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# Questions tagged [least-squares]

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 squares and least squares is the idea underlying the use of mean-squared-error (MSE) as a way of evaluating an estimator.

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### Help: Partitioned samples efficiency in OLS compared to one sample regression

As usual, we can estimate by OLS the model (in matrix form) $Y=\alpha+\beta*X+u$ with a sample of $n+m$ observations. The OLS estimator is $\hat{\beta}=(X^{T}X)^{-1}X^{T}Y$. Now, if we partition our ...
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### Asymptotic variance of linear regression with homoskedasticity assumption (Wooldridge Panel book Eq. (4.10))

Jeffrey M. Wooldridge Econometric Analysis of Cross Section and Panel Data Chapter 4 The Single-Equation Linear Model and OLS Estimation Section 4.2 Asymptotic Properties of OLS Subsection 4.2.2 ...
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### Prediction with uncertainty after least-square estimation

I've fit a model (the solution to differential equations or some other non-linear functions) to observational data to estimate the best-fitted parameters and their uncertainty by least-square methods (...
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### The Literature on the impact of outliers on ordinary least square (OLS) regression

I remembered I have encountered a paper in 1960s or 1970s that explore the impact of outliers on ordinary least square (OLS) regression. In the paper, it is shown that just adding one outlier will ...
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### If linear regression is parametric, do we need normality of the features and/or target? [duplicate]

From what I know, linear regression is a parametric model (as mentioned in here). Parametric tests requires normality of the variables. My first question is that this is an assumption of the linear ...
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### Linear regression model with a distribution over regression equations

Suppose that the observations $(y_t, x_t, k_t)_{t=1}^N$ satisfy the linear regression equation: \begin{equation} \begin{split} y_t = \begin{cases} x_t \beta + e_t & w.p. \; \theta \\ k_t \gamma + ...
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### How to manually calculate the variance of the least squares estimator in R [closed]

As stated in the title, how do you manually calculate the variance of the least squares estimator in R? I know that the least estimates have the following formula: $$\hat{\beta}=(X^TX)^{-1} X^T Y,$$ ...
1 vote
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### Independent variables affected by size, how I resolve this problem?

I am doing a research about the impact of trade unions on permanent contracts. The dependent variable is trade union presence (0,1), the independent variable is number of permanent contracts ...
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### Log of a log-transformed variable

I have been suggested to use the log of a log-transformed independent variable (i.e., log(log healthcare expenditure)). I am not sure how would this make sense. Is this a standard practice (in the ...
1 vote
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### How can I estimate the sum of coefficients

I am trying to estimate the cumulative effect. When I have an ols regression with many dummies as explanatory variables, can I sum the coefficients to find the cumulative effect? If yes, how do I find ...
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### Confidence bounds for coefficients of a fit of data set obtained with another fit

I fitted an equation to a set of data points. Then I substracted the fit previously obtained to another set of data points. After that, I fitted another equation to this new data (result of the ...
1 vote
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### How do I represent an OLS regression model as a mathematical equation?

I have created an OLS regression model as part a pre-test/post-test experimental design with a single factor (group membership). In order to investigate the interaction between pre-test and group ...