Questions tagged [linear]

For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.

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Testing for a linear relationship between a treatment value and outcome

Suppose there are five treatment groups, $D = 1, 2, ..., 5$, and also a control group $D = 0$. We are interested in the effect of the treatment $D$ on some outcome variable $Y$; and to this end, have ...
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20 views

Linear regression on data with associated errors in the x and y direction

I have experimental data that I need to linearise in the form $\ln(b/x)$ vs. $x$, where $x$ is an experimentally-derived quantity and the value of $x$ is dependent on $b$ (which varies). $x$ has some ...
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2answers
34 views

How to manually fit MA1 model with OLS?

We can manually fit AR1 model using linear model, as discussed here. But how to manually fit MA1 model? following code seems incorrect .., but how can we write the explanatory variable $w_t$ and $w_{t-...
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176 views

Why this OLS fitting will converge to (0,-0.5)?

In this AR1 model, if we fit y with diff(y), regardless the true coefficient, when N is large, it seems the model will converge ...
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1answer
20 views

How to manually fit AR(1) model?

I am trying to fit an AR(1) model using linear model fitting (lm in R). Why am I not getting the correct coefficient? (Ground truth from sim is ...
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13 views

Linear model selection - Subset, Forward

We use 2**p model variations in order to define best model in subset selection. In contrary, we use 1 + p(p+1)/2 models in forward selection. But in the book it states, "Since we perform guided ...
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26 views

How do I solve rank deficiency? [closed]

I am trying to do a mini project using a dataset sourced from online sources. It has 400+ observations with 8 variables. ...
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10 views

when we select a machine learning model, which perspective should we use intuitive or statistical?

I have invested a lot of time on the Linear regression model and how I select the error function and the other basic stuff, then I reached a confusing point, which there are two points of view one is ...
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1answer
43 views

X on Y Linear regression

Basically in a research project I am looking at the linear regression between my independent variable: Government Stringency Index, and dependent real GDP growth. One area I investigate assumes if ...
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6 views

Hyperplane minimizing correlation with response variable

Given a dataset X of shape $D \times F$ containing D datapoints each composed of $F$ features, and a response variable Y of shape $D \times 1$, I would like to find those directions in $X$ which are ...
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6 views

What is the conditional variance of sample predictor on population predictor?

I am using the book introduction to Statistical learning with applications in R chapter 3. I've been able to find the conditional expectations, as well as the unconditional variance, but I've read ...
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How to calculate the uncertainty of the slope of a linear regression line where each point has an uncertainty in the y-direction?

I am using the formula $m = \frac{\sum (x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum (x_{i}-\bar{x})^2}$ in order to find the slope $m$ of the linear regression of two sets of data $x$ and $y$ which both have $...
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Is the so-called “maximum likelihood” problem for linear regression really a “conditional maximum likelihood” problem?

I am reading the highly praised “Mathematics for Machine Learning” by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong. And in their development of the linear regression model, they write, ...
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1answer
26 views

Why does changing quarter to months of time series change the R-squared value?

When I use plot the average value month on month Vs quarter on quarter, I get different R-squared value. What does this mean for my regression? Do I pick month / quarter based on a higher R-squared ...
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What is the linear component behind a Mixed Effect Random Forest model?

I am a biologist with interest in statistics so in advance I want to apologize for the simplicity and misunderstanding of my statically (mathematical) assumptions and questions. In a GLMM no matter ...
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1answer
32 views

Theoretical Justification for Zellner's g Prior

What is the theoretical justification for Zellner's g prior for linear regression? I cannot see how it is possible to justify from a purely Bayesian perspective, in which probabilities are epistemic, ...
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Do these graphs fulfill assumptions of linear model?

Hi, I can see that there is a slight trend in the Scale-Location graph. I'm wondering if this is neglible enough to go ahead with a linear model? thanks! Eamon
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Interpretation of level-log when the outcome is binary [duplicate]

I know that textbooks state that when conducting level-log regression, I should generally divide the estimated coefficient by Beta / 100 for a percentage point interpretation. For example, a 1 % ...
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1answer
22 views

Linear model performs better on non-linear classification

I'm working on the following dataset : https://archive.ics.uci.edu/ml/datasets/gene+expression+cancer+RNA-Seq I start by looking at PCA/TSNE/UMAP to have a first sight, on all the data using the ...
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1answer
17 views

Likert style? Dependent variable and linear regression model

I’m a beginner to using R and have a project due in a couple of weeks I’ve been working on, basically choose any dataset and perform analysis on it. However you can only use a linear regression model ...
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24 views

Different estimate for slope error in linear regression?

In Simple linear regression the standard error of the slope is the root of the residuals in 'y' divided by the variance in x and the number of samples minus 2: $$ \Delta(slope)= \sqrt\frac{\sum \...
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2answers
26 views

Doing regression when the variables have no definite relationship

How can I do regression when the variables have no specific relationship (linear or non-linear)? I looked at scatter plots and correlation tests to discover any linear relationship. I also did a curve ...
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1answer
15 views

How to isolate a linearly correlating subset from data?

I have a data set of a few thousand data points, and some of them show strong linear correlation. I would like to isolate these data points into their own subsets. What would be the best approach for ...
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43 views

linear regression using other norms

Let us consider the linear regression model in finite dimensions given by $Y = X \beta + \epsilon$ where $Y \in \mathbb{R}^n, X \in \mathbb{R}^{n \times m}, \beta \in \mathbb{R}^m$, and $ \epsilon \in ...
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1answer
92 views

$E[(\beta_n-\beta)^2|\mathbf{X}]=\sigma^2(\mathbf{X}^T\mathbf{X})^{-1}$, what about $E[(\beta_n-\beta)^k|\mathbf{X}]$ for $k=3,4$?

Ultimately my goal with this post is to find the orders of magnitude of $E[(\beta_n-\beta)^k]$ for $k\ge 3$ as $n \to \infty$ so that I can be sure that is safe to drop higher order terms in a Taylor ...
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Why is Linear Discriminant Analysis called Linear Discriminant Analysis?

If this is the wrong place to put this question please let me know and I will be happy to switch it to the correct place - I just assumed this would be the correct place. I've Googled around and I can'...
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1answer
18 views

Linear Regression Coefficients

In simple linear regression, we have that given some $(n \times 1)$ matrix of response observations $y$ and a $(n \times p)$ matrix of observations $x$, the least-squares solution for $\beta$ is $$\...
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11 views

Fitting a model after step with missing values

If I initially fit a linear model using only complete cases, and I then perform stepwise regression to obtain a nested model, which no longer includes some of the variables which had missingness. ...
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28 views

How do you find the derivative (gradient) of the general linear regression method?

I am very new to statistical learning (I'm a graduate student in experimental biology with very little exposure to math or statistics) and I'm working my way through Introduction to Statistical ...
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2answers
89 views

Creating new function in R equivalent to the lm() for finding coefficients b0 and b1

I have a task to estimate the model to obtain b0 and b1 on the generated data (yt, zt and wt) using my created function and I'm not sure, how to do it. It's written that I should not use the existing ...
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12 views

Is there a statistics method similar to Anova for groups of data that change over time (or other independent variable)?

My dependent variable (temperature), is time dependent (time groups 1-8, each 15 minutes apart). 5 different plants were measured. I want to know if there is a significant difference between the ...
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1answer
37 views

Total sum of squares [duplicate]

In the lecture notes, in order to prove that TSS=ESS+RSS. My instructor writes that: $$TSS = \sum_t^n (y_t -\bar{y})^2= \sum_t^n y_t^2 -n\bar{y}^2$$ I don’t understand the second equality. Instead, I ...
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23 views

What to report with mixed-effect models?

I am running a mixed-effect linear regression model: DV ~ IV + (1|RandomEffect). DV is a numerical variable, and IV is a categorical variable. Now I am confused about what to report about the results ...
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49 views

Linear Regression with constraint(s): need s.e., t-stat, and p-values of the regressors

I am performing a linear regression and what I need is (1) to constrain the sum of the regression coefficients to 1, and (2) to constrain the sum of regression coefficients to 1 AND each regression ...
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1answer
76 views

Variance of dependent vs independent variable

If the dependent variable Y follows normal distribution (N), which one has the higher variance (i.e. wider CI range), independent variable or dependent variable? Why?
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63 views

Simple linear regression with skewness, kurtosis and heteroscedasticity

I have several issues with a very simple linear regression. I cannot get Skewness/Kurtosis and Homoscedasticity assumptions to be met, even after removing outliers, adding polynomial terms and using ...
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1answer
40 views

Why are covariance matrices projected by both right and left multiply?

I've been doing a lot of Kalman filtering work recently. I've derived all the equations starting from a basic linear inverse problem, so strictly speaking I know where everything comes from. I also ...
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8 views

Classification in LDa [closed]

I am new at using linear Discriminant Functions. Currently I'm finding it difficult to find the threshold for three classes. And creating an algorithm that assigns each parameters to any of the ...
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1answer
23 views

Steady state distribution overdetermined linear system

I am trying to find the steady state distribution of the transition matrix given by the discrete and time-homogeneous Markov Chain with state space $S \in \{0,1,2,3,4\}$. The transition matrix is the ...
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1answer
23 views

Specification of the categorical variables in a linear model in r

I have three variables: number of house sales month (in couples) region of a city (N-W-E-S) and I want to create a linear model with the region and the month as the predictors with this form $y_{ij} ...
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0answers
26 views

Can I fit linear mixed model here?

I have measured heart rate(HR) in different rooms of the house and I have used two different groups of participants. The rooms they go through are from 1 to 8 in that order. Now I am interested if ...
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1answer
13 views

Please help me choose which is the fixed and which is the random effect in a linear mixed effects model

Hi. I am a beginner in statistics so please bear with me. I have a dataset where I randomized participants into 2 conditions (Agency and Non-agency) then had them report their ethical responses on a ...
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1answer
42 views

Non-normal data transformation - what does it imply exactly and what does my results mean?

I am missing some understanding here. I am inspecting the relationship between the heart rate variability (HRV) and errors in the Sustained Attention to Response Task. When I conduct a basic linear ...
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0answers
22 views

Regress X with Y, what can you say about beta [closed]

Simple Linear Regression. You regress $Y \sim X$, and You know $\beta_{y,x}$. Now, if you regress $X \sim Y$, what can you say about $\beta_{x,y}$, what about its range? $\beta_{x,y} = \beta_{y,x}\...
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1answer
39 views

R: emmeans back tranform clr data using clrInv

I have a set of data that I am transforming using the clr function library(compositions) clr(my_data) Now I used ...
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2answers
32 views

Equivalent formulation of a regression (subtracting something from a dep var or controlling for it)

From my Stata experiment, the following two approaches give the same coefficient and standard errors for X. ...
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0answers
44 views

Why does the slope of the same coefficient change when we add new variables? [duplicate]

There is this question that I could not really find an answer to online. Let's say that we do a simple linear regression model with y and x1, and we compute the slope of x. Then, we make a multiple ...
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28 views

Can I correct a bias, or “skew” in my data using linear regression? [duplicate]

My supervisor has suggested that I correct a bias, or "skew" in my data using linear regression. Apparently the line of fit in the plot below should be horizontal (example attachted) Its a ...
3
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1answer
66 views

$Var(y)$ in linear regression

in linear regression, Why is $Var(y)$ different? $$Var(y) = \sigma^2$$ But somebody says, it should be that. What???? $$Var(y) = \beta_1^2 Var(x) + \sigma^2$$
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1answer
29 views

Interpreting a non-significant interaction when only one of the first order effect remains significant

I'm trying to figure out how to interpret these results. In my first regression, I include both of my two independent variables (IV1 and IV2) to predict a Dependent Variable (DV): IV1 is significant ...

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