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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1answer
15 views

Regression imputation of missing data

Suppose a two-way experiment with interaction. Is it correct to estimate the missing values by OLS, input those values in the data (fill the blanks) and now perform a polynomial (or any kind of) ...
4
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1answer
108 views

Understanding QR Decomposition

I've got a worked example (in R), that I'm trying to understand further. I'm using Limma to create a linear model and I'm trying to understand what's happening step by step in the fold change ...
2
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1answer
41 views

Bayesian regression full conditional distribution

I have a problem with the derivation of the full conditional distribution of the regression coefficients in a simple Bayesian regression. The source of the following equations is: Lynch (2007). ...
2
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2answers
52 views

Solve $X^TX b = a$ for $b$ using $XX^T$ for a short and wide matrix $X$

I have a matrix $X$ of dimensions $n \times p$ and a fixed $p$-dimensional vector $a$, with $p \gg n$. How can I efficiently solve a problem of the following form? $$X^TXb = a$$ Perhaps using the $n ...
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0answers
17 views

Regression model for Cumulative data in R

I am having a daily data for 3-4 months and another variable which is the cumulative sum. It starts with some value on the first day and it keeps on adding and at the end of 3 months, it would be sum ...
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1answer
20 views

How to check if the correlation between two continous variables is influenced by a categorical factor?

I have a data frame (df) where I see correlation between two continuous variables (c1 and c2). I need to know whether the observed correlation between the two variables differs between groups, which ...
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0answers
9 views

Clarification in CRLB for linear model

Paper : CRAMER-RA0 BOUNDS FOR SEMI-BLIND, BLIND AND TRAINING SEQUENCE BASED CHANNEL ESTIMATION? Download link presents the CRLB expression for non-blind ...
2
votes
1answer
37 views

Forming a prior based on the solution to a linear system

On p. 115 of the 4th edition of Machine Learning a Probabilistic Perspective, we have the following: Let $\epsilon\sim N(0,\frac{1}{\lambda}\text{I})$ and let $L$ be a matrix of dimension ...
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0answers
10 views

Time series data plotting and reduction with maintaining significant changes [closed]

I have time series data with second resolution for 5 years so its huge data for plotting. I have to plot graph for month and year wise as well. Now plotting each year how to reduce the dataset so ...
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0answers
30 views

Gini Coefficient - Variable Importance Measure

There is a whitepaper for selecting important variables in a linear regression model. The URL of the whitepaper is http://support.sas.com/resources/papers/proceedings15/3242-2015.pdf . It explains ...
3
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1answer
30 views

R - lm how to get standard deviation coefficients

I have a very simple problem but I cannot find the answer anywhere. I run a linear model with lm() and I want the standard deviation coefficients in order to compute the confidence interval. I know ...
0
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0answers
34 views

Linear regression, $R^2$

While computing $R^2$ for the test data set, what mean value should be used - the mean from the training and test or just the test data set?
2
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1answer
17 views

Do I need to adjust the degrees of freedom returned by pool.compare() in MICE?

I am analyzing a multiply imputed dataset produced from the MICE package in R. To assess the overall significance of my linear model, I am using pool.compare() to compare my "full" model to an ...
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0answers
13 views

How to interpret the direction of a covariate's effect in a 2-way ANOVA?

I use SPSS's GLM (general linear model) to analyze an data set based on a 2x2 between-subjects experimental design. The design has two factors: a). congruence (yes or no) and d). primed image ...
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0answers
22 views

A linear model with prior information

Suppose I have this experimental data: I have measurements of drug response from patients (let's say its blood pressure). Specifically, I have measurements after being treated with drug A (30 ...
0
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0answers
18 views

Multiple Comparison Correction for Linear Regressions with Dependent Variables

I could use some help clarifying the use of multiple comparison corrections for a series of linear regressions when some of the variables being tested are calculated from each other. Toy problem to ...
2
votes
1answer
72 views

Regression performed using Principal Component Analysis

I have a dataset consisting of 10 correlated variables. I need to explain a response variable using these 10 variables, so I am using PCA to reduce dimensionality. Say, I use the first 3 components ...
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0answers
16 views

Linear Model learnt on several frequency

Sorry for the unclear title but I did not know how to call this POST, I'll try to be clearer. I have data that I need to forecast with external variables. This data is a time series available on a ...
2
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0answers
22 views

linear path models vs. pls path models (structural equation models)

Assume we have the following linear path model: Structural (inner) model: $Y_{1} = \beta_{1}Y_{2}+\theta_{1}\delta$ Measurement (outer) model: $X_{1} = \lambda_{1}*Y_{1}+\epsilon_{1}\delta$ ...
0
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1answer
42 views

Deleting Outliers in a regression model

Working on a linear regression problem in R, I created a first model flights_lm = lm(freq~dist+capa+nbrt+depf+lcco+prbi) where freq is frequency, dist is ...
0
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1answer
32 views

What is criterion for Breusch-Pagan test?

Could someone explain to me what is criterion for interpretation of Breusch-Pagan test? I have applied ncvTest test from the package car in R on a simple linear regression with one predictor variable ...
2
votes
1answer
22 views

Regression with Probabilitistic Explanatory Variable

Let X be a categorical variable. Instead of knowing for certain whether a particular observation is equal to a given level of X, I have a probability distribution over the possible values of X. So, ...
0
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0answers
28 views

What measure to use in finding the best linear model

I have a bunch of linear models (say 20 of them), and a bunch of datasets (e.g. 400). I wrote a code in R so that each dataset is exposed to each model, and the goal is to select the best model that ...
1
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1answer
22 views

Coefficient of determination increases with the number of regressors

Suppose we deal with the linear regression model $Y=X\beta+\epsilon$, where $X$ is determined matrix, $\beta$ - the vector of coefficents, $\epsilon$ - the vector of errors. I often meet the ...
0
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1answer
21 views

Testing OLS Model Prediction Accuracy?

How can I test the accuracy of my ordinary least squares model? Is it a simple comparison between the predicted values of my test set and their actual values (with perhaps a maximum threshold of ...
0
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0answers
27 views

Should I delete the intercept [duplicate]

I'm working on a small project where I need to create a multivariate linear regression model to predict the frequency of some airline companies. I'm a bit confused as I don't know if I have to remove ...
3
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2answers
149 views

Least Squares Regression Step-By-Step Linear Algebra Computation

As a prequel to a question about linear-mixed models in R, and to share as a reference for beginner/intermediate statistics aficionados, I decided to post as an independent "Q&A-style" the steps ...
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2answers
70 views

Regression analysis low R2 value - Result interpretation

When I run linear regression on my test data I get the following report: You can find the test data in here. The graph of actual vs predicted looks like: I would like to know if this is fairly a ...
0
votes
1answer
22 views

How to finalize the factors to be considered for simple linear regression

I have a list of 100 variables from which i want to filter down to the most important variables to be considered for applying simple linear regression? Is there a method for this? Or do i have to ...
0
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0answers
29 views

Understanding lm() function in R with weights

Consider the following simplified dataset (sales and percent of color-type sales by region): ...
3
votes
3answers
105 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
votes
1answer
40 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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0answers
47 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 ...
1
vote
1answer
49 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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0answers
10 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. ...
0
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0answers
11 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 ...
3
votes
1answer
106 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 ...
2
votes
2answers
132 views

How to verify a linear model?

Given a dataset and liner model, how can I verify its sufficient quality? ...
0
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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 ...
3
votes
2answers
125 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 ...
0
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0answers
42 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 ...
1
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0answers
21 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 ...
1
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0answers
73 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 ...
0
votes
1answer
75 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; ...
0
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0answers
67 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 ...
0
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0answers
20 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 ...
2
votes
2answers
53 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 ...
4
votes
1answer
99 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 ...
1
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0answers
22 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 ...
0
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0answers
18 views

Compute confidence cutoff for scatterplot

I have data collected from two different individuals for different treatments, like this: ...