The parameters of a regression model.

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Density plot of parameter estimates from linear regression model

I am running a linear regression model in R: data(iris) fit1.iris = lm(Sepal.Length ~ Petal.Length+Petal.Width , data=iris) summary(fit1.iris) These are my ...
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21 views

Regression without intercept [duplicate]

I saw that here explain how to get the formula for getting a regression without intercept but I already know it (for example in R you get it outomatic with ...
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1answer
16 views

Multiple Regression - Converting Standardized Coefficients to Unstandardized

I recently performed a multiple linear regression using a standardized set of data, and I was wondering if it possible to convert the standardized coefficients from the regression into usable ...
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21 views

Finding standard error of beta coefficients in ridge regression using lambda

I need to get the standard errors of coefficients with Ridge Regression, by calculating the SE of the beta estimates after I choose the right lambda. ...
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1answer
35 views

Method to identify the point in which the slope of a predicted probability becomes significant

I'm running a logistic regression in which I'm predicted a binary response from a continuous predictor... I'm interested in determining the exact point in which the predicted probability ...
3
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1answer
87 views

Clarification: The covariance of intercept and slope in simple linear regression?

Help me understand this relatively simple (I think) concept: The covariance of the intercept ($\beta_0$) and the slope ($\beta_1$) in simple linear regression. Furthermore, what range of values ...
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1answer
90 views

Describing Results from Logistic Regression with Restricted Cubic Splines Using rms in R

Updated I have been developing a logistic regression model based on retrospective data from a national trauma database of head injury in the UK. The key outcome is 30 day mortality (denoted as ...
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57 views

Regression coefficients significance

What are theoretical reasons to keep variables which coefficients are not significant? I have several coefficients with p > 0.05. What's causing large p values?
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1answer
79 views

Why are the signs of my coefficients are different?

My code is: library(survival) attach(veteran) survreg(Surv(time,status)~karno+diagtime+age+prior+trt ,dist="w") My analysis and the one in a book are as follows: ...
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54 views

Undesirable direction of beta coefficient in simple linear regression

The beta coefficient for independent variables surprisingly become negative, and with significant p-value. e.g. smoking (independent) and risk of lung cancer (dependent) Regression coefficient for ...
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2answers
171 views

How to interpret standardized regression coefficients and p-values in multiple regression?

I've been using R to analyze my data (as shown in example below) and lm.beta from the QuantPsyc package to get the standardized ...
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25 views

Regression with related coefficients

I've worked out that some physical process has the form $y = ax_1 + (1-a)x_2$, and would like to perform regression to find $a$. I thought about multiple regression of $y$ on $x_1$ and $x_2$ and ...
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25 views

Comparing influence of single independent variable on two dependent variables (time series)

Scenario description: Temperature has been measured at $k+2$ different depths in a borehole. Measurements of the temperature were taken once each hour over a period of about 3 months. So observed data ...
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29 views

How can I create a linear regression model with some negative coefficients in R? [duplicate]

What I'm trying to do is to construct a linear model in a form like $$ Y = \beta_0X_0-\beta_1X_1+\beta_2X_2 + \beta_3 $$ where $\beta_0$, $\beta_1$ and $\beta_2$ are coefficient of predictors $X_0$, ...
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5 views

How to interpret results. Pre-post survey. Post-only IV, pre and post scores as DV

We are working with an organization that has recently gone through a merger. We did a survey of the entire organization immediately after the merger, and another survey one year later. Our hypotheses ...
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35 views

Proving a linear model is not identified

Suppose there is a linear model: $$Y_i=\beta_0+\beta_1X_i+\varepsilon_i$$ How do I formally prove that without further assumptions $\beta_1$ is not identified. I thought to define a new set of ...
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1answer
57 views

What is the value of “X” in a regression equation when dealing with a time series?

I am using excel to add a polynomial trend line to a chart. The chart and the formula of the trend line are shown below. I want to add lines indicating different confidence intervals so I need to find ...
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31 views

How use standardized regression coefficient in analyzing Likert scale questionnaire to calculate the weight of each factor?

I have a Likert scale questionnaire of 5 scales (from not important at all to very important) and i want to analyse this questionnaire to find out the weight of each factor. and then get to a maturity ...
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12 views

Normality violations in multiple regression - report bootstrapped CIs, p values & t values?

I have analysed some data for a research project using multiple linear regression. However, normality assumptions for this method were not met in my data (and could not be resolved using ...
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8 views

Accuracy Assessment: Do I still have to use any other test statistics?

I have a training set and a separate test set. In both sets, I have extracted two different parameters and I have compared the predicted values of these parameters to the actual values. So, I have ...
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1answer
46 views

lmer: standardized regression coefficients

I have analyzed some data (the exact nature of which, I assume, is irrelevant for this question) using linear mixed effects models with the lmer() function from lme4. There has been at least one ...
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1answer
50 views

Need an Introduction to Generalized Non Linear Multiple Regression

I have been searching the internet for a generalized method for doing regression analysis on non linear data. My model can be represented as $$Y = \beta_0f(X_0) + \beta_1g(X_1) + ... + \beta_nz(X_n) ...
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52 views

The variance of linear regression estimator $\beta_1$

Can we say $$\text{Var}(\beta_1) = \text{Var}\left(\frac{\sum (x_i-\bar x)y_i}{\sum (x_i- \bar x)^2}\right) = \left(\frac{\sum (x_i-\bar x)}{\sum (x_i- \bar x)^2}\right)^2 \text{Var}(y_i) \;\;??$$ ...
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Interpretation of interaction term

I have a model: $$ \ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables. I have interpreted $b_1$ and $b_2$: ...
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29 views

How to make beta coefficients comparable?

My study design delivers both, count data and continous outcomes (e.g., numbers of taxa vs. an diversity index). As these variables are used as response variables, I have to use negative binomial glm ...
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29 views

Hierarchical weighted linear regression through the origin and varying slopes within groups

I am trying to fit a hierarchical linear regression model. My data includes samples with 10 different classes, and samples have varying numbers of data points (from 1 to ~1000). I want to fit a ...
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1answer
57 views

Modelling Fixed effects in panel data regression models

I was given the following equation: $$\sigma_{it} = \beta_0 + \beta_1 x_i + \beta_2y_i + \beta_3vs_{it} + \beta_4vm_{it} + \sum_{i=1} \gamma_i \alpha_i + \sum_{t=1} \omega_t \phi_t + \epsilon_{it}$$ ...
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29 views

Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across ...
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1answer
67 views

Interpretation of betas when there are multiple categorical variables

I understand the concept that $\hat\beta_0$ is the mean for when the categorical variable is equal to 0 (or is the reference group), giving the end interpretation that the regression coefficient is ...
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0answers
25 views

use many lms or random effects (lmer) to estimate a bunch of slopes?

I have what is probably a very simple question, but I just need someone to verify my thinking. I have a dataset that consists of a variable (var1) measured at 3 time points for about 80 people. At ...
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1answer
24 views

b-coefficient numerical value from pls r package

Has any body encountered a problem finding numerical values of b-coefficients while developing partial least squares regression model from spectroscopic data using ...
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32 views

Confusion about features selection for inference analysis with lm/glm

I need a bit of tutoring about grasping the true meaning of linear regression analysis. I'd like some help in understanding well the relationships between predictors and and the meaning of adding and ...
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1answer
110 views

How can I optimize coefficients of an arbitrary model?

This might be terribly easy but I'm probably lacking the keywords to search for. Assume the following (dummy) data: ...
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1answer
46 views

Changing polynomial degree leads to changing p-values in OLS regression

I have a question about interpreting coefficient $p$-values when fitting a polynomial function with ordinary least squares. When I sequentially fit a linear, then quadratic, then cubic etc. ...
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19 views

Linear spline coefficient

I am looking for help in interpreting the coefficients of linear splines. I have read everywhere that a linear spline coefficient is the degree of the change in the outcome with every unit increase in ...
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1answer
60 views

Simple linear regression and sampling

I have a small dataset (60 elements) for which I fit a simple linear regression model, and obtain a small coefficient of determination ($R^2 = 3\%$). I'm a beginner in statistics so I'm trying to ...
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49 views

creating a equation for non linear multiple regression to predict a value based on the inputs given in excel

I have data with 5 columns namely Botany,Zoology,Chemistry,Physics and Rank in a excel sheet . The data here is non linear . So I want to generate a equation in the form of y=a+bx1+cx2+dx3 In ...
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1answer
256 views

Interpreting intercept for the log model in linear regression in R for small predictor

I have a dataset. Assume that y is the dependent variable and x is the independent variable. My goals for this analysis is mainly on the following hypothesis: Expecting x=0 to imply y=0 Expecting ...
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1answer
89 views

How to proof relationship between inverse covariance matrix and linear regression coefficients?

Edited: I would like to work out the above relationship, more precisely: Let $(Y_{1}, ..., Y_{m})$ be a zero-mean vector with covariance matrix $\Sigma$, and let $S \subset \{1, ..., m\}.$ The ...
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48 views

Regression produces a high coefficient of determination, but also a high MSE

I've ran several regression models on a dataset (the SEER cancer dataset). I'm trying to use regression to calculate how many months a cancer patient can expect to live. Each record consists of around ...
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36 views

efficiency - bias trade-off

Under which conditions would a researcher choose optimally when there is a trade-off between the variance and bias of an estimator? I hope this question is not too broad... Any help would be ...
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Describing the association between dependent and independent variables [duplicate]

I’m somewhat confused about the (wording of the) interpretation the coefficient (b1) of a classic OLS regression: Y = b0 + b1*X + e In the literature, the two interpretations: b1 reflects the ...
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1answer
150 views

Does fixing coefficients in a regression make sense, and if so how to do it?

I have a generic question about whether it might sometimes make sense to fix specific regression coefficients to predetermined values. And if this makes sense in particular cases, how do you best go ...
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83 views

Positive coefficient but negative marginal effect in mlogit

Is it plausible to have a positive coefficient with a negative marginal / impact effect after running multinomial logit model?
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66 views

Imputation model: Pooled model is insignificant. How to interpret?

I have ordinal data on three IVs ranging from 1 to 5 as below: IV1: Not at all Important - Very Important IV2: Not at all Satisfied - Very Satisfied IV3: Performs much Worse - Performs much better ...
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37 views

Confidence interval for a regression parameter via prediction

Consider a simple Poisson-regression - GLM - model. There $\exp\left(\beta\right)$s are used as Incidence Rate Ratios (IRR), but their calculation is sometimes not completely straightforward, for ...
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Population parameters of a regression

So this has really been bothering me and I was hoping for a (simple!) explanation if possible. Suppose I've specified a linear regression model: $$ Y = \beta_0 + \beta_1 X + \epsilon $$ And an ...
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1answer
46 views

Issues in estimation and plot

I am learning adaptive filters and testing the performance of using Least Squares and Kalman filter for parameter estimation for $y = X + \text{noise}$. The model is autoregressive AR(2) model $$y(t) ...
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67 views

How to interpret Dickey Fuller (DF) test results in R (for unit test)

I read 1) Intuitive explanation of unit root and 2) http://www.r-bloggers.com/unit-root-tests/ for doing unit root test. I have basic questions: 1)should I check for unit root on both 'x' and 'y' ...
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Regression equation formatting

I have a simple question for you, which has to do with style. Since I am a novice in writing research papers, I have the small issue of not knowing how to represent an equation in an acceptable way. ...