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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Shapley, cooperative games and linearity
Shapley values grant that the additivity property hold. However, I am in understanding cases where additivity in cooperative games does not hold. Specifically, I am looking for a practical example of ...
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Does the linear regression fit follow the inverse relationship? [duplicate]
I fitted a X =logA, Y=logB with a weighted linear regression and I got the result as log B =(0.53 $\pm$ 0.054)logA + (17.41 $\pm$ 1.7). When I did the fit with X=logB, Y=logA, I expect the ...
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swapping DV and IV in the presence of an interaction
I'm hoping someone could help with a problem that I'm sure has a simple explanation. I have conducted a visual test on 2 groups of people 1) healthy controls 2) patients (with a vision problem) using ...
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If there are cubic polynomial features, then isn't this a polynomial regression, not a linear regression? [duplicate]
I have the following problem:
Consider a Linear Regression problem with two features. Based on your visualisation of these 2D features, $x_1$ and $x_2$, on the training set, you noticed that using ...
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Which analysis instead of linear regression?
I have collected data pertaining to suffering (scale from 0 to 8, higher is worse) and cognitive distortion (0 to 40, higher is worse) for a study with ~ 200 participants. My hypothesis is that there ...
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on a linear regression analysis, the determination coefficient is 0.99, but the residuals are not distributed normally. How do I interpret this?
So to preface I'd like to say that this is for homework and I am not very good at statistics. Please explain things to me like I am 5 years old.Also english is not my first language.
So the homework ...
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If R2 is not appropriate for non-linear ML algorithms such as Random Forests, can a Pearson or Spearman correlation be used as performance metric?
$R^2$ is not appropriate for non-linear models, such as Random Forest (RFs) models.
https://arxiv.org/pdf/1611.03063
Is R-squared truly an invalid metric for non-linear models?
https://...
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Difference between regression methods
When to use logistic regression and when to use beta regression in statistical modeling for given data? How do know the difference between them? And when can I fit just a linear regression and not ...
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Online updating of $t$-value for simple linear regression
Suppose I am regressing a dependent variable $y$ onto a single independent variable $x$ using a simple ordinary least squares regression model $y = \beta_1 x + \beta_0$. Suppose I start with $n$ data ...
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Simple Linear Regression, impact of standardizing data
Let's assume we have $(X_i, Y_i), 1 \le i \le n$ a series of $n$ observations.
I want to explain $Y^T = (Y_1, \dots, Y_n)$ as a linear function of $X^T = (X_1, \dots, X_n)$. My model is:
$$
Y = \...
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Adding a confounder `Factor` vs. subtracting within-level mean
In order to account for a known confounder, one can add an additional factor (that describes the confounding effect) in linear regression.
For example in R, we ...
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Interpretation of linear regression results
I ran a linear regression model with 2 IVs (both are dichotomous) with an interaction:
y = a + b1x1 + b2x2 + b3x1x2
The model and only x1 were significant....
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Making linear to logistic regression with sigmoid function - why is a transformation of predicted y needed?
I noticed that one can run a linear regression for binary outcomes and get the same predictions as from a logistic regression after using a sigmoid function. That is what I awaited. But the surprising ...
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Target encoding in linear regression
I have a dataset with the loss rates of each contract as dependent variable. As independent variables I have country (four values), profession (5 values) and income (continous variable). I apply ...
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Linear regression results do not match expected ones [duplicate]
I am fitting a simple linear model. First I sample $X\sim\mathcal{N}(0,1)$ and $Y\sim\mathcal{N}(12,3)$. Then I impose the following linear model for $Z = 2+2X-\frac{1}{4}Y+\mathcal{N}(0,\frac{1}{2})$....
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