The parameters of a regression model.

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1answer
24 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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20 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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27 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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2answers
59 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
16 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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25 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
50 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
24 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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1answer
118 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: ...
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11 views

mat.regress/set.cor [migrated]

I am having a problem with the function mat.regress in the psych package that I was hoping someone would be able to give guidance on. I have a correlation matrix that is [76,76] with the first ...
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0answers
20 views

Normalizing regressors in logistic space

I have a bunch of sklearn sgd models that have beta coefficients in the logistic space. I want to see if these models cluster ...
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29 views

How to calculate 3 predictors with 1 criterion by hand?

so we got this homework with 3 numeric predictors and 1 criterion. We have to calculate the 3 predictors (regression coefficients) B1, B2 and B3 by hand. It's easy to calculate a regression model with ...
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12 views

Statistical tests to compare sigmoidal regression equations

Data from my experiments (sample shown below) can be fitted using a sigmoid function. The equation I used to fit the data is: y = A2 + (A1-A2)/(1+(x/x0)^p). Each experiment yields data (and a ...
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1answer
32 views

Confidence interval for a multiple of regression coefficient

I am trying to model relationship between length of stay of patients in hospital(Y) vs Age in years(X). The data set I've got doesn't specify the unit of length of stay. So now estimated value of my ...
0
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1answer
30 views

Formula for regression coefficients for log-transformed predictors

A few years ago I came across a formula for computing the coefficients for a linear regression using log-transformed predictors, so that predictions made in the original (not log-transformed) ...
1
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1answer
23 views

Interactions - using ratio of variables

I have 3 variables, colony size, colony age and growth rate (colony size/age). I am interested to predict various other properties ($y$) of a colony using these 3 variables; $y = a_1 \text{ size} + ...
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2answers
110 views

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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24 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
24 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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43 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. ...
0
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1answer
37 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
100 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
102 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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74 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
80 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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1answer
58 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
222 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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28 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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8 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
59 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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38 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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24 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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9 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 ...
0
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1answer
63 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 ...
3
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1answer
52 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) ...
2
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2answers
141 views

The variance of linear regression estimator $\beta_1$

Can we say $$\text{Var}(\beta_1) = \text{Var}\left(\frac{\sum (x_i-\bar x)y_i}{\sum (x_i- \bar x)^2}\right) = \left(\frac{\sum (x_i-\bar x)}{\sum (x_i- \bar x)^2}\right)^2 \text{Var}(y_i) \;\;??$$ ...
3
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1answer
103 views

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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32 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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0answers
33 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 ...
1
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1answer
59 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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33 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 ...
2
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1answer
77 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 ...
2
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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
27 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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0answers
34 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
114 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: ...
3
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1answer
51 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. ...