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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20 views

Troubles reporting transformed variables for log and sqrt into a general equation

Good morning everybody, I see CrossValidated has really high level of questions and answer; I am just a student so I hope this question is not too basic... Suggestion of further readings available ...
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0answers
35 views

Linear model / models analysis

Above are three plots of the Linear model I am trying to analyze. The first one is a basic plot of the linear data: ...
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0answers
23 views

What is Linear Projection [closed]

Can anyone help explain the linear projection and its application? In Wooldgridge's textbook of Econometrics, he introduced the basics of linear project, which I understand what it is but I still ...
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1answer
28 views

Modelling interaction

How does adding interaction term in the model adjust for it or why do we need to add interaction? I am working on logistic regression model with treatment and race as predictors. I have added ...
12
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3answers
448 views

How to discuss a scatterplot with multiple emerging lines?

We have measured two variables, and the scatterplot seems to suggest multiple "linear" models. Is there a way to try to distill those models? Identifying other independent variables has turned out to ...
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0answers
21 views

How to improve linear model generalization when autocorrelation is present?

I have features $X_t$ and response $Y_t$ (all continuous variables) and my objective is to find the best estimate of $f(X_t)=Y_t$ where $f$ is linear, and 'best' is defined as lowest generalisation ...
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1answer
32 views

LSmeans - Unbalanced data with interactions

I wish to analyze an unbalanced data set with 3 variables Tleaf, Tair, and orientation (factor with two levels). Considering the effect of the factor "orientation", I wish to determine if "Tair" has a ...
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1answer
41 views

What is the benefit of knowing the F statistic in multiple linear regression?

One of the basic figures you get when running multiple linear regression using almost any off-the-shelf software is the F statistics. However, I cannot recall one situation, where the F value was low ...
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1answer
153 views

Is a linear model OK?

I carried out a linguistics experiment where I gave a text for people to comment on. I recorded and transcribed their comments. I would like use the number of utterances per sentence in the text they ...
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0answers
53 views

Show alias coefficient of Plackett Burman design equals $r_{ij}=\frac{c_{1i}'c_{2j}}{N}$

Consider a Plackett Burman design with N rows and let $\beta_{1}$ be the of the regression coefficients corresponding to the main effects and let $\beta_{2}$ be the vector of the regression coefficients ...
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22 views

Drop1() and Summary() on lm object

I need to analyse unbalanced data through linear regression: modJuin=lm(TleafMax~TairMax*orientation, na.action="na.exclude", data=aJuin) "TairMax" is a ...
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0answers
29 views

How to compute/run LDA with 3 classes

I couldn't find one example on how to compute LDA with 3 classes (nor what is the algorithm). for example i have the following observations and classes: (each observation in one-dimensional) $ ...
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30 views

Identifiability in linear regression and time series

The multivariate linear regression model is given by $\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}$, where $\boldsymbol{\epsilon} \sim \mathcal{N}(\mathbf{0, ...
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1answer
101 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: ...
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1answer
38 views

Multiple Linear Regression: Obtaining a Stable Model

I am working with a data set of ~1200 rows and 60 variables, and I'm trying to build a multiple linear regression model. I do this by separating 10% of the dataset to be used for validation and I use ...
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0answers
25 views

Fuzzy regression (using linear programming)

I want to replicate a fuzzy regression using a linear programming problem approach. I have the following information: " A fuzzy regression analysis with only one independent variable X results in ...
5
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1answer
107 views

Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom

Background Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$ where $\mathbf{\beta}$ ...
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1answer
48 views

Comparing coefficients of linear “ Stochastic Frontier Production and Cost Functions” in R

I am using the function frontier::sfa() in R to obtain the Stochastic Frontier Production and Cost Function as followed: ...
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0answers
21 views

Linear model with longitudinal data, predicting difference

I have a set of data for 2 visits in patients and I would like to see whether there is a effect of a difference of one variable on another. So, lets say, my variables are A, B, age + gender. I want ...
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0answers
15 views

Multiple objective allocation function

I have an allocation problem where, for a given good, I have buyer $i$ willing to buy up to quantity $b_{s,i}$ and seller $j$ willing to sell up to quantity $s_{s,i}$. There are $N$ buyers and $M$ ...
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11 views

Why normalized feature weights for linear regression are bad feature importance predictors

I am trying to interpret a linear regression model. I assumed using absolute value of feature weight coefficients as indicators of influence of input variable onto output variable. However, it seems ...
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13 views

Probability that independent variables have significant regression coefficient

suppose to have a dataset $X\in \mathbb{R}^{n\times p}$ and $y\in \mathbb{R}^n$. Independent variables. In general $cor(X,y)\neq 0 $ and so if we fit a linear model we can have that some of the ...
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1answer
21 views

Refitting with different contrasts vs. pairwise comparisons

Say, I fit a linear or generalised linear model in R with dummy coding (contr.treatment for ...
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1answer
45 views

Ok to use 0 and 1 for a varaible in a linear regression?

Ok this is a simple quesion that's been bugging me. The question is how to encode a linear model variable with only two possible values and avoid any trouble introduced by using zero. Say you have a ...
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34 views

Estimate the covariance matrix of a normal distribution if the mean vectors is given by a linear rule

Let $X=(x_1,\ldots,x_n)^\top\in\Bbb{R}^n$ be a random vector that follows a multivariate Gaussian distribution with known mean vector $\mu=(\mu_1,\ldots,\mu_n)^\top\in\Bbb{R}^n$. The covariance matrix ...
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24 views

Performing a linear regression on small dataset and trouble with modeling small predictor values

I have a dataset. y: the dependent variable (representing a ratio between the number of objects bought with the given money & the total number of objects bought) x: the independent variable ...
2
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1answer
77 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 ...
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3answers
56 views

Simulation from linear model with additional variables

I want to test the performance of a variable selection method in linear regression with normal errors using simulated data: $${\bf y}= {\bf X}{\bf \beta} + \epsilon,$$ where, as usual, ${\bf y}$ is ...
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2answers
30 views

Proving Linear Estimator (beta) is BLUE?

In the book Statistical Inference pg 570 of pdf, There's a derivation on how a linear estimator can be proven to be BLUE. I got all the way up to 11.3.18 and then the next part stuck me. After ...
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1answer
40 views

adjustment of covariates in linear model

I am trying to understand the adjustment of covariates in the linear model such as multiple logistic regression. How does adding a covariate adjusts the coefficients for that covariate (any intuitive ...
0
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1answer
56 views

Compare linear regression models (same and different response variable)

How can I (1) compare two linear models between years and (2) Can I compare 2 models with different response variables? My data have 4 variables: y_meas, x, year, y_calc. "y_meas" is a lab measured ...
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0answers
23 views

Building a linear mixed effects model?

Study Design I have a dependent variable (PP), collected under two different conditions (Condition) in ten subjects (Subject) of varying heights (Height), across three different trials (Trial). Both ...
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3answers
42 views

Compare influence of same set of independet variables on two different dependet variables

I'm currently doing two multiple linear regressions. Each of them with the same set of predictors (measurements for real estate quality) $X_1,...,X_n$, but with different dependent variables (one of ...
2
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1answer
45 views

Random intercepts as response variables: Is there a name for this method?

I'm trying to find the name of this method (and ultimately a reference). The approach is as follows: 1) Fit a mixed-effect model with a random intercept $$ E(Y_{ij})= ...
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51 views

How to calculate p value from ANOVA function for LMM results?

I have used ANOVA function so that I can get the overall p value of significant factors: ...
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28 views

To get the overall significant p value, am I on the right track for LMM?

According to this document: http://www.bodowinter.com/tutorial/bw_LME_tutorial2.pdf I can get the overall p-value of fix effects by comparing models that I would like to know to null model. In my ...
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0answers
15 views

Temporal trends with missing values

I need to calculate the temporal trends for some climate variables with missing values. For example, last frost days defines as the last day of year with minimum temperature less than 0C. However, ...
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0answers
18 views

Can I combine two pairwise comparisons?

I am using LMM in lmer. To find the most optimal model, I compare models of three-level with two level using ANOVA function. If it turns out that no significant difference between these two, then I ...
3
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1answer
74 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 ...
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0answers
30 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) ...
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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
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1answer
57 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
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1answer
73 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
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1answer
160 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
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2answers
40 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
194 views

Mixed effect linear regression model output interpretation

I just fitted the following linear mixed effects model: ...
0
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1answer
60 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 ...
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0answers
85 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 ...
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3answers
399 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?
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2answers
63 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 ...