Tagged Questions

The parameters of a regression model.

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When adjusting for X1, have we adjusted for X2, to the extent that X2 is related to X1?

I've just read Elizabeth Stuart's paper on matching methods (http://biostat.jhsph.edu/~estuart/Stuart10.StatSci.pdf), which I find very informative. She discusses propensity score methods and the ...
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Standardized Regression Coefficients for categorical interactions: lm.beta() vs. regressing standardized variables

I am working with a regression model from which I would like to compute standardized regression coefficients. I am writing primarily regarding an observed discrepancy between coefficients obtained by ...
44 views

How to decide whether a variable belongs to a linear model?

I have a set of inputs $x$ and noisy outputs $y$. I think that either $$y = a_0 + a_1 x$$ or $$y = a_0 + a_1 x + a_2 x^2.$$ How can I determine which model was more likely to have generated the data? ...
88 views

Can logistic regression be modified to predict a distribution, not just point-estimate? Other ways to learn a beta distribution from binary events?

Currently I'm using high dimensional logistic regression to predict the probability of a rare event. I use this probability for both ranking and for other calculations which need it to be ...
28 views

Where does the correlation come from in the regression coefficient equation for simple regression

In simple linear regression. $\beta = \frac{Cov(x,y)}{s_x^2}$. This is often written as $\beta = r_{xy}(\frac{s_y}{s_x})$ Where does the correlation come from in this equation? From my understanding ...
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bootstrapping a regression with autocorrelated error

I have to verify that on two variables, $X_t$ and $Y_t$ hold the followings: $Y_t=\beta \times X_t+\varepsilon_t$ and that $var(Y_t)=\gamma \times X_t^2$. In order to give evidence / support to these ...
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Relationship among parameters from models with different link function and scaled response variable

Given the model, $\log(A_i) = \alpha + \beta \, covar_i$, with $i=1,\dots,1000$, $\alpha=4$, $\beta=0.2$, and covariate $covar \sim U(-1,1)$, I derived $\log(A)$ values (in $\texttt{R}$) as: ...
17 views

Upon transforming coefficients, how do I transform SE, z value and Pr(>|z|)?

From a Negative Binomial regression, I obtain the following coefficients: ...
36 views

Are sufficient statistics for regression equivalent in the frequentist and Bayesian cases?

If I have a Poisson regression such that $\lambda = \alpha + \beta t$, $\alpha + \beta t \geq 0$ $\forall t, \alpha, \beta$ and $Y_t \sim \textrm{Poisson}(\lambda_t)$ for which I have 10 observations ...
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Model selection with ncvreg

I'm quite new to R programming and was wondering, How can I read the output of the ncvreg function to find the model it selected (say with the MCP penalty)? Also how can this package be used to ...
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Testing Various Hypothesis Test for Coefficients in R [migrated]

I Know in R it returns for a Multiple Regression it returns hypothesis test for $\beta_i=0$ but what if you want to test such tests like $\beta_i=1$. Is there any easy command for this or if not how ...
22 views

Interpretation regression coefficients predictors and dummy variables

I have to run a regression predicting the DV (continuous) from an equation with: Y = X1(dichotomous factor, coded 0-1)+X2(dichotomous factor, coded 0-1)+X1X2+M1+M2+M3+...+Mn, where M1...Mn - ...
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How to decide which main variable is modified by the interaction term?

Given the following linear model $Y=int+aX1+bX2+c(X1*X2)+e$, where $X1$ and $X2$ are the main variables, ($X1*X2$) is the interaction term, and $a$, $b$, and $c$ are the corresponding coefficients. ...
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Testing the statistical significance of regression coefficients in a logistic regression

Are only the p-values relevant when testing the regression coefficients of a logistic regression? Does the z-value of a coefficient give any further information about the significance of the ...
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Is the significance of difference in slopes equivalent to the significance of the slope of the difference of two series?

Say you have an independent variable, $x$, and two dependent variables $y_1$ and $y_2$. I want to calculate whether these two variables have a significantly different slope. I can do it by calculating ...
6 views

Proof of equivalence between results obtained from alternative event study approaches

Consider two common approaches to an event study in the case of an asset return time series: 1. The event window model We define an estimation window and a distinct event window. We fit a model of ...
38 views

Percent change interpretation in log-transformed regression: Percent change from what?

I am dealing with a regression model where both the DV and IV are log-transformed. I have found this explanation of how to interpret the effects (both in the Cross-Validated hyperlink and in ...
15 views

Solve intercept coefficient Dummy Variable regression

Suppose we have the model $y=\beta_0+\beta_1 x_2+\beta_2x_3+e_i$ where $x_1, x_2, x_3$ are binary variables, taking on values 0 and 1, so for example, if $x_1=1, x_2=x_3=0$. Now we want to regress ...
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Gelman & Hill ARM - Question 5.11

Gelman Hill textbook has a question using election / voting data (http://goo.gl/ff8ryn); After fitting a logistic regression model for year 1964 using inncome, race, gender as a covariate, ...
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I'm referring to a method called PLS PM: http://cran.r-project.org/web/packages/semPLS/vignettes/semPLS-intro.pdf http://gastonsanchez.com/PLS_Path_Modeling_with_R.pdf Not going into detail, I just ...
23 views

What does the sign of a coefficient estimate tell us about the sign of the correlation between two variables?

Say I have a simple multiple regression model with two variables. If the coefficient estimate for beta2 is positive, and the coefficient estimate for beta1 is negative, does the sign of beta2's ...
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Finding the amount of error with a multiple regression formula that is determining stock returns

I'm brand new to statistics and I'm using C# and Math.Net to perform multiple regression on a formula with 3 inputs and 1 output. I was told that finding an rsquared value isn't recommended for a ...
59 views

standard error of transformed regression coefficient

I have the regression $y= \beta_0 + \beta_1 \,x + e$, along with the standard error of $\beta_1$ I would like to find the standard error of the elasticity at $\bar{x},\bar{y}$, which is given by ...
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Java and R: Least Squares Coefficient Estimation - Start at time Zero?

This is the data set I have: vector <- c( -7.459981, 13.26651, 12.10128, 2.380662, 26.42393) Doing an estimation of the coefficient with a linear regression ...
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Standard error/deviation of the coefficients in OLS

In OLS, the variance of the regression coefficients are computed as $$\mathrm{Var}(\hat{\beta}) = \sigma^2(\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}.$$ Now, if I need to compute the standard ...
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oaxaca decomposition: how to treat error term and do intercrossing intercepts matter

I am just wondering if I can decompose a difference in earnings let's say between year 1999 and 2002 into the difference due to a higher education level of labour market participants and due to higher ...
52 views

Model selection

I have a small dataset of 37 observations with students' performance on both cognitive tests (5) and professional tests (6). My goal is to predict professional tests (DV) with cognitive tests(IV). To ...
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Running all possible additive combinations of a linear model and averaging the coefficients

I have nine predictor variables and one response and when I run a linear model in R I'm getting negative coefficients and non-significant p-vales for essentially all the estimates. I've examined the ...
37 views

Slope estimate dependent on covariance?

I am trying to perform a linear regression with equal errors on x and y (ex =1 and ey=1) in a Bayesian framework (using WinBugs). Using Winbugs (solid line in the Figure), I managed to reproduce the ...
57 views

Testing a regression coefficient against 1 rather than 0

Brief caveat- I haven't dusted off my stats knowledge since some university courses a few years ago, and I'm struggling with cobwebs. I have a model where a linear 1 to 1 relationship has been ...
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Why is there no intercept in a regression model equation with standardized coefficients?

Let's say my model is this: $y = -0.372 + 0.045x_1 + 0.03x_2 - 0.205x_3 + 0.114x_4$, and my standardized model is this: $y = 0.635β_1 + 0.618β_2 - 0.466β_3 + 0.232β_4$. Why is there no intercept in ...
46 views

How to determine the significance of an interaction?

My question is simple: How do you determine the overall significance of an interaction (i.e. the marginal effect of $X$ on $Y$ for different values of $Z$)? But the background is a bit ...
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Online Learning of GLMs

I am thinking about learning GLMs (well, actually a Zero-Inflated Negative Binomial model) in an online manner. As far as I know, there is no direct way to learn GLMs in an online manner. Therefore, ...
66 views

Extreme differences in Odds Ratios in Logistic Regression with or without a predictor

I was trying to get an intuition for the interpretation of the coefficients in a logistic regression that was intended to reproduce to some extent that presented in a youtube video ...
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Poisson Regression Model - How to interpret the IRR and Base-Ratio?

By studying the Poisson regression model to analyze count data, I chanced upon the Incidence Rate Ratio (IRR). Browsing on the internet, I found different interpretations of that. For instance, ...
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Deforestation Scenarios using Logistic Regression (Stata)

I used Logistic Regression to model the contribution of a range of explanatory variables on deforestation processes (being my dependant variable - Deforested=1, No Deforestation=0) in the Brazilian ...
38 views

Prior for the coefficients of a linear regression model

I have a linear regression model $\bf Y=\bf{X}\bf{\beta}+\epsilon$. I want to assign a prior on $\bf\beta$ in order to derive the posterior predictive model $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...
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What to make of countervailing spatial regression coefficients?

I am running regressions across a country's counties (N about 300). I divide the country in two regions A and B to control for potential unobservables. My explanatory variable varies at the county ...
28 views

Standardized Coefficient (beta)

I am doing research on advanced manufacturing technologies such as Computer Aided Design, Computer Numerical Machines and Computer Aided Engineering. When I found their Standardized Coefficient ...
38 views

Bootstrapping on Regression Coefficient

I want to see if my logic is correct. Say that I have 250 data samples and for each of the sample I run a simple OLS $y=\beta x$. I then have 250 $\beta$. Now my objective is to see if, on average, ...
84 views

Distribution of linear combination of OLS regression coefficients

I have a simple linear OLS regression $Y_i = \alpha+ \beta_1 X_{1i} + \beta_2 X_{2i} + e_i$ where $e_i \sim N(0,\sigma)$. I have estimated the regression from the data and obtained estimates for my ...
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Can't derive some equivalences between regression coefficients formulas

I stumbled upon this set of equivalences between different formulas for $\beta$ : http://upload.wikimedia.org/math/0/d/d/0ddedb446f7520df577fcf48aa7012e2.png . However I cannot go from the first step ...
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Equivalence of intercept beta test to one-sample t-test in linear regression model with categorical variable

I am testing my understanding of the equivalence between basic linear regression with categorical variables, and one-sample / independent samples t-tests. I don't think this corresponds to an existing ...
83 views

Logit - comparison of predicted probabilities

I am analyzing, for two different time periods, the probability that an individual will have outcome Y (=1 or 0) given that an event X has occurred (=1 or 0). A number of demographic variables are ...
I am trying to do non-linear regression by using Levenberg Marquardt least square fitting (in R). I know that it can do the fitting for a function in the form of $f(x) = sin(Ax)+cos(Bx)$ to ...