Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least ...

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Determining two most similar objects based on multiple variables

I am trying to determine the two most similar years based on a number of environmentally variables. For example, I would like to choose the most similar year to 2015, from the set 1989 to 2016, based ...
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53 views

MLE of heteroscedastic model

I'm doing some practice questions for an upcoming exam and am unsure whether I've understood the problem correctly. Can anyone confirm what I've done or point out where I've gone wrong? My final ...
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1answer
37 views

Ways to approximate multiple samples of same function in R

Example dataset (simplified): ...
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60 views

Reducing variable candidates for multivariate regression step by step

I have a set of possible candidates that I want to use in a multivariate regression. I am trying to reduce this set by the following procedure (using Stata): Step 1: univariate regression (if ...
3
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1answer
123 views

Things that I am not sure about “LASSO” regression method

I have read the chapters that are related to "LASSO" regression in: The elements of statistical learning (Tibshirani et al.) Statistical Learning with Sparsity: The Lasso and Generalizations. (...
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15 views

Why coefficients are different when pooled ols and random effect applied?

Does anybody know why the coefficients of an equation which is estimated by Random effect estimators and Pooled OLS is different from each other?
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21 views

VAR and coefficients with OLS

I have a model like $Y_{it}=\beta_{0it} +\beta_1x_{1it}+\beta_2x_{2it}+\beta_3x_{3t}+\beta_4x_{4t}+e_{it}$ I have the data for all the variables and I know that $x_3$ and $x_4$ follow an AR(1) process....
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2answers
85 views

Analytical solution of a simple regression with fixed intercept

I would like to know how to find out the analytical solution of a simple linear regression with fixed intercept = 0: $$ s = e^{-ht}$$ $$ y = -ln(s) = h\cdot t$$ Here ist the background: I have ...
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1answer
30 views

Standard error of residuals v.s. standard error of regression

We know that in simple linear regression the variance of the regression error, $\sigma^2$, is estimated by $\frac {\sum_{i=1}^{n} (y_i - \hat y)^2} {n-2}$, i.e., the Mean Squared Error of the errors. ...
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13 views

interaction continuous*dummy: is it possible to treat the continuous variable as the moderator?

This is my first post here so please be kind to me! :-) For my thesis my aim is to run a moderation analysis between organizational commitment and training. My dependent variable is job satisfaction. ...
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25 views

weighted mean of least squares [closed]

I need to calcualte a total LSE composed of other four LSEs. Each LSE comes from a measure that quantifies each of n images. LSE=$(AVG(n~images)^s-AVG(n~images)^e)²$. The four measures are used for ...
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7 views

How should I exclude results using standard error info - Levenberg-Marquardt

I have a 3D data map of estimated physiological values in the brain. i.e., 1 value for each 'voxel'. These values are that of a parameter resulting from a non-linear curve fit, using the Levenberg-...
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154 views

Simple linear regression, p-values and the AIC

I realise this topic has come up a number of times before e.g. here, but I'm still unsure how best to interpret my regression output. I have a very simple dataset, consisting of a column of x values ...
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1answer
35 views

What does strict exogeneity condition of OLS really mean?

In Hayashi's Econometrics, it is stated that one of the assumption of classical OLS is: $$\mathbb{E}(\epsilon_i\lvert\mathbf{x_1}, \mathbf{x_2}, \ldots, \mathbf{x_n}) = 0 \text{, for } i=1, \ldots, n. ...
8
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1answer
127 views

Weighted least square weights definition: R lm function vs. $\mathbf W \mathbf A\mathbf x=\mathbf W \mathbf b$

Could anyone tell me why I am getting different results from R weighted least squares and manual solution by matrix operation? Specifically, I am trying to ...
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2answers
86 views

What is parameter identification in the context of OLS?

Can someone explain what identification means in the context of an OLS model? I have a fair grasp of the derivation using either the method of moments or by minimizing the squares, but am failing to ...
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1answer
42 views

How to show the least square estimator of $b$ has the minimum variance in the class $\sum a_iy_i$

Consider the regression model: $$ y_i=bx_i+e_i,1\leq i\leq n.$$ where $x_i$'s are fixed non-zero real numbers and $e_i$'s are independent random variables with mean zero and equal variance. $(a)$...
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13 views

Random sampling as a Gauss-Markov assumption [duplicate]

In Wooldridge's Introductory Econometrics it is stated that random sampling is a Gauss-Markov assumption. As such it is a necessary condition for the unbiasedness of OLS estimators. While this can ...
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2answers
266 views

What are the consequences of “copying” a data set for OLS?

Suppose I have a random sample $\lbrace X_i, Y_i\rbrace_{i=1}^n$. Assume this sample is such that the Gauss-Markov assumptions are satisfied such that I can construct an OLS estimator where $$\hat{\...
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0answers
21 views

How to interpret non significant F-test for main effect (genotype), but significant differences in the means of the genotypes?

I am analyzing an experimental data set based on the trait values under drought condition. The experiment was carried out on three separate drought environments. First, I have done a single ...
12
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4answers
744 views

Why is Ordinary Least Squares performing better than Poisson regression?

I'm trying to fit a regression to explain the number of homicides in each district of a city. Although I know that my data follows a Poisson distribution, I tried to fit an OLS like this: $log(y+1) = ...
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5 views

Comparison between default, robust unclustered and cluster robust standard errors

I regress from my data lnhr on lnwg, first with the default OLS (POLSiid), second with the robust unclustered option (POLShet), third with the cluster robust option (POLSpanel). I understand with the ...
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1answer
38 views

Manually compute the regression coefficients of a multiple regression model with numerical and categorical variables

I am going to explain my question using a reproducibile toy example. I would like to regress a numerical variable using a multiple regression model with either numerical and categorical variables. I ...
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14 views

Relationship Between Correlations and Contour Plots for OLS

In the paper, "Simultaneous Regression Shrinkage, Variable Selection and Supervised Clustering of Predictors with OSCAR" (Bondell, Reich), the authors state: "As the contours are in terms of $X^TX$ ...
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17 views

Auto-correlation Assumption

I am testing the auto-correlation assumption of OLS. My study is conducted on the most active companies on the Egyptian stock exchange over a period of 5 years. Not all companies included in the ...
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1answer
18 views

Mixed effect - Pooled ols Different results interpretation

I have a question. I have collected data regarding the performance of companies and their board structure. I want to find the effect of the Board structure upon the performance and I am using pooled ...
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1answer
25 views

Simplification in proof of OLS inconsistency

I'm a little confused right now regarding the LLN "jump" from probability limits to expectations and variances/covariances: Say we have a linear regression model of the form with $S$ observations: $$...
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34 views

OLS, phenomenon { alpha = - mean(beta_2*x_orig)} : coincidence?

as suggested in the title, when with some data I perform this model: y ~ alpha + beta_1 * x_1 + beta_2 * (x_1)^2 + error term with OLS I SOMETIMES fall into the ...
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14 views

How to interpret and constrain the 'bias' from an OLS multiple regression?

I'm trying to solve a linear system with OLS and understand how the output coefficients deviate from the input values of mock data. The basic ideas are as follows. For the linear system ...
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16 views

Quadratic fitting raw time series data vs linear fitting its derivative

I have time series data $f_i(t_i)$. Is there a difference between the following two strategies: Fitting $\hat{f}(t)=at^2+bt+c$ to the original data Fitting $\hat{g}(t)=2at+b$ to the time derivative ...
4
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1answer
36 views

$Y=\epsilon$ in GLM?

In general linear model $$Y=X\beta +\epsilon $$ the LSE for $\beta$ is $$\hat \beta=(X^TX)^{-1}X^TY$$ and so $$\hat Y=X\hat \beta=X(X^TX)^{-1}X^TY=HY$$ where $H=X(X^TX)^{-1}X^T$. Then the ...
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1answer
52 views

Can I apply OLS (multiple regression) to panel data to identify significant variables?

I have panel data for a 5-year period and want to explore the determinants of car prices (number of doors, house power, etc.). Is it appropriate to use OLS or multiple regression to explore the ...
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2answers
64 views

How to compare results from two regressions?

We have performed two linear regressions (OLS), one with data from 2009 and one with data from 2014. All the variables are the same, both the dependent and the six independent variables. The sample ...
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0answers
16 views

What are some motivations for using nonnegative least squares?

I'm having a hard time understanding the reasoning behind it. Imagining the case of a single independent variable, if the correlation between it and the dependent is very negative, a nonlinear least ...
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1answer
173 views

Why is the intercept of linear regression biased?

Out of curiosity, I conducted the following simulation (code below). Why is it that when the variance of the error term is large coefficient associated with the intercept is biased? Can you recommend ...
6
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2answers
376 views

How does OLS regression relate to generalised linear modelling

Can anyone please shed some light on the relationship between OLS and generalised linear model? Has it to do with the distribution of the error terms, general linear model requires normality in the ...
3
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0answers
33 views

What is ordinary, in ordinary least squares?

A friend of mine recently asked what is so ordinary, about ordinary least squares. We did not seem to get anywhere in the discussion. We both agreed that OLS is special case of the linear model, it ...
0
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1answer
20 views

What is the intuition behind the regression coefficient matrix in multivariate linear regression model?

Consider the usual multivariate linear regression model where we solve for $\mathbf{\hat{b}^{OLS}}$ We have the equation $$\mathbf{y}=\mathbf{X}\mathbf{b}+\mathbf{u}$$ where $\mathbf{y}$ is the ...
0
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1answer
50 views

Linear Regression with Time Series Data

I am in the process of completing an applied econometrics project and want to find the effects of my chosen independent variables (fertility, gender wage gap, years of schooling, etc) on my dependent ...
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0answers
21 views

$R^2$ for Regression through origin (RTO) - Comparison with models having intercept [duplicate]

I've read [Removal of statistically significant intercept term increases $R^2$ in linear model Now, the question is - do we have a measure, using which we can compare goodness of fit of 2 linear ...
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0answers
36 views

Covariance Between $\hat{\beta_0}$ and $\hat{\beta_1}$ [duplicate]

Our model is $Y=\beta_0+\beta_1X+U$. We know that $\hat{\beta_0} = \beta_0 + \sum\limits_{n=1}^N c_nu_n$ and $\hat{\beta_1} = \beta_1 + \sum\limits_{n=1}^N k_nu_n$, where $$k_n = \frac{(x_n-\bar{X})}{...
0
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1answer
36 views

Can nonlinear regression with least squares estimations be used for testing hypotheses with data containing dependent observations?

I counted the number of animals of a certain species in 6 fixed locations on a monthly basis for 18 months. I now would like to test the effects of location, starting density, and time on the dynamics ...
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0answers
4 views

parameter estimation of fractional factorial design

I've been asked to estimate the parameters of fractional factorial design model which is normally estimated using least square method in R (code is lm). I want to know that, is it possible if I change ...
2
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1answer
27 views

3 Stage Least Squares or 2 Stage Least Squares

I am planning on running a 3 equation simultaneous equation model where each of the dependent variables depend on each other (i.e. Y1 is based on Y2 and Y3; Y2 is based on Y1 and Y3; Y3 is based on Y1 ...
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14 views

OLS or Ridge in Multicollinearity data

I am new to stats and linear regression. I just want to understand the exact scenario and usage between Ridge and OLS. Here is the data sample i have been using. In this both Weight and BSA are ...
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2answers
57 views

Zero conditional mean assumption (how can in not hold?)

Zero conditional mean of the error term is one of the key conditions for the regression coefficients to be unbiased. My question is: how can this assumption at all be violated if errors are equal to ...
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1answer
122 views

Regression analysis using weights

I am referring to the book titled " Beating the commodity trap: Maximize your competitive position and increase your pricing power" by Richard A. D'Aveni. In the price-benefit analysis method in the ...
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0answers
14 views

Which numbers should I include in the analysis (and how exactly) for an OLS regression model?

I am currently writing my undergraduate thesis for international relations. The first part of my analysis is quantitative and will revolve around a regression model I came up with. I have 10 ...
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10 views

Does downsampling affect regression results?

How is linear regression affected by downsampling the explanatory variable? To be more precise, I would sort all the values of $x$, and then split into a a number bins with equal number of points in ...
1
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1answer
18 views

Interaction of regression and averaging

Let's say I run a simple OLS of y on x. Then I average out all values of y that correspond to the same x, and run the regression again. Should the results of the two regressions differ? If so, why? ...