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Questions tagged [regression]

In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors').

"Regression" is a general term for a wide variety of techniques to analyze the relationship between one (or more) numerical dependent variables and independent variables. Typically the dependent variables are modeled with probability distributions whose parameters are assumed to vary (deterministically) with the independent variables.

Ordinary least squares (OLS) regression affords a simple example in which the expectation of one dependent variable is assumed to depend linearly on the independent variables. The unknown coefficients in the assumed linear function are estimated by choosing values for them that minimize the sum of squared differences between the values of the dependent variable and the corresponding fitted values.

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Infinite Variance Regressors

Many presentations of OLS have a condition, $E(X'X)<\infty$ and is invertible. My question is, why is $< \infty$ critical? Consider, $$y_i =\beta_0 +\beta_1 x_{1i} +\varepsilon_i $$ The condition, $E(X'X)<\infty$ in this setting is equivalent to…
Michael Gmeiner
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Alternative to linear regression

I'm third year economics student and all econometrics we had so far and basically all empirical studies in economic subjects we had so far are linear regression. Is there any alternative, can anyone suggest any reading material or direction in which…
econ
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What happens when I leave out empty cells in regression?

I'm using Stata 14.1 to do a regression, and I got a matsize too small error. It gave some more output to tell me possible reasons for this problem, and I think this was the reason that applied to me If you are using factor variables and included an…
user4207
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Why don't economists do regression diagnostics?

There is a lot of talk about regression diagnostics in tutorials on the web, but then in economics research papers nobody actually reports residual plots, collinearity checks etc. Is there any reason for this?
Papayapap
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Suggested model for dependent variable of different groups

I want to test the impact of X on Y. The dependent variable Y is being employed. Now, I want to see if the impact of X is different for those employed in agriculture (A) and non-agriculture (N) sectors. What is the right model to do this? Do I need…
D_B
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Transforming a matrix of explanatory variable in regression

Given the partitioned regression equation (into $X_1$ and $X_2$), I want to transform $X_1$, say $X^*_1$, such that $X_2$ and $X^*_1$ becomes orthogonal ie. $X_2^T$. $X_1^*$= 0. A matrix can be transformed as $X_1^*$ = $X_1$.p where P is…
Elina Gilbert
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Can I use calculated data for regression

Can I use calculated data for regression analysis. case 1: first run OLS $y = \alpha+\beta x$, and get $\hat\beta$, then calculate $z = h^\hat\beta$, at last run $m = \gamma + \mu z$. case 2: follow the same settings as case 1, run $z = \zeta + \rho…
XJ.C
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Can I multiply two dummy variables together?

Are there any rules about multiplying dummy variables in a regression? For example can I say: y = D1D2x1 + x2 + x3 Would I be able to state D1*D2 as I want both criteria to be met before x1 is included? Would the correct notation then be as…
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Regarding the starting point and assumptions of linear regression model

Here is my understanding of the linear regression model with single regressor: We suppose that the population regression function takes the form of $Y_i=\beta_0+\beta_1X_i+u_i$. Furthermore, for the parameters to have causality meanings, we assume…
WinnieXi
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rotating and exchanging x for y's in regression

I was just wondering what happens generally if i send all my x points to y's and y's to x's (i.e reflect along the y=x line) - if I change the x's and y's will my old error minimizing line still be the error minimizing line after reflection? How…
bob
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Compute the inverse of a conditional quantile regression output

Short Clarification : This question was asked at the Cross Validated SE (Question at CV) but one highlighted in the comments, that this might be more applicable to this SE due to its economic topic. Feel free to migrate the question (if possible) to…
mugdi
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Specification bias - estimated variance is biased estimator of true variance of error term

Consider the two models $ (a) y = X\beta + u $ where $X$ is $n \times K$ and (b) $y = Z\gamma + \omega $ where $Z$ is $n \times r$. Under classical assumptions (and $Z$ and $X$ are non-stochastic) if model (a), that is $y = X\beta + u$ is the true…
Elina Gilbert
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OLS estimator derivation: second-order condition to prove global minimum?

In deriving our ordinary least squares estimates, we can partially differentiate the sum of squared errors $\sum_{i=1}^{n} {e_i^2} = \sum_{i=1}^{n} {(Y_i- \hat{\alpha}-\hat{\beta}X_i )^2}$ with respect to our estimators $\hat{\alpha}$ and…
rchng
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Relationship between parameters estimates of continuous variables and dummy variables

I had asked this question on cross validated before, and have deleted it. Suppose we have a standard wage equation: $$w_{i}=β+β_{1}educ_{i}+x_{i}'\gamma+ϵ_{i}$$ where educ corresponds to education levels, $x_{i}$ is a vector of covariates. If we…
ChinG
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Regression coefficients interpretation

Can anyone help me with finding out the computations for reaching this conclusion? "In terms of magnitude, the point estimate implies that going from the average of 8% blacks in the same-gender cohort to 10% (an increase of around 1 within-school…
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