Tagged Questions

The parameters of a regression model.

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25 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
25 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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6 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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0answers
7 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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7 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
34 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
43 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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2answers
39 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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1answer
85 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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0answers
22 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
21 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
49 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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0answers
19 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
58 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
21 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
18 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
30 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
106 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
42 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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0answers
16 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 ...
0
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1answer
56 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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0answers
36 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
139 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 ...
2
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1answer
75 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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2answers
45 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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2answers
34 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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0answers
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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 ...
2
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1answer
144 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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2answers
56 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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1answer
59 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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0answers
36 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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2answers
61 views

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 ...
0
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1answer
43 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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0answers
53 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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0answers
16 views

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. ...
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2answers
55 views

Test for equality of coefficients from 2 different samples

I have a model that I fit on two different samples (each representing a region in a country, with different sample sizes): ...
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0answers
12 views

Change in regression coeficient using multiple regression [duplicate]

I have a simple question: I'm using mutiple regression to assess various background information as predictors of mental health. When adding more predictors, the dummy coded variable of being born in ...
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2answers
102 views

Testing slopes in multivariate adaptive regression splines (MARS/earth)

I am using the earth package in R to estimate the number of breakpoints in a curve. There is only a single predictor. I was ...
0
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2answers
35 views

Model regression of means different size and variance

I want to explain the relation between getting a reply and posting in a e-commerce. I want to know how much a reply increases postings. I know I could do a regression of postings=f(replies) but the ...
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1answer
75 views

Multivariate model and large regression

I am not familiar with the concept of multivariate model and just learning about regression model. I am familiar with Autoregressive model and Moving Average. Multivariate regression model provided ...
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0answers
24 views

Comparing beta estimates within the same sample, same independent but different dependent variables

I have a GLM with 5 independent variables (Gen-Score (GS) (independent variable of interest), Gender, Age, Sibship and year of birth) and I want to show that the GS predicts measurements of lean mass ...
0
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0answers
41 views

Estimate linear regression using items randomly selected from an item pool

I am asking this question against the background of a linear regression with single predicted variable $Y$ and multiple predictors $X$. $X$ comes from a survey using an "item pool" which suggests that ...
0
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0answers
37 views

Interpretation of the coefficient of dummy regression?

I found this for a week, but I still cannot find anything about it. In a regression, Y = a + b * X + controls +e If we add dummy D=1 for group A and 0 for others, it becomes Y = a + b*X + c*D + ...
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0answers
60 views

Why is the ratio of $B$ and $e^{B}$ for some variables very large?

I want to know how variables affect travel mode for different trip purposes (i.e. leisure trips, work trips and shopping trips) in a specified region. I have 450 respondents in three different ...
0
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1answer
31 views

Understanding Regression vs. Means/Median Results

I am having a little difficulty understanding my results - could someone help me understand how to interpret, and if my process is sensible? Here is an example of what I am doing I am trying to ...
0
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1answer
16 views

Interpretation of two indexes Interaction Term

Respected Fellows. I will thankful if someone help me to explain my model results.my model is as follows. Yit=αPFit+βPSit+δ (PF*PS) it+εit Where Y is GDP per capita PF=Political Freedom Index ranges ...
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1answer
92 views

How to capture & present lm model output from R

After running iterations of lm() in R, I am now stuck with which components of the model's output to present and how to present them. I know that the $R^{2}$ value, ...
0
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1answer
360 views

Compare coefficients from two separate panel regressions in Stata

I am trying to compare the coefficients of two panel data regressions with the same dependent variable. What I am aiming at is the following: ...
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0answers
19 views

What is a “concordance score” for regression coefficients?

I came across this "concordance score" in a set of slides called Penalized regression methods for ranking variables by effect size, with applications to genetic mapping studies, by Ji Zhu: $$ ...
2
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1answer
91 views

Calculate coefficients in a ordinal logistic regression with R

Following the question about manually fitting logistic regression, can someone provide the same 'manual' way to fit a ordinal logistic regression with ordered categorical response?