# Questions tagged [linear-model]

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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### Pairing conditions to run lmer

I have six conditions and would like to create three pairs of conditions, so that when I run lmer it compares conditions 1 & 4, 2 & 3, and 5 & 6. Here's what I have at the moment: ...
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### Which model is a better fit?

Suppose I have 2 linear model such that: Linear model 1: ...
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### Comparing significance of variables between each other

I would like to determine the significance of my variables in my model and compare them with each other. I have 6 explanatory variables. Here is my summary of the model: ...
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### Is there a formal terminology to describe $X^T \beta - X^T\hat{\beta}$?

We know that a linear model is represented as \begin{align} y = X^T \beta + \epsilon \end{align} where $\epsilon$ is some unobserved error and $\beta$ are the population parameter(s). Let us ...
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### Confused on ARIMA's linearity assumption

The AR(I)MA model or Auto Regressive Integrated Moving Average model is one of the most popular linear models in time series forecasting. In an AR(I)MA model, the future value of a variable is assumed ...
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I am analyzing a gradient descent implementation of a linear classifier. Before each gradient update, the learning rate is updated as: ...
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### How to fit the intercept

I'm practising using R and I'd like to do this task: So I fitted the model: ...
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### Is the following a GLM?

We know that the standard linear model is a partial case of the GLM scenario by taking the identity link function, i.e. $$g(μ)=μ=η=x_i^Tβ$$ However, in one of our past papers we are asked to ...
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### Linear Discriminant Analysis for newbie (What is the meaning of dataset is linear separable?)

What is the meaning of "LDA dataset is linear separable"? "the classes are non-linearly separated" "the features have nonlinear relationships" As I know in maths for linear equation and non-linear ...
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### MAE regression gives biased regression parameters for symmetric error?

Consider a linear model, $$y_i = \beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i.$$ From the Gauss-Markov theorem, I know that, under nice conditions, the $\hat{\beta}_{OLS}=(X^TX)^{-1}X^Ty$ ...
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### Unbiased estimator and biased error

I'm having some trouble relating unbiased estimators and bias error. By bias error, I mean the bias error we talk about when analyzing "bias-variance tradeoffs." Is this bias error and an unbiased ...
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### How to deal with problems like this ? What machine learning algorithms should be used?

I am new to machine learning and this community too. So please pardon me if i make any mistake while putting up this question. I am trying this https://www.kaggle.com/doaaalsenani/usa-cers-dataset ...
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### OLS fit interpretation using p-value

I wanted to find the relation between temperature and infected cases. Can I conclude that AvgLow was significant to predict the number of infection cases? I appreciate your suggestions!
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### Effect of choosing a linear model with only weights but with an extra X entry that is always set to 1

If we are to choose a linear model with only weights but augment X with an extra entry that is always set to 1, what effect does it have on the assumption and estimation on the resulting linear model....
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### how to get predicted intervals? code no giving me those values [closed]

I am doing a cross validation in a training data and I am getting my predicted values with my test data. I want to do a plot with predicted versus observed with the predicted intervals but my code is ...
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### write model based on R code

As shown, y is Wear. X is Brand (total 5 brands). Why summary show 4 brands variable? How to write model based on R code? Is model wear=beta0+beta1*brandAjax+beta2*brandChamp+beta3*brandTuffy+beta4*...
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### 1D representation for 2D toy data (about linear separability)

suppose there is a dataset with 2 features x1, and x2. the points (-1;-1); (1; 1); (-3;-3); (4; 4) belong to class 1 and (-1; 1); (1;-1); (-5; 2); (4;-8) belongs to class 2. I am confused in terms of ...
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### Correctly apply linear model for categorical independent variable

This question is about the way to go with a very common statistical model: Continuos dependent and categorical independent variable. In my stats class I learned to use the ANOVA: check assumptions, ...
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### How much heteroscedasticity need to be present in order to justify the use of robust standard errors?

Im trying to figure out if my data is heteroscedastic and if I need to use robust standard errors (Huber-White standard errors). The dataset contains 70 000 rows and 5 columns. Y is a numeric ...
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### Comparing coefficients in GLM with unknown dispersion parameter

If $\alpha$ and $\beta$ are two coefficients in a GLM with unknown dispersion parameter, is it possible to perform the Hypothesis test $H_{0}: \alpha=\beta$ vs $H_{1}: \alpha \neq \beta$ ? I ...
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### linear regression indicator for variables all have different values in R

I have 6 values: id, age(=0 if<24;=1>24) sex(=0 if female;1=male) week blood trt(1,2,3) Question asks write a model for each group with linear trend in week, age, sex, and all their ...
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### Comparing coefficients in GLM: a consistency issue

We have a GLM, and we wish to check if coefficients within the model are equal. However, we have come across a small consistency issue and we are not sure how to proceed. For example, let $\alpha$ ...