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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2answers
34 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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0answers
32 views

Basic questions about a econometric analysis of paneldata [on hold]

For a research project in economics, I want to study the several determinants that affect the decision to enter the private rental housing market in the United States. There is a special focus on ...
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0answers
25 views

How do I derive a reduced form equation?

I understand what reduced form is, however I'm struggling to figure out how to actually derive a reduced form equation by myself. I have -> log(wage) = B0 + B1educ + B2age + B3married + B3black ...
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0answers
16 views

(stata) How to plot nonlinear least squares equation on tw scatterplot? [on hold]

I created a great non-linear least sqares equation for two variables, reqgrade and year. It is: nl exp2 : reqgrade year And when I do a scatterplot of my two ...
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1answer
120 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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0answers
6 views

Running OLS multiple times in Matlab [closed]

I'm trying to run a series of dependent variables that I obtained from bootstrapping and that are organized in a matrix (1000 columns which will be my dependent variables) on two vectors of ...
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0answers
9 views

Estimate the production for 1995 and 2005 with the helps of following data: [closed]

Years Production(in Lakh ton) 1990 180 1995 ? 2000 250 2005 ? 2010 320 2015 400
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0answers
6 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
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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0answers
28 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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0answers
20 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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0answers
28 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
61 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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0answers
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 ...
1
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1answer
86 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. ...
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0answers
16 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 ...
1
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0answers
15 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
114 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
46 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 ...
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0answers
23 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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0answers
36 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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0answers
12 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 ...
1
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1answer
75 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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0answers
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 ...
1
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0answers
44 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
votes
1answer
73 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
65 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 ...
0
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1answer
20 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 ...
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0answers
21 views

How to iteratively learning two matrices in least squares regression?

I have a problem which has the instances (vectors) belonging to two different classes c1 and c2 (same dimensions). I want to learn two matrices M1 and M2, such that sum(M1*x_{c1} - M2*x_c{2})^2 is ...
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0answers
24 views

Alternating Least Squares Test Error better than Train

I have been running some trials for recommendations using Collaborative Filtering, specifically Alternating Least Squares (ALS). I am using two versions of ALS, one with fixed lambda regularisation ...
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0answers
36 views

Orthogonal matching pursuit - am I using it wrong?

I am trying out this method as a regularized regression, as an alternative to lasso and elastic net. I have 40k data points and 40 features. Lasso selects 5 features, and orthogonal matching pursuit ...
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0answers
10 views

Bias and Expected Value of Residuals

If I am running an OLS regression is it always the case that the residuals sum to 0? Or, if there is a bias, for example, their exists endogeneity, then when I run the OLS regression the sum of the ...
3
votes
1answer
100 views

What to do when a linear regression gives negative estimates which are not possible

I am using linear regression to estimate values that in reality are always non-negative. The predictor variables are also non-negative. For instance, regressing the number of years of education and ...
1
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0answers
30 views

Least Square Estimators of Alternate Model

We are given the following regression model: $y_i = \beta_o+\beta_1(x_i-c)+\epsilon_i$ where c is a constant. We are asked to derive the least squares estimators. Then assuming c is the mean of the ...
0
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0answers
8 views

Beginner explanation between least squares and distance from mean [duplicate]

I have just started learning statistics and I am struggling with some very simple things. I understand that you square the data points in order to avoid the situation that their sum is zero from the ...
1
vote
1answer
51 views

How to understand interaction effect

I do research on differences in corporate tax burden by different types of enterprises (3 categories). As we can see in the picture categorie 3 has a significant ...
1
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1answer
42 views

Why can we assume normally distributed errors in probit but not in LPM?

Why are we able to assume normally distributed errors in probit models but not in linear probability models (LPM)? When used with a binary dependent variable, LPMs violate a few necessary ...
1
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0answers
21 views

Linear regression: Estimator for OLS and Minimum Absolute Deviations

I've received conflicting information in 2 different statistics classes, and I want to better understand the problem before I ask either of them for clarification Prof 1: We use OLS for linear ...
0
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0answers
11 views

Are there any situations in which an OLS estimation of probability (with a binary dependent variable) might come in handy? [duplicate]

Most textbooks that I've read mention the nonsensical results that you might obtain with an OLS estimation of a probability of a variable being 0 or 1 -- as such, you use the transformations of the ...
1
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0answers
20 views

OLS and Probit Model regarding a dummy variable being dropped

I've been trying to run a regression using a probit model, but I keep getting a dummy variable being dropped from the regression (in Stata's output) because it predicts the success perfectly. The OLS ...
3
votes
0answers
35 views

Sign and size of OLS bias for Tobit models

I have a question related to the sign and size of the OLS bias in the case of a Tobit model. Consider the following model (1) Sample of observations $\{X_i,Y_i\}_{i=1}^n$, i.i.d., $X_i$ is a vector ...
0
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0answers
8 views

Correlation in longitudinal data analysis

There is a thesis claiming a significant negative correlation between variable A and B. It used the ordinary least square controlling for 4 other variables C,D, E, F (some are continuous, some dummy) ...
3
votes
0answers
22 views

Existence of OLS estimator

Having a look at some mock exams from my econometric course, I bumped into a question that left me doubtful. I've been asked to prove the existence of an OLS estimator. Honestly, I have no idea how ...
3
votes
1answer
71 views

Objective function of canonical correlation analysis (CCA)

Given two vectors of random variables $X$ and $Y$, Canonical Correlation Analysis (CCA) finds the transformation matrices $A$ and $B$ so that $\operatorname{corr}(A_{1*} X, B_{1*} Y)$ is first ...
3
votes
1answer
46 views

OLS Regression : Efficiency of the estimator of the variance of the residuals under the assumption of normality

My question is probably already answered somewhere but I did not find it. In the standard linear regression model under the assumption that residuals are normally distributed, we have a result ...
0
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0answers
18 views

Root Mean Square Value Contribution

I have the following values: 0.157,-0.345,0.183,0.445,0.348,-0.302,-0.074,-0.054,0.113,0.251. Each of these values is the result of a subtraction between a measured height value and an interpolated ...
0
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0answers
19 views

My predictors have strong collinearities, yet linear regression performs as good as partial least squares. Why?

I am trying to predict a single response from twelve explanatory variables. There exist strong correlations between my variables. The correlation matrix looks as follows, and the data have a ...
1
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0answers
9 views

Can using robust standard errors solve the problem of measurement error in dependent variable?

I have a sample in which there is measurement error in the dependent variable. I understand that the estimates would be consistent, but the standard errors would not be correct. So can using robust ...