# 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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### Dealing with Dominant Past Sales Predictor in Linear Regression for Store Sales Inference

I am using linear regression to do inference and know how much each predictor affects sales. In have data for several stores with features and sales during a certain time frame. There is not much ...
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### Which linear model should I use?

I have data collected from an experiment in which 24 subjects did the same task 4 times. So in total I have 96 data points. My research hypothesis is that there are always linear relationships between ...
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### Can you use linear regression to predict individua or group player performance from team performance in a Public Good Game?

I am doing an analysis of the experimental data I have collected. In particular, I should do a panel regression. I have collected data from my experiment on public goods. My variable of interest is ...
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### Two contradicting derivations of the Covariance Matrix for Linear Regression

I am looking to compute the variance covariance matrix for the standard linear regression coefficients $\hat{\beta}$ when: $$Y = X \beta + \epsilon$$ and $\epsilon \sim N(0,\sigma^2)$. I have derived ...
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### Obtaining Residual Sum of Squares from a large OLS problem using a naive sequential approach - why doesn't it work?

Suppose we have an OLS problem with a large number of predictors: $Y = X_1 + X_2 + \cdots + X_p$. I want to obtain its RSS. I don't need to know the regression coefficients or individual residuals, ...
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### Why do we differentiate the RSS with respect to minimizers?

I am having a hard time understanding simple linear regression. I got to a point, in this website to which I can see the closest answer to my question : To minimize our error function, S, we must find ...
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### If the error term in a regression is squared can it still be a linear regression?

So basically I’ve been taught that in a linear regression model the parameters alpha and beta cannot be squared when defining the equation of our model, does this also apply for the error term (...
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### Understanding the kernel trick [duplicate]

I need to understand the kernel trick in order to understand methods like KRR and GPR for machine learning and I think I am getting too confused over some very basic questions. I have read in various ...
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### What is the conditions to use a weights argument to a linear model, when the dependent variable is a proportion?

My data consists of the independent variable (x) which is slope gradient (°) and the dependent variable (y) is collar GPS point density/km². For each slope gradient, the independent variable was ...
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### Should I transform my positively skewed predictor in hierarchical regression?

I'm doing a hierarchical regression trying to understand how intelligence (first predictor) and personality traits (second predictor) influence general knowledge (dependent variable). The problem is ...
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### Can linear regressions be used, given these diagnostic plots? [duplicate]

I'm using several linear regressions on a big dataset (about 1000 datapoints) with one numerical dependent variable and several independent variables (both dummy and numerical): ...
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### Questions about adding polynomial features to a dataset for linear regression

Apologies if this belongs to Data Science instead of here (I can move the question) but this seems related to the math aspect more than ML. In our course we just ...
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### Linear model with categorical variables (and constant variable) in R

I'm trying to estimate days spent in hospital (length of stay, continuous variable) based on a clinical severity score (...
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### All OLS assumptions not satisfied

I sorted some portfolios using the constituents of the S&P500 and then estimate the linear multi factor models. Now, based on my first criterion I constructed 3 portfolios where all of them had ...
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### Model comparsion for robust linear mixed models (robustlmm)

I'm currently working on a project where I've fitted 4 robust linear mixed models. However, I've hit a bit of a roadblock when it comes to model selection. I've been using the AIC (Akaike Information ...
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### Linear Regression with Multiple Input and Output Variables, Matrix Invertibility Condition?

I'm trying to work out a linear regression model where both inputs and outputs are multidimensional. Suppose we have $n$ input variables, $m$ output variables and $k$ observations. Each observation ...
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### Bootstrapping a linear mixed model with R's lmeresampler

I have a data of participants in 3 Groups, with 6,6,10 participants respectively. Each participant are measured 6 times in the combination of 2 conditions A and B, A of 2 levels and B of 10 levels. ...
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### Determine 'w' and 'b' in hard margin SVM

I have been asked the following question related to SVM (Hard Margin) in the exam, and I failed to answer it. Can anyone help me find the solution? Consider the dataset M: \begin{align*} & \left(\...
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### Sensor To Sensor Variability - Generalizing One Sensor Calibration To Many

I have 7 different sensors of the same type that try to qualitatively estimate soil water content (SWC) based off of the capacitance of the soil/medium they're touching. However, I have read a few ...
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### Linear regression model: adding a boolean dependent on y [duplicate]

Ciao, I have to perform an estimation of price fluctations. There are some outliers in the price, namely above 350€ and above 950€. My first feeling is to add two booleans representing prices between ...
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### How to calculate standard error of a regression coefficient given R output

Given the following regression equation $mpg_i=\beta_0 + \beta_1 weight_i+ \beta_2 ln(hp_i)+ \beta_3 diesel_i + \beta_4 ln(torque_i) + \beta_5 ln(torque_i) + \beta_6 year_i+\epsilon_i$ with the ...
331 views

### Mediation analysis with a log-transformed mediator

The very basic framework for mediation analysis (as I understand it) is below (DV = dependent variable, IV = independent variable): Step 1: DV ~ IV Step 2: Mediator ~ IV Step 3: DV ~ IV + Mediator – ...
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### Do I want the linear regressions fixed, random or marginal effects as the "adjusted values"?

my apologies ahead of time if it's not as clear as I would like it to be. I'm using a linear mixed effect (nlme package) to determine the association between a modularity score (on a range of -1 to 1)...
281 views

### Categorical variable in simple linear regression

I'm new to statistics. I have data that measures the effects of two different drugs (A and B) on the size of rabbits. The data consists of triplets $(\textrm{dose}, \mathrm{size}, \mathrm{type})$. I'm ...
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### Doing OLS, we can add new features by G-S orthogonalising. What is the fastest way to compare MSE improvement between two potential new regressors?

[Q] Working through ESL, looking at QR decomp for OLS. Lets say we want to add a few new features: we can iteratively add them by orthogonalising. If we only want to include a subset, how could you ...
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