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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22 views

Understanding lm() function in R with weights

Consider the following simplified dataset (sales and percent of color-type sales by region): ...
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3answers
74 views

linear regression - modelling explanatory variables which depend on each other

I'm trying to estimate the value of an apartment, by doing a regression through similar apartments. The regression model looks now like this ...
3
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1answer
29 views

How can we have non-random patterns in the plot of simple linear regression residuals vs the predictor variable?

A) When considering a simple linear regression model, it is important to check the linearity assumption. Graphing the residuals vs the predictor variable can often give a good idea of whether or not ...
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43 views

Correct interpretation of linear regression coefficient?

Let's say I'm running a survey and I ask "Are you confident in the economy, yes or no?" Then I ask the respondent "are we spending too much or not too much on scientific funding? I let the answer ...
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1answer
46 views

Show $J(I-H) = 0$

This is in multiple linear regression. Given $m, n \in \mathbb{N}$ and matrices $X \in \mathbb{R}^{m \times (n+1)} (m > n + 1), H = X(X'X)^{-1}X' \in \mathbb{R}^{m\times m}$, the hat matrix, $, I = ...
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9 views

Weighted linear model with few different values

I am trying to come out with a model but I am encountering many problems as it is very unbalanced. The model is a weighted linear model where one of the points has a much higher weight than the rest. ...
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10 views

How to find the distribution of Betas of a Single/Multiple Linear Regression model?

How would I go about finding the distribution of betas for a multiple linear regression? That is, a matrix with the same dimensions as the data whose column means are the regression coefficients ...
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1answer
92 views

Linear regression with violated assumptions

I am trying to find out the determinants of cognitive function. The outcome variable is the mini–mental state examination which is a 30 point questionnaire response that has score values from 0 to ...
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13 views

Modelling interactions with only a subset of the levels of a factor in R [migrated]

Let's first look at lm. I have a continuous explanatory $X$ and a factor $F$ modelling seasonal aspects (in the example 8 levels). Let $\beta$ denote the slope ...
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2answers
126 views

How to verify a linear model?

Given a dataset and liner model, how can I verify its sufficient quality? ...
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0answers
21 views

Selecting proper Linear Model with interaction considered

Data consists of Temp(3lv Factor), Water(num), Fert(num), and Growth(num). Considered model is LM with DV: Growth, IV: Temp with Water and Fert as covariate. Fitted 2-Factor ANCOVA (Full Model) and ...
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2answers
101 views

Best Subset Selection Questions

I am reading Introduction to Statistical Learning and I have a question about the Best Subset Selection Algorithm. The algorithm goes like this: Suppose there are $p$ predictors, the aim is to ...
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39 views

How to exploit relationships between independent variables?

Data: Each instance (representing a document) is a bag-of-entities (like BOW, except they're Wikipedia entities instead of words), so each feature is a binary or tfidf-like score based upon the ...
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19 views

Data Smart Book Exercise [closed]

In the book, Data Smart, by John Foremann, at the end of chapter 4, the reader is asked to optimize a model where only 95 % of the sampled scenarios are met by the model constraints. The relevant ...
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64 views

Regression on unbalanced two-way with interaction

I am developing my own algorithm to calculate it for me. I am interested in type III SS and using the overparametrized design matrix to estimate my parameters vector and then proceed to the cubic ...
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1answer
66 views

How to test two lines from the same model are parallel

If I have two sets of data each with 5 entries for X&Y, I built a model to incorporate this using a dummy/indicator variable for when X is in Set B, so obviously I get two parallel lines; ...
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32 views

What is the difference between Average Partial Effects (APE) and Average Marginal Effects (AME)?

In this answer, the terms Average Partial Effects (APE) and Average Marginal Effects (AME) are used interchangeably. But in this paper, the terms are used to mean different things (page 75). But it's ...
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8 views

Problem with model with multiple data points per subject and a covariate

I'm trying to build a general linear model to test a really simple hypothesis: a Behaviour (continuous variable) I observe in 64 Children depends upon Condition (a manipulation I did, two-level fixed ...
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2answers
42 views

Is parametric equivalent to linear?

Some supervised learning techniques, such as GLM (e.g., logistic regression), are linear and parametric. On the other hand, one of the claimed advantages of nonparametric supervised learning ...
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1answer
67 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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21 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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14 views

Compute confidence cutoff for scatterplot

I have data collected from two different individuals for different treatments, like this: ...
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1answer
31 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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44 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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27 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
56 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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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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1answer
74 views

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
24 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
125 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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13 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
37 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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16 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
33 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: ...
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2answers
43 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
47 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
113 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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1answer
36 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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38 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 ...
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1answer
82 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
25 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, ...
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1answer
52 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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25 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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20 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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36 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
315 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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36 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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24 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 ...
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1answer
26 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 ...