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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1answer
18 views

How to prove that $Cov(\hat{\beta},\bar{Y}) = 0 $ using given covarience properties

To quote: It is well known that, if $W_1, ..., W_n, Z_1, ..., Z_m$ are random variables and $a_1, ..., a_n, b_1, ..., b_m$ are constants, then $Cov ( \sum_{i=1}^n a_iW_i, \sum_{j=1}^m b_jZ_j) = ...
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0answers
20 views

Using confidence intervals with Simple Linear Regression

So simple linear regression is performed on 3000 data points, and 1000 data points are withheld. How can we use confidence intervals, along with the withheld data points, to assess the predictive ...
0
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1answer
16 views

Effect in linear model versus effect in mixed model

Consider a dataset with 3 observations pertaining to 5 patients. This can be modeled in several ways, two of which are that $$ X_{ij} = \xi_i + Y_j + \epsilon_{ij}, $$ $i = \{1,..,3\}$, $j = ...
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2answers
25 views

Which of the 3 cases should my data matrix belong to ideally?

I found this question, and while useful, I wanted to ask something more spcific: I am trying to get a good handle/intuition for the two types of data dimensionalities (number of data samples, and the ...
2
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1answer
16 views

Linear mixed model with partially crossed effects

I'm new to Linear Mixed Models and I'm not sure if I'm specifying the right model. I'd appreciate any feedback that confirms / disproves my model. Here's some background about my data: I have a list ...
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1answer
24 views

How to apply linear regression to one sensor so that it will match readings from better sensor? [on hold]

I have one sensor which has the best accuracy and the other sensor which I want to calibrate using some linear regression (or something else?) - by modifying the software. How to calculate that linear ...
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0answers
11 views

Linear regression summary in R: Standard vs car.Anova

I am running some linear regressions in R. I am dealing with a linear dependent and linear as well as categorical independent variables using lm. So far, I have looked at the output that ...
0
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1answer
30 views

Can I iteratively transform a variable with log10 until it fits a linear model?

I have a response variable, $Z$, for which I'm trying to make a linear model. Here are some of the fit diagnostics plots: From the fan-like shape of the residual-vs-predicted value plots, I ...
1
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1answer
13 views

The prediction at the average of the covariates is different from the average of the predictions

I read in Stata manual : "The prediction at the average of the covariates is different from the average of the predictions" after a logistic regression. If I compute predictions for a linear ...
1
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0answers
14 views

Which analysis is best for my data with repeated measures and 2 treatment groups?

I'm working in R. I have a data set of 21 fish, roughly half in each of 2 treatments. I measured their behaviour over 10 minutes and want to analyse this to look for changes over time (gradient) and ...
1
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1answer
13 views

Expression for correlation in terms of hat matrix H

In a linear regression model $Y = Xβ +ε$ with $E(ε) = 0$ and $E(εε^ T ) = σ^ 2$ I, let $e_1,..., e_n$ be the residuals obtained from the least squares fit. Derive an expression for the correlation ...
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0answers
11 views

Leverages and effect of leverage points

I just got some question about the hat matrix in linear models. My first question is Why in a balanced one-way layout $(n_1=...=n_c=n_0)$, all leverages $h_{ii}$ have the same value $\frac{1}{n_0}$? ...
2
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1answer
25 views

Prove that $Var(\hat {Y_i})=\sigma^2h_{ii}$

I just got a simple question. In general linear model, we have $$\hat Y=HY$$ where $H=X(X^TX)^{-1}X^T$ and the residual $$E=Y-\hat Y.$$ Now I want to prove that $$Var(\hat {Y_i})=\sigma^2h_{ii}$$ ...
0
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0answers
34 views

How to perform a repeated measures test on my data in R? [closed]

I have a dataset of fish whose behaviour has been measured before and after a treatment, and there are 2 genotypes of fish which I am looking at. I'm using R but any advice on which statistical test ...
0
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0answers
19 views

Conditional expectation of random vector given one variable

I would like to find the conditional expectation $E(Y_i|X_i)$. Here $Y_i=\mu+\beta X_i+\gamma X^{T}+\epsilon_i$ where $X=(X_1,X_2,\ldots, X_n)$ is a $n\times 1$ vector, $X_i$ is iid random variable ...
0
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0answers
41 views

Why are the both of two models' AIC the same?

I would like to ask a question of AIC when we use Generalized Linear Model with R. I show you 4 my models. "x" is continuous variable. "f" is categorical variable and has two levels, C and T. "x*f" ...
1
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1answer
29 views

Regression technque to use for continuous data behaving like ordinal

I am trying to create a model to explain/predict fulfillment ratio of a product by a store i.e orders placed divided by orders delivered.The QQ-plot of the fulfillment ratio is: The QQ-plot of the ...
0
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0answers
19 views

R linear model where data points are grouped/correlated

I am attempting to build a linear model where I technically have multiple responses for each observation. I am working with corn field data. Management practices for each field were recorded like ...
3
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0answers
34 views

How to test that a categorical factor doesn't have an effect?

I have two categorical values in an normal linear model and the mean value specification is that they both have an effect but there is no interaction. In R, this was modelled as lm(x~ A + B). I ...
1
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0answers
15 views

What are some motivations for using nonnegative least squares?

I'm having a hard time understanding the reasoning behind it. Imagining the case of a single independent variable, if the correlation between it and the dependent is very negative, a nonlinear least ...
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0answers
30 views

Need help interpreting linear/nonlinear time series

I have a set of data, which i am tasked to find out anything that i could from this set of one dimensional data. Im looking at the ACF and PACF plot. Can anyhow determine if below indicates ...
0
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1answer
28 views

From interaction model to additive model

I have two factors, and I've fitted a interaction model in R with $lm( \sim factor1*factor2)$. The parameters belonging to the interactions between the two factors are all non-significant (p-values ...
0
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1answer
25 views

Categorical factors in normal linear model

If I have two factors, $A$ with 2 levels, and $B$ with 3 levels, what should my base model be if I want to test if there is an interaction between the two factors? Do I choose the interaction model ...
0
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1answer
60 views

What's the interpretation of `lm( y ~ x*z)`? [closed]

My intuitive understanding is that if $x$ and $z$ are categorical factors, then each observation $y_i$ is given a mean value which is equal to the mean value given to $y_j$ if $y_i$ and $y_j$ belong ...
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0answers
11 views

Linear Mixed Model with few and ranked subjects

I am studying linear mixed model recently, and my data have only 6 subjects and those are ranked groups of observations (Tier 1 customers > Tier 2 customers > Tier 3 > ... > Tier 6) The formula looks ...
0
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0answers
15 views

Variance assumption in normal linear model

How do we test the assumption of equal variance in a normal linear model? The normal assumption is tested by QQ-plot, the independence assumption is tested by the design of the experiment or of how ...
0
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0answers
11 views

Want to test equality of regression parameters for two longitudinal data

Suppose I have $p-$dimensional vectors $Y_1,Y_2,...,Y_n$ and $Z_1,Z_2,...,Z_k$ all independent such that $Y_i=\alpha_11+\beta_1x+\epsilon_i$ and $Z_i=\alpha_21+\beta_2x+\eta_i$ where $x$ is a ...
1
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1answer
25 views

Fitting a regression model

I'm trying to solve a question from a Chinese "linear statistical models", and the chapter containing this question is about weighted least squares. The question and the way I solve it are as ...
3
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0answers
31 views

What is ordinary, in ordinary least squares?

A friend of mine recently asked what is so ordinary, about ordinary least squares. We did not seem to get anywhere in the discussion. We both agreed that OLS is special case of the linear model, it ...
0
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0answers
6 views

question about the conditional error term in linear regression

Suppose we are given $n$ i.i.d. random vectors $\{ y_i,X_i \}$ where $y_i$ is a random scalar and $X_i$ is a random vector. Further suppose that $\epsilon_i$ is a linear function of $\{ y_i,X_i \}$. ...
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2answers
20 views

Does a linear classifier has spatial awareness?

Say we are trying to classify images using a linear classifier, and in our training set we have say cars in the middle on a white background. If in our test set, we shift the cars to the right but ...
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0answers
12 views

SPSS: Interpretation of coefficients - OLS

I could need some help interpreting my findings. I've been conducting a linear OLS regression with the following output: I'm trying to discover what the influences are from an acquisition on the ...
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0answers
13 views

How to add hard negatives to original training data?

I have 2 class binary classification problem with original training data of size N=n_pos+n_neg in general case n_pos!=n_neg but now we can assume that number of positive and negative examples near the ...
0
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1answer
25 views

Linear AIgebraic interpretation of Standard Errors in ANOVA using R function

Background (can safely skip): I'm working towards some sort of computer illustration through a Monte Carlo, plotting, or linear algebra explanation, I don't know, of the effect of sample size on the ...
2
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1answer
29 views

How to compare a Log-Log regression models with a Support Vectors Machine model (SVM)?

I have developed a log-log model which gives me a rmse of 0.1. I want to compare the results with a SVM model. In the SVM i didn't initially use the log transformed variables. RMSE from the ...
0
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1answer
54 views

fmincg vs fminunc

I have the following script in octave: ...
0
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0answers
5 views

One-way Fixed model

Duppose we have 12 treatments, and to start the experiment we choose these treatments, randomly. However, after selecting one treatment, all the samples are gathered and we shift to the next treatment ...
0
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0answers
34 views

Getting estimate and CI for dummy variable in linear model

I have a linear model based on some variables (age, gaming and tasks) on response time. It looks like this: ...
1
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0answers
18 views

What is the difference between Stochastic Regressor and Non-Stochastic Regressor in Linear Regression?

Suppose the regression specification is $$y_i=\beta_0+\beta_1x_i+\epsilon_i,$$ No matter $x_i$ is stochastic or not, we will need the assumption that $\epsilon_i$ is distributed the same for all $i$. ...
3
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0answers
55 views

Why Type III ANOVA is used for this analysis of coefficients

Note that I'm giving (what I believe) is minimal information to solve this problem. If more details than what are provided here are needed, please let me know, and I can provide them. I have a model ...
0
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0answers
27 views

Obtain lasso regression coeficient based LS when $X'X = I$

I need to obtain coefficients of lasso regression based in coefficients of Least Square regression method when $X'X = I $. any help will be appreciated.
0
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0answers
46 views

Can L1 linear regression perform worse than vanilla linear regression on fewer features?

I have a data set with 2 features and I'm trying to predict one real-valued variable. I use linear regression and I measure the error using 10-fold CV and absolute mean error as a metric. I noticed ...
5
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1answer
69 views

Bayesian model comparison in high school

I teach physics to high-school students, and I would like my students to conduct a rudimentary Bayesian model comparison for data from their experiments. I figured out a way for them to do so (see ...
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0answers
23 views

How to deal with outliers and feature selection simultaneously?

I've been given some data and need to pick what I consider to be the best features from it and use them to build models that fit the data. My issue is that all the tests I've seen for outliers assume ...
1
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4answers
80 views

Does a GLM count as a linear least squares model?

I'm doing some work for a summer school project and I've been asked to model some data using a 'linear least squares' model. I've done all that and analysed the results and the summary statistics look ...
0
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0answers
10 views

How do I derive the Discriminant Function in Linear Discriminant Analysis

From An Introduction to Statistical Learning with Applications in R on page 143, the authors talk about obtaining the discriminant function in the case of LDA for >1 predictors. Assuming that we are ...
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2answers
59 views

Linear Model: Why is my R² positive while my abline shows negative trend?

This easy model is plotted with: ...
5
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1answer
115 views

Analytically linking coefficients from alternative linear models (OLS)

The general problem: I have two alternative models I could use for my estimation Model A: $y = \alpha^A+ X \beta^A_0 + Z\beta^A_1 + \varepsilon^A$ Model B: $y = \alpha^B + X \beta^B_0 + ...
1
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0answers
46 views

Lasso Regression - model predictions are not correct. low r-squared

I am attempting to use Lasso to choose the best variables from a set of 20. I have managed to construct a model using LassoCV, however when using the test data to compare the predicted returns to the ...
2
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1answer
125 views

Codification of Matrix $X$ in $Y=XB+\epsilon$

The variables for the data below is age, group (treatment 1,2,3), Y response variable. ...