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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27 views

Derivative of softmax and squared error

I'm trying to understand the derivatives w.r.t. the softmax arguments when used in conjunction with a squared loss (for example as the last layer of a neural network). I am using the following ...
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42 views

Derivation of Olsens LS Selectivity Correction

There are many estimation procedures that correct for sample selection. The most famous is Heckman's two-step selectivity correction (in two equations) that assumes bivariate normality of the error ...
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43 views

What does “special case of GMM” mean?

I was researching purchasing this text book: http://www.amazon.com/dp/0691010188/ref=wl_it_dp_o_pd_nS_ttl?_encoding=UTF8&colid=2QTISO1Y8TYVW&coliid=I3FUEFWL47AC4L In its description it talks ...
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1answer
25 views

A question on notation in the least squares method

I am reading some nice lecture notes on basic statistics, learning some basic topics on estimation of parameters. Reading the chapter about the method of least squares estimation I meet the following ...
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15 views

Pooled OLS with Common Shock

I have the following dataset: ...
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2answers
153 views

What is the interpretation of the covariance of regression coefficients?

The lm function in R can print out the estimated covariance of regression coefficients. What does this information give us? Can we now interpret the model better or diagnose issues that might be ...
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1answer
30 views

Common trends with Difference in differences

For OLS to have good properties, we should assume that $E(u|X)=0$. When using DiD, is it then this assumption which requires the so-called common trend assumption (need for the DiD to have good ...
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377 views

I have a line of best fit. I need data points that will not change my line of best fit

I'm giving a presentation about fitting lines. I have a simple linear function, $y=1x+b$. I'm trying to get scattered data points that I can put in a scatter plot that will keep my line of best fit ...
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25 views

R-squared value when using offset — how is it calculated?

I have a linear model with a test score variable as a dependent variable and a vector of covariates. I have an offset variable in the model. So the formula is= $$\text{score}_i = B_0 + B_xX_x + ...
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1answer
47 views

Least squares with exponential model

I'm trying to fit values from this model $$y(x)=ae^{−bx}+c$$ where a, b and c are 3 different parameters that I want to find with least squares. So using least squares I want to find the value of a, ...
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2answers
60 views

Fit exponential distribution with noise

I'm trying to fit an exponential with noise (which in this case is a constant $c$) like this one $$ y(x) = \alpha e^{- \alpha x} + c \text{ ,}$$ having $(x_i, y_i)$ values (So $\alpha$ and $c$ are ...
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1answer
30 views

Interaction between time-variant and time-invariant variable in FE model

I want to estimate the effect of several variables $x_{1,it}$, $x_{2,it}$, $\dots$ on $y_{it}$. All of these variables vary across countries $i$ and time $t$. I use OLS to estimate a model with ...
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21 views

How do I weight inputs to a regression model so that one figures into the model more than the other?

I have obtained a series of weights from a text mining algorithm. Unfortunately, my algorithm is not capable of doing certain tasks that are too similar without some sort of regression analysis, say ...
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26 views

Weighted Least Squares Normalization for Parameter Uncertainty

I want to fit a function $f(x_1,x_2..)$ to (noisy) data with unknown variance. For each datapoint, I have a weight $w_i$ which is proportional to the reliability of that particular datapoint. The real ...
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6 views

Different number of observations for two samples in pooled ols?

In a Pooled OLS regression, on stata, would it matter if my first sample had 100 observation (100 countries) and my second sample which is independent of the first sample, contains 120 observations ...
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32 views

Moving window forecasting in Python

I am looking to create some code that will out-of-sample forecast the HAR-RV model. The model itself is formulated as the following, and the betas are estimated through HAC-OLS or Newey-West. ...
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10 views

Hausman for comparing ols versus fixed effects

Can we use a hausman test to compare between fixed effects and pooled ols? If yes, can you link me to a proper source which suggets this?
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5 views

Implications of LInktest

I have a panel dataset and I am doing a pooled ols on it. When I doo linktest, my model is misspecified. Could it possibly mean the misepcification is because the data has region or time effects and a ...
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1answer
43 views

OLS versus IV regression results

I am doing an IV regression after OLS. From OLS I get significant results but I want to control for endogeneity and check reverse causality. So when I do IV, the sign of my main explanatory variable ...
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66 views

What is the name for this unintuitive result with OLS on a very “asymmetric” regressand, and how should it be addressed?

Say our sample consists of about a hundred Belgian (x = 0) and Swiss (x = 1) chocolate bars. We test them to see if they have safe (y = 1) or lethal (y = 0) levels of arsenic. As it turn out, 90% are ...
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2answers
36 views

Heavy-tailed residuals for OLS regression with large n. Implications?

I am trying to fit a multiple regression on a dataset with n=8619. First of all, using an untransformed Y as the response variable (ie Y = aX + bX +..) resulted in a residual plot with increasing ...
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42 views

Least squares regression of NPS

I would like to monitor customer satisfaction over time and would ideally like to use NPS for that. Specifically, I would like to see if there's an overall trend over time. Could I regress Net ...
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11 views

OLS exam question [duplicate]

have an econometric methods exam coming up and don't have access to any mark schemes, so the more detailed the better! (a) In what sense is the OLS estimator a linear estimator? Distinguish this ...
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160 views

Assumptions to derive OLS estimator

Can someone briefly explain for me, why each of the six assumptions is needed in order to compute the OLS estimator? I found only about multicollinearity—that if it exists we cannot invert (X'X) ...
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25 views

Pooled OLS versus Fixed Effects [duplicate]

I have an unbalanced panel data and I run a pooled ols and my results are fine. But when I do the diagnostics, linktest and ovtest fails. I then do Hausman to compare between ols and fixed effect. I ...
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32 views

VECM model output - where is the long run relationship?

So I'm getting the following EViews output, but where on earth is the long run relationship? Do I have to estimate it separately using OLS? If you have to estimate it yourself via OLS, I've already ...
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19 views

When is OLS and FD equal?

I am running an OLS and FD regression. The estimates (on the parameters that appear in both models) are exactly equal, how can this be? By FD I mean: OLS applied to the first difference of the ...
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1answer
75 views

Assumptions and terminology for dynamic regression with endogenous offset ($y_t=y_{t-1}+\beta X_{t-1}+\epsilon_t$)

I'm dealing with a fairly simple time series regression model with the following basic form: $y_t=y_{t-1}+\beta X_{t-1}+\epsilon_t$ I'm assuming that observations of $y$ are known without error. $X$ ...
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17 views

Applying Dynamic OLS

I am trying to analyze the cointegration relationship between I(1) variables using DOLS and want to check whether the following steps are OK: Select optimal lag of leads and lags using information ...
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31 views

Interactions and Multicollinearity

I have a question concerning multicollinearity in OLS. I built a very simple model: y = a + x(x) + y(x) + e. In this case x is a significant predictor, y is not. Both of them are time related ...
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15 views

How to find least squares solution with multidimensional data?

I have a data set, on which I want to learn the matrices A and b. So my model is : $$ Y = Ax + b $$ and let's say $x$ is of size $11$x$1$, and $Y$ is $9$x$1$. And I have $50$ observations ($50$ ...
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29 views

Stata - regression homework question [closed]

I'm currently attending an econometrics class at my university and it's not my strongest side. So we got a homework problem set and I am having trouble solve it. Here it is: ln E[Y | X1, X2, X3] = ...
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13 views

MATLAB: bounding the parameter values in nonlinear modelfitting and AICc scores

I am trying to fit a number of nonlinear models to a dataset, and I need to bound the model parameter values to all be positive. I tried lsqcurvefit function and it works. However, I also need AICc ...
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38 views

Prediction Intervals for Incremental OLS regression

I am implementing incremental OLS regression algorithm where the data points arrive one at a time. As the regression parameters are determined by the formula, $(X'X)^{-1} X'y$ and the Sherman-Morrison ...
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1answer
32 views

Expectation of squared error

In machine learning, we let $X$ be a real-valued input vector and $Y$ be a real number output, with joint distribution $P(X,Y)$. We are looking for a function $f(X)$ for predicting $Y$ given the ...
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1answer
56 views

How to calculate the prediction interval for an OLS multiple regression?

What is the algebraic notation to calculate the prediction interval for multiple regression? It sounds silly, but I am having trouble finding a clear algebraic notation of this.
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26 views

What is t in ordinary least square?

What is t in this formula? where X is a matrix of independent variables, with the elements of the first column set to 1, and Y is a vector of observations of the dependent variable
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2answers
118 views

How to change the null hypothesis of the coefficient in the least squares fitting?

I have a least square fitting like this: fit = lsfit(log10(M), log10(RS), wt) This function lists statistics and p-values for the coefficient considering the ...
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5answers
1k views

Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter?

When we conduct linear regression $y=ax+b$ to fit a bunch of data points $(x_1,y_1),(x_2,y_2),...,(x_n,y_n)$, the classic approach minimizes the squared error. I have long been puzzled by a question ...
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1answer
37 views

Why can OLS account for non-linearities even though linearity is assumed?

One standard example when introducing OLS in econometric classes is modelling the log-wage by education and experience. Often, the example models account for experience by not only by the experience ...
3
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1answer
70 views

Estimation process in OLS with categorical variables and dummy coding

In my question (Cox model on bank customers) regarding the estimation process in regression with categorical variables, @Scortchi write the following: Any coefficient in a multiple regression ...
3
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1answer
38 views

Recovering original regression coefficients from standardized

Suppose I use Least Squares to estimate coefficients in the standard linear model with design matrix $X$'s columns standardized, so the model is $$ E[y] = X^*\beta^* $$ where $X^*$ is $X$ with columns ...
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1answer
34 views

Least-squares training error

In classification problems, the training error typically decreases as further training examples are acquired. However, in my current least-squares problem, the training error actually increases as ...
2
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1answer
42 views

Estimation of individual demand for gasoline

Quantity and price of gasoline are clearly endogenous because the quantity and price are determined by the supply and demand. However, the estimation of individual demand for gasoline is often done ...
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1answer
23 views

Interpreting OLS Cross-Sectional Macro Data

I have the following model: $y=a_0+a_1(x_1/z_1)+a_2(x_2)+e $, where $y$ = the average log of variable y, $x_1$ = the average ratio of $ x_1/z_1 $, $x_2$ = is the averae log of the variable $x_2$. ...
2
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38 views

Adjusting for the past using OLS regression with single lagged response

There are many fine ways to handle a time series error structure in regression, for example as discussed in Time Series with Autoregressive Error. But consider a panel regression model of the form $$ ...
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1answer
29 views

Mean squared error versus Least squared error, which one to compare datasets?

I have 3 datasets of the same system. But for the first one, I have 21 measurements. For the second and the third one I have only 9 measurements. Now I made a model using these 3 datasets (so 3 ...
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26 views

Interpreting interaction terms

I have 9 regional dummies (using only 8 in a regression equation to avoid collinearity, omitted the richest region) and a few explanatory variables such as formal housing (1 if an individual lives in ...
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1answer
31 views

OLS regression user defined function in Python

Is there a way to handle complex functions for OLS regression in Python? For example, if my function is $y = a - bx^{c} + e^{dx}$, then how I can use a Python library to estimate $a,b,c$ and $d$? i ...
2
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3answers
107 views

Estimation of unit-root AR(1) model with OLS

Given a random walk $x_t$, $$x_t=x_{t-1}+\varepsilon_t,$$ consider estimating the slope coefficient $\beta$ in $$x_t=\beta x_{t-1}+\varepsilon_t$$ by OLS. This question and the following answer ...