Refers to any model where the a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

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2
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1answer
38 views

Design of matrix of contrasts in R

I am doing some post-hoc comparisons (in lme4, but here I'll just present a simple linear model), and I am having a hard time making sure that I am building the right matrix of contrasts to test ...
0
votes
0answers
20 views

Hidden Markov Models relationship

I have a question regarding a small investigation that I have been conducting into the relationship between the length of observation sequence, T, on which two decoders (BCJR and classic Viterbi) ...
0
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0answers
6 views

example of a non-trivial data where leverages would all be equal

i was asked to describe a non-trivial data (n not equal to =/1) example where the leverages would all be equal for QR decomposition question. could someone help?
2
votes
1answer
45 views

Consistency of OLS in presence of deterministic trend

For consistency of OLS estimator for linear model $$ y_i = \beta^T x_i + \epsilon_i, \; i = 1,\cdots, n, $$ the model assumptions are usually (the ones I am familiar with) The sequence of random ...
0
votes
1answer
51 views

Linear model- Understanding performances on training and test sets

I have a small normalized data set, 30 observations and 18 Predictors. All are continuous and some variable are related. I ran linear regression on it using Weka. The model automatically dropped some ...
3
votes
1answer
98 views

Rule of thumb to rule out reverse causality in the OLS model

Let' say I have a regression model: $y=a+b*x+error$ Suppose $x$ is income and $y$ is consumption. The hypothesis is that higher income leads to higher consumption and hence, the coefficient on $x$ ...
2
votes
2answers
21 views

AR terms and independent variable as regressors

After trying several models with my data, R^2 and p values are showing my model looks like below. ACF plot tells me AR term is significant. Insights into data tells me change in 'x' would have ...
2
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0answers
69 views

Mixed effect linear regression model output interpretation

just fitted mixed effects model: Linear mixed model fit by maximum likelihood ['lmerMod'] Formula: price ~ variable + (1 | product) Data: podzbior ...
0
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1answer
34 views

Differenence between hierarchical linear regression and moderated multiple regression

What is the difference between hierarchical linear regression and moderated multiple regression? If I have one and two moderator variables and my models are: model 1- IV model 2- adding two ModVs ...
5
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0answers
74 views

Confidence bands for QQ line

This question doesn't specifically pertain to R, but I chose to use R to illustrate it. Consider the code for producing ...
6
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3answers
347 views

What does “curvilinear” mean?

As far as I can tell, curvilinear is defined vaguely but means the same as nonlinear. Is that correct? Or does curvilinear have a distinct definition?
1
vote
2answers
56 views

Do you need to change instances to rates for OLS regressions

I am interested in performing a regression on data on a population. This population causes events X and Y. I have monthly data for population, event X, and event Y. Do I need to change my variables X ...
0
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0answers
22 views

How to calculate prediction intervals from a multiple linear regression with simulated future Xs

I am using a multiple linear regression model to generate 80% prediction intervals based on simulations of future X values. While I understand how to calculate prediction intervals typically (such as ...
0
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0answers
13 views

Can variance in error term be estimated without fitting a line?

In this exercise, I was asked to prove that the simple linear regression - ( $Y_i=\beta_0+\beta_1X_i+\epsilon_i$ with all the usual basic conditions) - of $\{Y_{ji}\}$ for each $X_i$ is the same as ...
0
votes
0answers
27 views

How can I use the sufficient statistics (variances, covariances, means) to estimate a linear regression model in R?

My question is simple: is there a function in R which estimates the linear regresion model in a similar fashion as lm, but only ...
1
vote
1answer
31 views

LASSO or other regularized regression with censored (missing) data

Here is my problem. I am looking at various time series curves. Let's call them total spend aggregated over all customers on various products versus time. At any given time, I want to predict the ...
1
vote
1answer
36 views

Is it necessary to plot histogram of dependent variable before running simple linear regression?

I was working on an assignment. The data set was really simple, only consisting one independent variable $y$ and dependent variable $x$. Someone suggested me plot a histogram of $y$ before running ...
1
vote
0answers
66 views

Joint posterior HPD region for the coefficients of the normal linear model

This problem appear in an exam put by Chris Sims (3): http://sims.princeton.edu/yftp/emet04/ConfidenceCredibilityEx.pdf Suppose the following model: $y=\beta_1 +\beta_2 X_2+\beta_1 X_3 +\epsilon$ ...
4
votes
2answers
71 views

Two simple questions regarding GLM

I'm currently doing a modelling project. However, I haven't taken a bunch of statistics classes, so I have to teach myself generalized linear models. I'm reading Generalized Linear Models for ...
2
votes
0answers
33 views

What is the best way to simulate data for a linear regression model?

I am concerned with simulating data for a linear regression model. I need to control the means, variances, and correlations (covariances) between the predictors and the criterion variable. In ...
1
vote
1answer
60 views

Closed form posteriors for a simple bivariate Bayesian regression

I'm analyzing a simple linear regression $Y_{i}$~$a+b*X_{i}+e_{i}$, with $e$ being normally distributed with known variance and where I have normal priors on $a$ and $b$. I'm trying to piece together ...
0
votes
1answer
36 views

Inconsistent x-y relationship from paired t-test and linear regression

I am analyzing an experiment comparing the effect of treatment A vs. B on the matched subject. Here are the measurements on 34 subjects: ...
1
vote
1answer
63 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
votes
0answers
24 views

center variable separately for each factor in linear mixed model?

I am working on a relatively simple mixed model where I have two continuous predictors with an interaction term and three sites. I am treating the two predictors as fixed effects and the site as ...
0
votes
0answers
41 views

Groups in linear regression with different intercepts. How do I find the differing variable?

This is more of a conceptual question. I have a coefficient estimate of .80 in a linear regression model with one IV and one dependent variable. However, plotting the data I see distinct groups, ...
2
votes
0answers
19 views

Number of significant linear predictors if predictors are not independent?

I would like to determine which of a set of candidate predictors $\{x_1, x_2,\ldots, x_n\}$ are significantly relevant to the linear prediction of $y$. Typically, one can compare a full model ...
1
vote
0answers
27 views

Which statistics to use calculating prediction interval of dummy linear regression?

I have performed a linear regression and found a model of the form: $$ \hat{Y} = \alpha + \beta_1 x+ \delta_{high} + \delta_{low} + \epsilon\\ $$ Where: $\beta_1$ is a continuously distributed ...
11
votes
2answers
143 views

Bayesian lasso vs ordinary lasso

Different implementation software are available for lasso. I know a lot discussed about bayesian approach vs frequentist approach in different forums. My question is very specific to lasso - What are ...
0
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0answers
11 views

Achieving high recall for smaller class in unbalanced linear svm

I have an svm-related question. I have an unbalanced dataset, meaning classA could be 1/10 to 1/35 of classB. Well I am interested in getting a linear svm which would separate the data and would ...
0
votes
0answers
13 views

Fitting a Mixed Model with Random and Repeated effects in SAS

I have want to fit a linear regression with repeated measures and random effects. The data come from clinical observations. In CT images The dependent variable is the diameter of a lymph node lesion ...
0
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0answers
26 views

dichotomizing a predictor variable [duplicate]

Does dichotomizing a predictor variable always reduce the power in a linear regression model? We have a normal distribution for a predictor and then have sampled just from the high and low parts of ...
0
votes
0answers
54 views

Linear model for data that follow gaussian distribution

I have a question about linear regression. We have the linear regression of input data $(X,Y)=((x_1,y_1),(x_2,y_2)...(x_n,y_n))$ is $$F=aX+b$$ a,b are factors of the linear line, $y_i$ is {-1,1}. ...
0
votes
0answers
14 views

Understanding Differential Expression Analysis in Microarray Experiments

Can someone please provide me a simple explanation of how differential gene expression analysis works? I know that this method is described in [1] and used in the R package limma. [1] Smyth, Gordon ...
0
votes
1answer
43 views

How to show linear model corresponds to exponential family

I am confronted with the exercise below. I have no given solution, so I hope someone can tell me whether my solution is right or wrong. I want to show the deterministic linear model $\quad ...
7
votes
1answer
134 views

Obtaining an estimator for z given an estimator for log z

As per gung's advice in Getting the equation from R's lm when using a product, I am starting a new thread for this question. I have a model $\widehat{\log z} = a + bx + cy + dxy$ for random ...
3
votes
1answer
36 views

Getting the equation from R's lm when using a product

Similar to this question: How to translate the results from lm() to an equation? in which the top voted answer said how to get the form of an equation from ...
0
votes
1answer
34 views

Question about using a multiplicative dummy variable

In many econometrics model, the changes in the response variables in certain intervals are more difficult than other intervals. But I believe this is often not considered when estimating the model. ...
2
votes
1answer
41 views

Boundary/threshold test for regression-type scatter plot

I am looking for a way to test weather a boundary threshold exists in a physiological response--a sample of the data is plotted below. My hypothesis is that the X-variable imposes a physiological ...
4
votes
2answers
180 views

cubic relationship after linear relationship

Sorry for my title, but I really don't know how to describe this question. I am fitting a linear regression in R now, and I find that there is one parameter showing linear relationship before certain ...
0
votes
1answer
60 views

How to treat x=0, y=0 in a linear model with no intercept?

Very often in the research we want to establish a linear relationship without intercept: $y=\beta x + \epsilon$ and the sample has many double zero observations $x=0, y=0$. I am wondering how to deal ...
7
votes
4answers
322 views

Is using deciles to find correlation a statistically valid approach?

I have a sample of 1,449 data points that are not correlated (r-squared 0.006). When analyzing the data, I discovered that by splitting the independent variable values into positive and negative ...
0
votes
0answers
30 views

In linear regression the prediction error range is increasing while the the mean of the error is decreasing

I conducted a linear regression on a large and highly skewed data set that contain 80 variables,about 1.0 Million of users that didn't spent money and about 15k of users that spend different amount of ...
0
votes
0answers
37 views

Linear model with categorical dependent variable

I need to identify relationships between multiple 'counting' independent variables (representing numbers of amino acids in a protein sequence) and one ordered categorical dependent variable (an ...
0
votes
0answers
39 views

Within-subject and between-subject fixed effects in mixed model

I've been trying to analyze some data using mixed models but I have some troubles to understand how should I include both within-subject and between-subject fixed effects in such models. Let's ...
2
votes
1answer
34 views

Coefficient of Determination: For the perimeter and area of a square: Why different?

When calculating the coefficient of determination for a square, why is it that if you use the data set for the side length of as X= (1,2,3,4) and the perimeter as Y=(4,8,12,16) the Coefficient of ...
2
votes
0answers
48 views

Understanding R lm function (weighted) – “coefficients not defined due to singularities”

I'm working on generating a weighted linear model in R using the lm function. My dataset has about 1200 observations. My independent variables are a set of 168 ...
1
vote
0answers
21 views

Power of maximum likelihood parameter estimates for a linear model

The maximum likelihood parameter estimates for the linear model where $\Pr(Y|X\beta) \sim \mathcal{N}(0,\sigma^2)$ are: $$\hat{\beta} = (X'X)^{-1}X'Y$$ How do you compute the statistical power of ...
2
votes
0answers
14 views

Estimate power for linear model with Bernoulli-distributed error

I want to estimate a linear model for a phenotype $y_i$ defined by a liability threshold model, using observable data $x_i, c_i$. $$y_i = \mu + \beta x_i + \epsilon_i$$ $$\text{Pr}(\epsilon_i | x_i, ...
1
vote
0answers
44 views

Reproduce a confidence interval of linear regression in Excel [duplicate]

After a series of tests and exploratory analysis, I have design a linear model in R, the model is the following: ...
1
vote
1answer
29 views

Using two one variable linear regressions on a single response variable to compare explanatory variables

I ran two single variable linear regressions $A$ and $B$. $A$ had a relatively large effect size $R^2$ = $.68$ while $B$ had $R^2$ = $.10$. Regressing the explanatory variable from $A$ (= $a$) on ...