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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8 views

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 ...
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1answer
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? ...
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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 ...
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1answer
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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3answers
214 views

In linear regression, what does $\beta_1 = 0$ really mean?

If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)? The model is: $Y = \beta_0 + \beta_1X_1 + ...
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16 views

How can I work out the response effect for categorical coefficients in a generalized linear model?

I have a set of different algorithms I would like to test on a set of different data. Running one algorithm on one datum gives a performance score. This score is log-normally distributed, and ...
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1answer
42 views

How to manually calculate dfbetas

I am trying to replicate what the function dfbetas() does in R. dfbeta() is not an issue... Here is a set of vectors: ...
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9 views

Comparing regressions: usual regressor vs regressed-out regressor

I'm comparing the regression coefficients between 2 models: Model 1: $$ Y = \beta_1X_1 + \beta_2X_2 + u $$ Model 2: $$ Y = \beta_1'X_1' + \beta_2'X_2 + v $$ where $X_1' = ...
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18 views

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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8 views

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: ...
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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: ...
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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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1answer
16 views

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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11 views

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 ...
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1answer
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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1answer
45 views

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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1answer
57 views

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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1answer
26 views

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 ...
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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 ...
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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 ...
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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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36 views

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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14 views

PLS PM: Multiplying outer loadings with inner path coefficients?

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 ...
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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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13 views

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 ...
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1answer
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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1answer
30 views

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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31 views

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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1answer
26 views

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 ...
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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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1answer
43 views

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 ...
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1answer
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 ...
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1answer
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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1answer
54 views

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 ...
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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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21 views

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, ...
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1answer
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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67 views

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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32 views

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 ...
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0answers
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 $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...
0
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1answer
38 views

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 ...
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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 ...
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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, ...
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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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1answer
17 views

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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62 views

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 ...
2
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1answer
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 ...
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1answer
32 views

Fitting non linear regression with coefficients in the form of polynomial with Levenberg Marquardt

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 ...
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228 views

interpreting estimates of cloglog logistic regression

Could someone advise me on how to interpret the estimates from a logistic regression using a cloglog link? I have fitted the following model in lme4: ...