# 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').

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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 ...
1answer
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### Confidence Intervals for Elasticity in Simple Linear Regression

I'm pretty sure this is a very simple question that I am missing something obvious. I have a simple linear regression with multiple independent variables. I want to calculate the elasticity (no ...
1answer
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### How to get the effect of one dummy variable against many others?

I have the following regression: wage = constant + (beta1)*michigan+ (beta2)*california+...+(beta49)florida+(beta50)education + u where michigan is equal to one if the person is from michigan and ...
2answers
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### How do I choose the correct model for a regression?

So the central question of my project is to what extent does a country's level of export contibution towards GDP (i.e. exports as a % of total GDP) affect its GDP growth. I'm comparing this ...
1answer
56 views

### Does anyone recognize the shape of this residuals vs. fitted plot?

Hello Stack Exchange community, I'm running a regression on a survey dataset which consists of 45,381 individuals in 36 countries using Stata. My model is specified as: ...
1answer
59 views

### Principal component analysis interpretation

Suppose a wealth index is computed using information on a set of 14 assets that a household possesses. The index is generated using principal components, as the 14 individual asset variables are ...
2answers
86 views

### 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 ...
1answer
58 views

### Should the control variables in an econometric regression be correlated with both the dependent and the primary independent variables?

If, for instance, my dependent variable is some happiness index, and my independent variable is a dummy for whether they experienced some randomly occurred natural disaster. I am trying to analyze the ...
1answer
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### In panel data application, when using Fama and MacBeth regression is preferable over the fixed or random effect model? thought

When discussing panel data, many econometric books, usually, focus just on fixed or random effect model as means of estimating regression for panel data. Despite this tendency, I have seen many papers ...
2answers
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### regression method for data that contain a number of observation for several years

I have a data set about 125 companies. For each company I have the salary and some other variables about the top 5 managers in each company. One observation contains the top 5 managers in each one of ...
1answer
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### Correct Equation for Pooled OLS Regression (with Time Dummies and Interaction Terms)

I have a question regarding a pooled OLS regression. Basically, Iām not sure Iām writing out the equation properly. The data is on feature films released between 2006 and 2016 (11 years); box office ...
1answer
84 views

### Linear Regression Assumptions of Homoskedasticity

When I studied linear regression analysis, one of the assumptions taught was that of homoskedatiscity. I understood that homoskedasticity was required for significance testing on the coefficients. ...