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
42 views

Predict results of Elections

I have information on the votes in my town and in the country. I want to predict the results in the country's elections knowing the results in my town. What methods I can use? I have thought of ...
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20 views

Regression with some observations having more than one factor level

I have data I want to analyze using multiple regression or machine learning: the response is cells for which I measured viability (a continuous response) and the independent variables are the genes in ...
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0answers
24 views

Correlation of 2 categorical variables in linear model

I have this dataframe with two categorical variables (Sex and Ethnicity (only Asian or European)) and I need to fit a linear model to estimate the weight of a fetus given the day of the echography and ...
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0answers
25 views

What is a good way to know if a variable adds value to an existing regression model without its components

Suppose someone gives you the fitted values to a regression model with $k$ terms, along with the fitted coefficients. If this is all you have, and you are investigating an additional "term" or set of ...
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5 views

Orthogonal projection onto additive subspace (normal linear model)

It is known that in a normal linear model $X \sim N(\xi, \sigma^2 I) \in \mathbb{R}^N$, if we group our observations using a factor $F$, i.e we claim that $\xi$ lies in the subspace $L_F$ where ...
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16 views

Covariance-residual technique for linear regression feature selection

When doing forward feature selection for linear regression, it is a well known trick that to select the next feature to add, we can compute the covariance of each candidate feature against the current ...
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1answer
42 views

Regression with a ratio as an independent variable

I'm regressing a response versus a ratio between two measurements as an independent variable. I'm getting a significant positive effect and I'd like to test whether the contribution of the increase in ...
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1answer
62 views

Fixed Prediction Interval

I want to place a Multiple Regression model into a production system and use the Prediction Interval as a threshold for anomalies. I've seen how I can calculate the Prediction Interval two ways: $$...
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2answers
49 views

Why should we not perform linear regression to predict ordinal dependent variables?

I am reading An Introduction to Statistical Learning. In this book, section 4.2, page 130 (text given below) mentions that linear regression would not be useful to predict ordinal variables because ...
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0answers
43 views

False discovery rate for across independent models with the same explanatory variables

I have a dataset of >10000 gene expression profiles and I would like to test the effect of 3 explanatory variables and their interactions on each gene expression profile using information criterion (...
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1answer
31 views

How does alpha relate to C in Scikit-Learn's SGDClassifier?

I'm trying to get the same linear SVM classifier model by using Scikit-Learn's SVC, LinearSVC and ...
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0answers
67 views

In linear regression, how do I extrapolate parameters obtained using preprocessed data?

Where $h_{\theta} = \theta_{0} + \theta_{1}x$, I am trying to minimize $J(\theta) = \frac{1}{2m}\sum_{i = 1}^{m}(h_{\theta}(x^{(i)}) - y^{(i)})^{2}$ I first transform every sample in the feature (...
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12 views

Can I prepare multiple linear model for a single problem by dividing independent variable into multiple clusters?

I have a single problem of predicting the expenses of customers? For that I have a linear model which is performing good for middle range of Income of family. This model has limitation at higher ...
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14 views

Reduction of models

In a normal linear model, I have working with 3 categorical factors, $A, B, C$, and my main model is the interactions model $A*B*C$. My question is as follows: If i wanted to see how far I can ...
3
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1answer
38 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
25 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 ...
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1answer
17 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 = \{1,...,...
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2answers
27 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
26 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? [closed]

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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1answer
21 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 ...
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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 ...
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1answer
17 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 ...
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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 ...
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1answer
14 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
12 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 $\frac{1}{n_0}$? ...
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1answer
26 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 $$Var(\hat {Y_i})=\sigma^2h_{ii}$$ ...
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46 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" ...
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1answer
31 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 ...
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0answers
21 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
40 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 ...
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0answers
16 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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32 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 ...
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1answer
31 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 (...
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1answer
65 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 ...
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0answers
16 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 ...
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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 non-...
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1answer
26 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 ...
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0answers
33 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 ...
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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
25 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
26 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 ...
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1answer
27 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
31 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 non-...
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1answer
88 views

fmincg vs fminunc

I have the following script in octave: ...
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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 ...
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0answers
35 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: ...