The parameters of a regression model.

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Inconsistent Performance of PCA Results from SPSS

I've completed PCA with my dataset (16 variables) and extracted 3 factors. I then created an Excel spreadsheet where I can enter in user provided data and calculate the scores for each of the three ...
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14 views

How to check for confounding factors

I have been doing an analysis using a difference in difference setup. In my raw sample I OLS and first difference (two time-periods) I get the effect that I would expect. Namely that shocks in the ...
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21 views

Is the constant value ignorable?

I am running a linear regression on SPSS. Basically I have 2 independent and 1 dependent variables; and I would like to understand which of my independent variable is more effective on the dependent ...
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11 views

Unit weighting for linear composites / regression

Cohen (1990) mentions a regression that I have not heard about before. Here is how I understand his description: Standardize the dependent and the independent variables Regress the standardized ...
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1answer
42 views

Large value of exp (B) in binary logistic regression SPSS what is wrong? [duplicate]

I had a very large value for Exp(B) in SPSS binary logistic regression. What is wrong and what should I do?
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1answer
22 views

Equation of a fitted smooth spline and its analytical derivative

I need to fit a spline function to a data set. I tried with bs, ns and smooth.spline. In my ...
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1answer
18 views

Beta coefficient interpretion with categorical and continuous predictors in a linear regression

I am trying to run a linear regression with both categorical and continuous predictors. I have coded the categorical predictor (with three levels) into three dummy variables, and entered the two dummy ...
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10 views

Covariance of the regression coefficient of two regression given the correlation between the independent variables

Given the following equations $$ Y=x_1\beta_1+\epsilon_1 $$ $$ Y=x_2\beta_2+\epsilon_2 $$ Where $Y$, $x_1$ and $x_2$ are all normalized, and that $x_1$ and $x_2$ are correlated with Pearson ...
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1answer
105 views

Trust of coefficients of Logistic Regression

I use logistic regression to model the probability of an event and all of my features are categorical variables. Note that some values of the categorical variables are more frequent than others. The ...
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28 views

Counter intuitive result from logistic regression

I am looking at how well test scores can predict disease status (case/control). There are 6 tests total, A, B, C, D, E, F. And for tests A-E, a higher score is worse (i.e, a higher score is associated ...
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86 views

Interpretation of continuous variable in dummy-continuous interaction

Similar questions have been asked before, but all of them focus on the dummy or interaction term. Say run an OLS regression on the model: $\ln( housePrice )= \beta_1 \times pollutionLevel + \beta_2 ...
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1answer
52 views

Multiple Linear Regression coefficents

I'm doing a linear regression, in R. The values are like this - ...
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1answer
38 views

Confused with SPSS ordinal regression output

I'm a bit (actually, totally) confused with SPSS ordinal regression output. Let say we have dependent variable score=1,2,3,4,5 (higher is better) and one predictor gender=male,female. We run Ordinal ...
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Standardized Coefficients and Partial r

Ive looked over a few of the posts here on regression coefficients and partial regression coefficients but haven't seen an answer to this question, which maybe easily inferred from the other answers ...
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34 views

Covariance of many simple regressions

Assume we have a true model of $$Y=X\beta+\varepsilon,$$ where $Y$ is some outcome , $X$ is a $1\times p$ vector of covariates which have a (non-diagonal) variance-covariance matrix $\Omega$, ...
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38 views

Is it appropriate to conclude the relationship “does not matter” because the regression coefficient is not significant?

Many papers (e.g. apps.washingtonpost.com/g/documents/national/does-the-amount-of-time-mothers-spend-with-children-or-adolescents-matter/1490/) try to claim an insignificant regression coefficient ...
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Significant digits for curve fit to numerically generated data

Say that I fit some data with some model, for instance a linear function $y = mx+b$. What is the proper way to report the fitted coefficients and the goodness of fit? Specifically, if I do the fit in ...
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15 views

Worryingly Huge Coefficients with Regression Discontinuity Design

I am running a regression discontinuity design for a project in the early stages. I'm unable to share the data or printouts at this point, for which I apologize, but hopefully the general issue I'm ...
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1answer
63 views

Interpreting what this means in a paper - significantly different at the .05 level? [duplicate]

I am having a hard time interpreting what something means in a paper I'm trying to get through. If you care, this is the paper: Gender Differences in the Effect of Education on the Slope of ...
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11 views

Cox/ Binomial Regression: How to reconcile Non-significant model with significant IVs

I'm been performing some survival and regression analyses corresponding to an event of interest being death or a certain surgical procedure, namely a shunt revision for pediatric neuro-surgical ...
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1answer
23 views

Why do we make a F-Test rather than a Beta-Test in ANOVAs?

When one performs an ANOVA, (s)he always end up calculating the observed F-ratio and comparing it to the appropriate F-distribution. From this post, I discovered that the coefficient of correlation ...
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238 views

Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?

I have built a logistic regression where the outcome variable is being cured after receiving treatment (Cure vs. No Cure). All ...
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22 views

Does the sign on a non-significant IV coefficient matter?

I have a logistic regression where I am forcing some IVs into the model. I am getting the "wrong sign" i.e. contrary to what is expected, but the association is not significant. Does the sign matter ...
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46 views

Variance of slope

I have a bunch of data that I fit a linear regression to, and now I need to find the variance of my slope. Is there an analytical way to get this? If an example is necessary, consider this my data in ...
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36 views

Transformation of regression model to estimate sum of coefficients

How can the model $y=\beta_0+\beta_1x_1+\beta_2x_2+e$ be transformed so that it estimates the sum of $\beta_1$ and $\beta_2$, that is, $\beta_1+\beta_2$ is a coefficient in the new model?
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drawing confidence interval graphs [migrated]

I've made regression model with 4 variables. And I have gotten the following regression equation $$ Y= 0.0761 - 0687X_1 - 3.46X_2 - 1.937 X_3$$ I calculated Confidence intervals for these four beta ...
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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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29 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
47 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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98 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
29 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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231 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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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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83 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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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: ...
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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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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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19 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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1answer
32 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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51 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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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
34 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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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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64 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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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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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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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 ...