Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.
0
votes
1answer
180 views
Can someone explain what plim is?
In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me ...
0
votes
1answer
18 views
Second order least squares problem with one parameter
I want to fit a set of measured data $x_i$ and $y_i$ to the expression:
$$
\beta^2 + \beta x_i = y_i
$$
$\beta$ is my only free parameter. Although this is a really simple expression, the standard ...
0
votes
1answer
55 views
Finding the value which minimises all residuals
I have a series of observations, measurements made at various times $t$. I now need to determine the most likely value of $R$ (distance) using the model below. The guide says I should find the value ...
0
votes
1answer
150 views
Recursive curve fitting
I have a few points for which I have to obtain a best fit. (I tried to use the least squares curve fitting method as Robert says, however, since it seems to be fitting rather poorly, any other ...
0
votes
1answer
74 views
Why Logistic Regression for Classification Problems?
In a class on machine learning, we covered classification problems. In such a problem, you are studying a property of some object, say malignity of tumors in a patient. You are first given a training ...
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votes
1answer
24 views
Optimization, solving for the 'error' coefficient
Given a modified regression equation:
$\hat Y = \exp(\beta_0 + \sum\beta_ix_i + \varepsilon)*F$
where:
$\hat Y = 11353$
$\beta_0 = 8.693021$
$\sum\beta_ix_i = 5.95487177696$
$F = 0.21829$
what ...
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votes
2answers
182 views
Overcoming Linear Regression Assumptions
I'm a beginner in econometrics (learning on my own, and not from school) and I'm trying to build an intuition to understanding linear regression. We know that modeling real world data is bound to ...
0
votes
1answer
48 views
P-value not shown when there are too many variables in a linear regression
x<-c(1,2,3)
y<-x^1.1+x
summary(lm(y~x+I(x^1.1)))
I have this code in R but it just is for the sake of easier understanding of what I am trying to achieve. ...
0
votes
1answer
85 views
How to convert the constants in a regression equation to constants in a linear equation
Hello dear mathematicians,
I'm not entirely sure what to tag this question with since I'm new here but I hope some more experienced user can guide me. Here is my problem:
I'm using an internal ...
0
votes
1answer
226 views
Strange behaviour with ode45 in matlab, probably some numerical error.
I'm having a problem with a parameter estimation in a non-linear model. I think the culprit is that ode45 (an ode solver in matlab) is not properly solving my ode. It's the in red highlighted part, ...
0
votes
1answer
84 views
Linear algebra with a linear model (Matlab)
Given the equation
$$r = B + e(r\cos(\theta))$$
and the corresponding data:
$\theta: 0.88; 1.1; 1.42; 1.77; 2.14$ and $r: 3; 2.4; 1.65; 1.25; 1.01$
How do you input these data for matlab to ...
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votes
1answer
95 views
Is this expression correct?
sorry I don't know how to post Latex here
I have to implement in Matlab the following formula and I'd like to know if the expression given here really corresponds to the minimum indicated, and why:
...
0
votes
1answer
1k views
How to calculate hyperbola from data points?
I have 4 data points, from which I want to calculate a hyperbola. It seems that the Excel trendline feature can't do it for me, so how do I find the relationship?
The points are: (x,y)
(3, 0.008)
...
0
votes
1answer
354 views
How do I fit a model with piecewise linear regression
I have a set of points in 3D (x,y,z). I ordered these points from the lowest to highest. So, I want to used linear regression to fit a line through these ordered points and then to find out a break ...
0
votes
1answer
191 views
If the covariance of A, B if E(A) = 0, does convariance of A, B = 0?
So I have got 2 variables, $A$ and $B$. I know for a fact that $E(A)$ = 0.
I don't know if they are independent.
$$Cov(A, B) = E(A B) - E(B) E(A)$$
I know that $E(A) = 0$.
Does that mean $E(A B) ...
0
votes
1answer
60 views
Estimating the equation of a line from its rounded values
So, I'm playing a game where there is a certain percent value that changes over time. I look at it occasionally, it seems to be approximately linear in time. However, the change is slow enough that ...
0
votes
0answers
10 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 ...
0
votes
0answers
10 views
FF neural network with single sigmoid output (calculation of probability)
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
12 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
15 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. ...
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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, ...
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0answers
18 views
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 ...
0
votes
0answers
45 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 ...
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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
30 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
$$
y = f(x_1, x_2, ...
0
votes
0answers
18 views
Simple calculation problem in linear regression model
Define
$$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 ...
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votes
0answers
40 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 ...
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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 ...
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 ...
0
votes
0answers
18 views
Trouble following this derivation regarding linear regression
$$ \displaystyle \sum_{i =i}^n e_i^2 = \displaystyle \sum_{i =1}^n ((v_i - au_i) - (b - \bar{y} + a \bar{x}))^2 $$
$$ \displaystyle \sum_{i =i}^n e_i^2 = \displaystyle \sum_{i =1}^n(v_i - au_i)^2 + ...
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0answers
24 views
Is $x_3$ important in the second model?
A data set contains $n= 32$ observations on four variables $y,x_1,x_2$ and $x_3$. Model $y=\beta_0 + \beta_1 x_1 +\beta_2 x_2 + \epsilon$
produced $R^2 = 0.8806$. But model $y = \beta_0 + \beta_1 x_1+ ...
0
votes
0answers
18 views
Finding lines from set of 2-dimensional points
Given a set of N 2-dimensional points, how can I retrieve lines by doing some kind of clustering from the points? It guess it is a kind of regression analysis problem but I am not able to solve it.
...
0
votes
2answers
223 views
Unconditional expectation vs conditional expectation in regressions - does it really matter?
I refer here to a simple linear regression whose true representation is given by the equation: $y_i=x_i'\beta+u_i$,
where as usual $x_i$ is a $Kx1$ vector of independent explanatory variables, ...
0
votes
0answers
13 views
Multivariable regression with any amount of variables
Does anyone know a general method to find the least square regression equation for any number of variables and any power? Assume that I have enough datapoints to solve for the coefficients in the ...
0
votes
0answers
25 views
Calculate the estimated residual series $\hat{u}_t = y_t + b_{OLS}$
I am struggeling with this excercise:
Use this data and the simple model $y_t = β + u_t$ and calculate the estimated residual series
$$\hat{u}_t = y_t + b_{OLS}$$
using the least squares estimator ...
0
votes
0answers
19 views
What's the difference between fixed design and random design?
I am thinking about the regression problem of random design.
Consider the model $Y=X\beta+\varepsilon$, where $X\in \mathbb{R}^{n*p}$.
I know that under the fixed design, if we have that the $i$-th ...
0
votes
0answers
34 views
Finding a closed-form formula for the variance of the absorption direct estimator
I need to solve a system of linear equations via monte carlo methods, i.e.
$$Ax=B$$
I need to derive the a formula for the variance of an estimator given that the estimator is equal to:
- let $Q$ be ...
0
votes
0answers
48 views
How does this affect the slope
This is a Linear regression question, where I have a list of values for Sales ($Y$) and Property ($X$), I have calculated the Mean for both $Y$ and $X$, resulting in $Y=52.2$and $X=17$, I have ...
0
votes
1answer
32 views
Minimizing a function with vectors
This is a part of a problem that I'm having, and I'm unclear how to do this particular step. I'm dealing with a ridged regression and I need to minimize the equation
$$\sum (Y_i - \beta^Tx_i)^2 + ...
0
votes
1answer
44 views
Determining slope of line relative to a maximum
In the following scientific report (Seismic Q estimation), a mathematical procedure of linear curve-fitting is described in words. The authors state:
The stratigraphic effects are minimized by ...
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0answers
33 views
Non-linear regression - least square regression
I was trying to get some insight into how to solve non-linear regression model problems. Unfortunately, I've never attended a lecture on statistical math.
Here is the link:
In page number 4, they ...
0
votes
1answer
88 views
How to find autoregressive coefficients of ARMA model
I am searching various sources to find the method of manually calculating coefficients of Auto Regressive Moving Average model. The following is the text I found in a book. My question is how a1 and ...
0
votes
0answers
52 views
Why Local Minimum is calculated for a derivative function instead of actual function?
In Machine learning regression problem, why the local minimum is computed for a derivative function instead of the actual function?
Example:
http://en.wikipedia.org/wiki/Gradient_descent
The ...
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votes
0answers
29 views
Standard deviation of a particular dimension in a multivariate Gaussian distribution
I have a set (cluster) of vectors in dimension $d$. From this I have calculated the sample mean and covariance matrix ( I make the assumption that they are from a multivariate Gaussian).
My question ...
0
votes
0answers
26 views
Regression Model Estimator
Assume regression model $y_i = \alpha + \beta x_i + \epsilon_i$ with $E[\epsilon_i] = 0, E[\epsilon^2] = \sigma^2, E[\epsilon_i \epsilon_j] = 0$ where $i \ne j$. Suppose that we are given data in ...
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0answers
27 views
What to do when the predictors do not accord with common sense/literature, but the model is fine/best according to log likelihood and LRT?
down vote
favorite
I would try to clarify the problem and then ask the questions.
The problem (variable names are masked due to confidentiality):
I ran a binary logistic regression, in which there ...
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0answers
22 views
Multivariate linear regression/aproximation
I'm solving a problem which features a function $f: \mathbb{R}^4 \rightarrow \mathbb{R}^4.$ I don't know the function, but I assume it's linear and it can be expressed as $ \mathbf{y} = \mathbf{A} ...
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0answers
30 views
differences between linear regression and generalized linear regression
I have found the R program of the linear regression for the consumer price index of a country, expressed in terms of years and quarters division. The formula obtained is:
...
