Refers to any model where 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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50 views

Is the true linear regressor equal to the average linear regressor?

Let me define my terms. Suppose I have a pair of jointly distributed random variables Y, X, where Y is numeric and X is a random vector. Note that I do not want to assume that Y and X are related in ...
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0answers
15 views

Why does a robust linear model fitting give a residual standard error?

The way I understood when to use a a robust linear fitting is for example when your variance is not constant (e.g. when you have heteroscedasticity as shown with a Breusch-Pagan test for example) or ...
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9 views

Compute confidence cutoff for scatterplot

I have data collected from two different individuals for different treatments, like this: ...
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1answer
25 views

How can I get a reasonable residual standard error for my linear model which faces heteroscedasticity?

My goal is to get the residual standard error of my model to be as small as possible. I have a linear model lm(y~x). When I plot the standardized residual errors in function of the explanatory ...
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0answers
25 views

Question on explanatory variables

I am given a data set including 125 occasions with 5 variables settings (hydrocarbon emitted (grams), initial tank temperature (°F), temperature (°F) of the dispensed petrol , the initial vapour ...
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0answers
26 views

Logistic regression vs. linear regression on class probabilities

I have a bunch of data points, each of which represent a success or failure. Each data point is from one of ~40 conditions, each of which contains approximately 40 data points. All of my predictor ...
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1answer
41 views

Reduce subsetting of the dataset?

I collected a lot of trapping data of a certain rodent species. I constructed a model to see what affects the individual's activity. I constructed this LM (linear model): ...
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19 views

Assessing the effect of a given predictor in multiple regression

I'm working with data from an observational study. Observations were recorded on several measures (comprising a response and $k$ predictors) and subsequently used to design a regression model with a ...
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4 views

Calculating the standard error of an estimator in a simple regression [duplicate]

I'm reading ISLR (http://www-bcf.usc.edu/~gareth/ISL) and I can't prove a statement about the standard error of the regression coefficients. Any ideas? Assume we draw $n$ iid samples $(y_1, x_1), ...
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24 views
+50

Collaborative filtering using a linear model

Consider I have a set of movies and a set of users ($A$,$B$,$C$,$D$) and a matrix with related scores (I can have gaps in this matrix). Consider a linear regression model where a specific user A's ...
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1answer
18 views

prediction interval formula

I have a model $Y_i= \beta_0 + \beta_1X_i+\beta_2X_i^2+\beta_3X_i^3+\epsilon_i$ with $\epsilon_i\sim\mathcal{N}(0,\sigma^2)$. Is the following formula correct for calculating the width of a 95% ...
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2answers
120 views

$Y_i ∼ N(\mu_i,\sigma^2)$. What does this mean?

The response variable $Y_i$ is normally distributed,has a mean of $\mu_i$ and a variance of $\sigma^2$ in an example I am given of a linear model. Hence $Y_i ∼ N(\mu_i,\sigma^2)$. I do not understand ...
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21 views

How do I plot an abline() when I don't have any data points (in R) [migrated]

I have to plot a few different simple linear models on a chart, the main point being to comment on them. I have no data for the models. I can't get R to create a plot with appropriate axes, i.e. I ...
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0answers
8 views

Good resources on General Linear Models

Unlike some other topics in statistics for which I usually find an abundance of good detailed resources, I seem to have a hard time finding good ones about GLM. I was taught about it in statistical ...
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1answer
36 views

Why can OLS account for non-linearities even though linearity is assumed?

One standard example when introducing OLS in econometric classes is modelling the log-wage by education and experience. Often, the example models account for experience by not only by the experience ...
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13 views

Choosing weights for linear regression lm in R for time decay?

I am modeling server performance. Basically load~hits. I want the older hits data to have less influence than newer because overtime different optimization and code have been installed/applied. In R, ...
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1answer
31 views

Mixed models and longitudinal studies: Is it ok to specify a random slope with time as a categorical?

My model is currently setup as follows either with just random intercepts: ...
2
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2answers
37 views

Z-score in the analysis of data

I am being provided z-scores of dependent and independent variables. I was checking if it can analyzed as such as raw data?
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1answer
29 views

Interpretation of Coefficients in linear regression using 'fitlm'

I require help with regards to the interpretation of linear regression results (I'm using the Matlab 'fitlm' function). My data has 8 features, and when each feature is plotted against the response ...
3
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1answer
105 views

Significance of intercept (as portrayed via an R formula)

I'm new to statistics in general (but a very seasoned developer). I'm trying to grasp why it seems like there's a lot of consideration given to intercepts, at least where it comes to models. For ...
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0answers
25 views

Specifying a model with nested subsamples within split-plot design

I am trying to specify a model for split plot design that acknowledges nested sub-sampling. Split plot designs are a little bit tricky to analyze, and I am new to R, so I provide my dataset along with ...
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0answers
35 views

Logistic regression: Estimation of marginal effects of predictors

I ran a logistic regression analysis with 12 independent variables (predictors). I heard that I could estimate the average marginal effects of these predictors using a linear regression model. Could ...
0
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1answer
60 views

Getting negative predicted values after linear regression

I'm using linear regression to predict a price which is obviously positive. I have only one feature which is gross_area. I standardized it (z-score) I got this kind of value: ...
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1answer
24 views

Linear models where the IV and DV both have temporal autocorrelation

I have weekly data from a lake over 3 months and I want to see if there is a correlation between concentrations of algae and richness of the bacterial community (number of bacterial taxa). However, ...
0
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1answer
37 views

Why do we use Gamma($\epsilon, \epsilon$) as non-informative prior for precision and Normal prior for betas in Linear Regression

Suppose my regression model is $$Y_i = \beta_0 + \beta_1X_{i1} + \epsilon_i $$ In most books I am seeing that the prior used for precision $\tau = 1/\sigma^2 $ is $Gamma(\epsilon, \epsilon)$. However ...
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1answer
23 views

Multivariate Linear Regression with continuous and discrete explanatory variable

I have some trouble to apply a multivariate linear regression on my data. I have two features gross_area which is continuous, nb_bathrooms which is discrete (1,2,3) and a dependent variable y which is ...
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0answers
23 views

Interpreting factor when intercept is not significant

I'm in the middle of doing a mixed model analysis. I'm interested in assessing the effect of a continuous covariate and a categorical factor (with two levels), including their interaction, on a ...
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18 views

Generalized linear model Gaussian distribution Linear Model

Is a generalized linear model with a Gaussian distribution the same as a linear model?
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32 views

First linear regression - interpreting results to guide next step?

This is my first time attempting to build a linear regression model and I am not sure what to do next given the results I have. I have a data set with 24 predictors and 1 response and there are 999 ...
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2answers
135 views

R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode

I was looking at the mtcars dataset and explore the relationship between MPG and the transmission modes (auto/manual). I choose to use the following linear models with the regressors specified in the ...
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0answers
30 views

multiple linear regression analysis with continuous and categorical data result interpretation

I have data from gene expression arrays and I have clinical data associated with the samples used. I am using gene expression (discrete), age at diagnosis (discrete) and ethnicity (categorical) to ...
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0answers
17 views

Observed vs. predicted values distribution misfit

After realising the problem with my predictors thanks to the comments in my previous question, I've tried to fix that somehow. However, I can't figure out how to transform my predictors and/or my DV ...
0
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1answer
25 views

How to account for correlation in a pre-existing linear model?

By using a pre-existing model we get weights $w_1, w_2 ... w_n$ assigned to $n$ variables. But the model does not take correlation between those $n$ variables into account. How can the correlation ...
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2answers
40 views

Independent variables in multiple linear regression

I have a set of experimental parameters and my task it to find reasonable descriptors to describe them (chemistry). Since I've got descriptors, I checked Pearson correlation for each of experimental ...
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51 views

Omitted Variable Bias in Linear Regression - Simulation

Is the following a reasonable illustration of the OVB problem? We build up fictional data around the regression line: $$y = 7.2 + 2.3 \, x_1 + 0.1 \, x_2 + 1.5 \, x_3 + 0.013 \, x_4 + eps$$ by ...
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1answer
48 views

Computational complexity for linear discriminant analysis

The linear discriminant analysis algorithm is as follows: I want to conduct a computational complexity for it. For each step, the complexity is as follows: For each $c$, there are $N_cd$ ...
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0answers
12 views

Equivalence of 2 forms of the $F$-statistic

Suppose we have a classical linear model $$ y=X\beta+u,\quad X\text{ fixed },\quad u\sim N(0,\sigma^2 I_T). $$ Here $\beta$ is $k\times 1$. Suppose we are interested in testing $H_0: R\beta=c$ where ...
2
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1answer
82 views

Goodness of fit and which model to choose linear regression or Poisson

I need some advice regarding two main dilemmas in my research, which is a case study of 3 big pharmaceuticals and innovation. Number of patents per year is the dependent variable. My questions are ...
3
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2answers
84 views

Identifiability of the linear regression model: necessary and sufficient condition

Let $\{(x_i, y_i), 1\le i\le n\}$ be the pairwise values of the observations and responses respectively. Let us fit the linear regression model: $y_i=b_0+b_1 x_i+\epsilon_i, ...
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1answer
48 views

Using Adaptive Linear Neurons (Adalines) and Perceptrons for 0-1 class problems

I am wondering how to adjust the Adaline algorithm to classify the classes 0 and 1 instead of -1 and 1. I found a section in Neural Networks and Statistical Learning by Ke-Lin Du, M. N. S. Swamy ...
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0answers
13 views

Concept of performing a t-test while controlling/adjusting for one or more variables? [duplicate]

Could someone please help me understand the concept of performing a t-test while controlling/adjusting for one or more variables? E.g.: Say I have a hypothetical data set, with the following ...
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0answers
35 views

When to apply logarithmic transformation to a variable? [duplicate]

My question is in which cases you should think about transforming your variable into a logarithmic one? My dependent variable in the number of patents a long a period of years and one of my ...
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0answers
90 views

How to report results from a linear mixed model “test of fixed effects” in SPSS?

What is the appropriate way to report results for linear mixed model based on the "test of fixed effects" table in SPSS? Is it just (F=xxx, p=xxx)? This isn't my data but this is an image I found of ...
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44 views

Comparing mixed-effects and fixed-effects models

Given three variables, y and x, which are positive continuous, and z, which is categorical, ...
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0answers
51 views

How can i calculate an effect size (cohen's d) from a linear random effects model (beta)

I am trying to figure out how to calculate a Cohen's d statistic for a linear random effects model. I did not do the analysis myself, I have read it in a journal article so i'm left to figure it out ...
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0answers
48 views

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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28 views

Heteroskedasticity and skewness in regression, “in general”

In another question of mine, I asked about fitting linear models based on the second-order Taylor expansion: $$ Y = \beta_0 + \sum_i \beta_i (X_i - x_{0i}) + \sum_{i,j} \beta_{i,j} (X_i - x_{0i})(X_j ...
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33 views

Quadratic and interacted linear models when one predictor is categorical

In another question of mine, I asked about fitting linear models based on the second-order Taylor expansion: $$ Y = \beta_0 + \sum_i \beta_i (X_i - x_{0i}) + \sum_{i,j} \beta_{i,j} (X_i - x_{0i})(X_j ...
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1answer
48 views

How to emphasize on specific data points in Linear Regression?

I'm now solving linear regression problems. $y = wx + b + e$ So I have $(x, y)$ data set and want to learn weights $w, b$. Additionally I know that certain data points are not polluted by noise ...
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1answer
26 views

Statistical independence of least square estimator and residual in multiple linear regression

I'm currently self studying linear regression. Following is an entrance exam problem of a graduate school. Consider the regression model with usual assumptions of the errors $y=X\beta+\epsilon$. Show ...