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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Alternative to plug-in estimation for log-tranformed linear model

I want to estimate a relationship of the form: $$y=ax^b\times\epsilon$$ If I log this model i get: $$\log(y)=\log(a)+b\log(x)+ \log(\epsilon)$$ If I then proceed and estimate this model using a ...
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Interpretation of related lower-order interaction when higher-order interaction is significant

How do you investigate lower-order interactions which include one factor that is part of a significant higher-order interaction? Let's assume a research design with 4 factors (A, B, C, D), each with ...
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In a linear model, how is correlation among the independent variables related to uncertainty in the model coefficients? [closed]

Suppose I have a linear model Y=AX, and I tune A based on observed data. I know that correlation among my independent variables, X, will increase the uncertainty in my model coefficients, A. How do I ...
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Unbiasedness and Variance of Predictions

Here is the problem I'm working on: I'm not quite sure if I'm showing either unbiasedness property right, and am stuck on finding the expressions for the variances. Here's what I've done so far. (a) ...
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What is considered as parameters/coefficients/weights?

I am doing lesson 2 of the fast-ai course, and I find myself with a doubt about the course. Are the weights/parameters only the slope and the cut of axis y of a simple linear function $y = ax+b$? ...
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Linear regression for multi-class classification

Linear regression can be used for binary classification where it competes with logistic regression. While the fitted values from linear regression are not restricted to lie between 0 and 1, unlike ...
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Linear Dependency

In the context of matrices, how would one explain the notion of 'linear dependency between two or more variables' in an intuitive way? Would that imply near-perfect or perfect correlation amongst ...
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Could data be described by a straight line when Pearson Correlation Coefficient has the highest absolute values?

Suppose that there is a dataset of 2D points $(x_i, y_i)$, consider the following statement: "When the Pearson Correlation Coefficient(PCC) between $x$ and $y$ is equal to -1 or 1 (highest absolute ...
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Why does the linear regression algorithm assume the input residuals (errors) to be normal distributed? [duplicate]

I am trying to know the assumptions of linear regression (LR). I understand linear regression needs the relationship between the independent and dependent variables to be linear, but LR also assumes ...
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Using a subset of parameters in joint confidence region of a linear model

For a standard linear model of the form $y = X\beta + \epsilon$, where $\beta$ is a vector of parameters. we can calculate an individual confidence interval for each parameter (of 1-$\alpha$ quartile)....
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Two different ways to write variance of OLS beta

I know that for OLS, we can write $var(\hat{\beta}) = \sigma^2 (X^{T}X)^{-1}$. Then for a the last variable $p$, we have $var(\hat{\beta}_p) = \frac{\sigma^2}{\langle x_p, x_p \rangle}$. However, we ...
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Screening candidate models before AIC comparison?

I am interested in identifying the best of 3 physiologically reasonable models that fits my continuous data. Data is some measure derived from neurons recorded from 3 adjacent regions of brain tissue (...
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Linear regression: an input variable as a multiplication/addition of other input variables

We have ways to identify collinearity in a multiple regression (using input variables' correlation matrix) and remove collinearity by dropping some of the collinear input variables. But what can be ...