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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12 views

applying Posterior predictive distribution on the data from which the coefficient of regression were estimated [on hold]

I am new to linear regression modelling. For the given linear model $Y_{current} = \mu+ \beta X_{current} + \varepsilon \sim N(0|\sigma^2)$ Generally, in regression analysis we estimate, coefficient ...
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0answers
11 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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10 views

Non-linear least square minimization using for three-dimensional data [on hold]

I have a 3D data and I would like to fit a non-linear model to the data using lmfit. This is the code I have written but it doesn't work. ...
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13 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
12 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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16 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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0answers
32 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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13 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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14 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 ...
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1answer
35 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
45 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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62 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
15 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
167 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 ...
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2answers
363 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 ...
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31 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 ...
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1answer
15 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 ...
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1answer
46 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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20 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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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 = ...
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1answer
33 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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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 ...
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1answer
22 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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12 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
47 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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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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8 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 ...
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1answer
16 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? ...
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31 views

Quantile Regression Simple Question

When i estimate a regression model using OLS, for example: $Y_t = \alpha+ \beta*X_t + \epsilon_t$ $\beta = Cov(X,Y)/Var(X)$ In my job that i working, $X$ is something like: $X_t = g_t - s_t$ so my ...
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23 views

How to deal with outliers and feature selection simultaneously?

I've been given some data and need to pick what I consider to be the best features from it and use them to build models that fit the data. My issue is that all the tests I've seen for outliers assume ...
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30 views

Model fitting: relative importance of SE of regression coefficient vs adj. R squared when estimating accurate coefficient is only objective

My objective is to infer the magnitude of a particular coefficient ($β_5$ in the equation below) as accurately as possible. I'm trying to decide between two models: the first which has a lower SE ...
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4answers
80 views

Does a GLM count as a linear least squares model?

I'm doing some work for a summer school project and I've been asked to model some data using a 'linear least squares' model. I've done all that and analysed the results and the summary statistics look ...
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7 views

How do I prove that using OLS on de-meaned data gives the same estimates as using a dummy variable regression?

I obtained the FOCs for the dummy variable regression and know that I have to manipulate them to get the FOCs for the regression on the de-meaned data but am not sure how to go about it, as in how to ...
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1answer
94 views

Hat matrix and leverages in classical multiple regression

What is Hat matrix and leverages in classical multiple regression? What are their roles? And Why do use them? Please explain them or give satisfactory book/ article references to understand them. ...
3
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2answers
95 views

Why is $SST=SSE + SSR$? (One variable linear regression)

Note: $SST$ = Sum of Squares Total, $SSE$ = Sum of Squared Errors, and $SSR$ = Regression Sum of Squares. The equation in the title is often written as: $$\sum_{i=1}^n (y_i-\bar y)^2=\sum_{i=1}^n ...
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19 views

least squares approximation to predict weather

I have daily temperature and rainfall data of fifteen years. I do not know much about stats. So here is my question. How do i use least squares approximation to predict temperature of at least three ...
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16 views

First difference of non-stationary - does the prediction accumulate the errors?

I am modeling a non-stationary process (I(1) actually), it looks like this: I have 146 data points (monthly data). The ideal model in my case should have: Macro-variables sensitivity Predict the ...
5
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1answer
115 views

Analytically linking coefficients from alternative linear models (OLS)

The general problem: I have two alternative models I could use for my estimation Model A: $y = \alpha^A+ X \beta^A_0 + Z\beta^A_1 + \varepsilon^A$ Model B: $y = \alpha^B + X \beta^B_0 + ...
1
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1answer
49 views

Panel data with country fixed effects

I am wondering about the estimation of a fixed effects model. It is just given in the paper that estimation is done via OLS with robust standard errors. Which method is meant by such explanation? Did ...
0
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0answers
26 views

Placement of lags & dummies

I am doing a regression of GDP per capita (dependent) on FDI (independent variable) - with 8 control variables and two interaction terms - to identify the effect of foreign direct investment on ...
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37 views

Principle application in First Differences & Fixed Effects

I'm slightly confused about specific use of these two estimators. I have gone through the mathematical make up of each, and how they both can remove unobserved endogeneity. I'm currently running ...
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16 views

Exact Solution for a Nonlinear Least Squares Problem

For any linear least squares problem, we know that a unique solution always exists and that it can be explicitly written down in a closed form. My questions is that, is there any example of a ...
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1answer
18 views

How to interpret coefficients in a regression model with two groups

given a linear regression model such as $ y= \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3D + \beta_4D*X_1 + \beta_5D*X_2 $ where $D$ is a dummy variable, what are the proper interpretations of ...
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1answer
78 views

The distinction between stochastic independent variable and measurement error in independent OLS variable

Assume that OLS regression of the form: $$Y_t = X_t'\beta + u_t$$ Suppose $X_t$ are stochastic, thus standard Gauss-Markov assumptions need to be accommodated. Given that: $$\text{E} {(\hat\beta)} ...
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16 views

Structural Change Cross Sectional Data

I am studying an introductory course of econometrics so sorry if this seems really obvious but, I am estimating a semi log wage equation of male workers where the covariates are Age, Experience and ...
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48 views

Non-linear least squares standard error calculation in R

I am using implementations of the Levenberg-Marquardt algorithm for non-linear least squares regression based on MINPACK-1 utilizing either the R function nlsLM() from minpack.lm or an implementation ...
3
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1answer
75 views

Is the least square estimator unique?

Given $X\in\mathbb R^{n\times p}$ and $y\in \mathbb R^n$, the least square coefficients are: $\hat{\beta} = \text{argmin} \| X\beta - y\|^2_2$. Is $\hat{\beta}$ unique in the case ...
4
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2answers
72 views

Online references giving introduction to OLS

I started to study ordinary least squares (OLS) estimators and am still at the very beginning. I already bought some books on econometrics but I did not find anything online. So I was wondering if ...
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1answer
23 views

Joint significance test before or after hettest in Stata?

I ran an OLS regression in Stata, then a hettest, and there is heteroskedasticity in the X variables. So I threw on a ,robust to ...