I am not exactly sure if this question belongs here but I could not think of a better place to ask.
So I recently discovered that various people on the internet have created equations for rather ...
0
votes
2answers
34 views
Fast way of finding RSS of Multiple Linear Regression
Is there any smarter way to compute Residual Sum of Squares(RSS) in Multiple Linear Regression other then fitting the model -> find coefficients -> find fitted values -> find residuals -> find norm of ...
0
votes
0answers
31 views
If $\underset{n \times n}{M}$ is a symmetric and idempotent matrix having rank $r$
If $\underset{n \times n}{M}$ is a symmetric and idempotent matrix having rank $r$ then
$$w'Mw \sim \sigma^2 \chi^2_{(r)}$$
where $\underset {n \times 1}{W} \sim N(0,\sigma^2 I)$
that is, $w_i \sim ...
0
votes
1answer
31 views
Techniques to find regression parameters for multiple datasets where a subset of parameters should be the same for all datasets
I have five sets of observations of measured y as some function of measured $x_1, x_2, x_3,\ldots$ and I want to fit five functions to these observations. They have the form
$$
y = f(x_1, x_2, ...
2
votes
1answer
66 views
Finding uncertainty in the slope/intercept for a non-linear least squares fit
I have the following function:
$$M = a(\log_{10}W-2.5)+b$$
I also have a set of data with actual measured values of $W$ and $M$ (each have individual $\pm$ errors). Here's a small sampling of the ...
1
vote
1answer
13 views
Initializing Variables using Shrinkage
I have a user-user model which which users can rate their friendships(r) with others and also can have activities with them(a). I am using Matrix Factorization and Gradient Descent for updating the ...
1
vote
0answers
25 views
About the weights assigned in the linear regression
I have this confusion related to linear regression. Lets say I have two predictors $x_1$ and $x_2$ and the target is $y$. I learn a linear regression with $y \sim x_1,x_1 \cdot x_2,x_2$ with $x_1 ...
0
votes
1answer
71 views
Prediction Model for forecasting using Linear regression
I am very new to inferral statistics. I am trying to build a prediction model for forecasting the revenue for physicians based on some historical data. I was planning to use Multiple Linear Regression ...
1
vote
0answers
31 views
Sequential problem for n=1, non linear regression
I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment.
The function of the line is very simple:
$$ln(Y_i) = ...
2
votes
1answer
60 views
Least Squares Regression To Half of a Parabola
I have a set of points in two dimensional space, and I know a priori that they approximate half of a parabola. I want to find the coefficients for a quadratic function where all of the points fall on ...
2
votes
3answers
60 views
Condition for $\det(A^{T}A)=0$
Is it always true that
$\det(A^{T}A)=0$, $\hspace{0.5mm}$ for $A=n \times m$ matrix with $n<m$?
From some notes I am reading on Regression analysis, and from some trials, it would appear this is ...
1
vote
1answer
60 views
Proof that a and b in linear regression are random variables
Does anyone know how to prove that the variables $a$ and $b$ that are used in linear regression are random variables? For me the assumption would be that these are dependent on the values of $x$ and ...
1
vote
3answers
78 views
Exponential extrapolation
Given a set of points on 2D surface $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$ and a function $f(x)=k+ab^x$, the task is to find values of $k,a$ and $b$ that minimize the following sum:
$$\sum_{i=1}^n ...
0
votes
0answers
18 views
Simple calculation problem in linear regression model
Define
$$Y_i=\beta_0+\beta_1 X_i+\epsilon_i$$
$$\bar Y=\beta_0+\beta_1 \bar X+\bar \epsilon$$
$$\bar Y=\frac{\sum_{i=1}^{n} Y_i}{n}$$
$$\bar X=\frac{\sum_{i=1}^{n} X_i}{n}$$
$$\bar ...
0
votes
0answers
41 views
What is the difference between random and nonrandom?
In a simple regression model $Y_i=\beta_0+\beta_1 X_i+\epsilon_i$, $X_i$ is nonrandom.
But we don't know $\beta_0, \beta_1$ value (we should estimate them in our model), $Y_i$ is random.
I wonder what ...
1
vote
2answers
80 views
Fitting exponential curve to data
If I have a collection of data points that follow an exponential curve relationship, how can I manually construct the equation that defines the best-fit exponential curve for the data?
1
vote
1answer
111 views
How to find a line of best fit of the form $y=ax$?
We have the following points:
$$ (0,0)(1,51.8)(1.9,101.3)(2.8,148.4)(3.7,201.5)(4.7,251.1)(5.6,302.3)(6.6,350.9)(7.5,397.1)(8.5,452.5)(9.3,496.3)$$
How can we find the best fitting line $y=ax$ ...
1
vote
0answers
39 views
Correlation coefficient.
A linear regression gives us a correlation coefficient $r=0$.
What is the equation of the best fit line?
Give an example of data with $r=0$
What is the value of the correlation coefficient of data ...
1
vote
1answer
36 views
How to gather useful information from a residue plot
You can usually see how good your linear regression line is by looking at the residue plot. If you see the points randomly distributed, you're good. But if you see a pattern, it means there is ...
1
vote
1answer
44 views
What is the way to determin how good a sequence will interpolate?
Say I have to sequences of numbers:
$$[5, 10, 14, 21, 27, 31]$$
$$[1, 20, 21, 22, 30, 31]$$
Even though they both get to $31$ by the $6$th element, logic tells me that only the first one is a good ...
2
votes
1answer
38 views
Why is $\sum x^2 _t \times \text{Var}(\beta)=\frac{\sum x^2 _t \times \sigma^2}{ \sum x^2 _t} = \sigma^2$?
I do not get this connection.
Is is reliable to divide this equation by $\sum x^2 _t$ to get just $\sigma^2$ ?
$$\sum x^2 _t \times E(\hat \beta - \beta)^2=\sum x^2 _t \times ...
0
votes
0answers
28 views
how to determinte 3 parameter by best fitting?
I have a bunch of experimental data given by someone else which should fitting into the following form
$$
y = A\exp(-b/(x-\mu))
$$
where $A$, $b$ and $\mu$ are constant but not known. I am ...
1
vote
1answer
20 views
How to interpret these regression values?
If GPA(gpa after fall semester in college) is the dependent variable and SAT (score on the SAT) is the independent variable and I have the following parameter estimates:
Intercept: .66306
SAT: ...
0
votes
0answers
40 views
Omitted Variable Bias?
The question is more involved on how to calculate the omitted variable bias. We were given data and are supposed to use SAS to run regression models. First, how do you know if results suggests there ...
1
vote
0answers
20 views
Coefficient of determination
$$ \displaystyle \sum^n_{i = 1} (y_i - \bar{y})^2 = ( \displaystyle \sum^n_{i = 1} (y_i - \bar{y})^2 - \displaystyle \sum^n_{i = 1} (y_i - \hat{y}_i)^2 ) + \displaystyle \sum^n_{i = 1} (y_i - ...
0
votes
0answers
18 views
Trouble following this derivation regarding linear regression
$$ \displaystyle \sum_{i =i}^n e_i^2 = \displaystyle \sum_{i =1}^n ((v_i - au_i) - (b - \bar{y} + a \bar{x}))^2 $$
$$ \displaystyle \sum_{i =i}^n e_i^2 = \displaystyle \sum_{i =1}^n(v_i - au_i)^2 + ...
1
vote
2answers
77 views
Linear regression question
I don't understand the following derivation:
$$ e_i = y_i - ax_i - b$$
$$ e_i = (y_i - \bar{y}) - a(x_i - \bar{x}) - (b - \bar{y} + a \bar{x}) $$
I don't really understand what they do and why they ...
0
votes
0answers
24 views
Is $x_3$ important in the second model?
A data set contains $n= 32$ observations on four variables $y,x_1,x_2$ and $x_3$. Model $y=\beta_0 + \beta_1 x_1 +\beta_2 x_2 + \epsilon$
produced $R^2 = 0.8806$. But model $y = \beta_0 + \beta_1 x_1+ ...
0
votes
0answers
18 views
Finding lines from set of 2-dimensional points
Given a set of N 2-dimensional points, how can I retrieve lines by doing some kind of clustering from the points? It guess it is a kind of regression analysis problem but I am not able to solve it.
...
0
votes
2answers
241 views
Unconditional expectation vs conditional expectation in regressions - does it really matter?
I refer here to a simple linear regression whose true representation is given by the equation: $y_i=x_i'\beta+u_i$,
where as usual $x_i$ is a $Kx1$ vector of independent explanatory variables, ...
0
votes
0answers
13 views
Multivariable regression with any amount of variables
Does anyone know a general method to find the least square regression equation for any number of variables and any power? Assume that I have enough datapoints to solve for the coefficients in the ...
2
votes
1answer
112 views
Arriving at the Logistic function from a Binomial Distribution and Maximum Likelihood
I've been trying to understand the origin of the Logistic function in Logistic regression:
$$\Pr(Y=1|x;\theta)=\frac{1}{1+e^{-\theta x}}$$
I was lead to beilive that one could somehow arrive at this ...
0
votes
1answer
52 views
How to solve multi-variate linear regression analytically?
We have $n$ variables $x_n$ and one stochastic function $y$ of these variables. We assume that function $y$ depends on variables in the following way:
$y = c + \sum_{i=1}^n k_i x_i + \varepsilon_i$,
...
0
votes
0answers
25 views
Calculate the estimated residual series $\hat{u}_t = y_t + b_{OLS}$
I am struggeling with this excercise:
Use this data and the simple model $y_t = β + u_t$ and calculate the estimated residual series
$$\hat{u}_t = y_t + b_{OLS}$$
using the least squares estimator ...
0
votes
1answer
63 views
Forecasting using multiple regression
I have data in the form given below, and I want to perform forecasting using multiple regression. I found definition of multiple regression from this link: http://otexts.com/fpp/5/1/ . I have these ...
0
votes
1answer
59 views
Non-Linear regression
Imagine that I have a function $ f(x,y) $ to model a physical phenomenon.
I believe that functions is defined by $$ f(x,y) = A*x + B*y + C*x*y$$
I have many values for $ (x,y,f(x,y)) $, how can I ...
1
vote
1answer
32 views
Cointegration for Price levels Time Series
I don't understand why is the difference between price levels is a stationary process while the time series of price levels themselves is a non-stationary process.
For example:
...
