# Tagged Questions

Refers to any model where the 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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### linear (?) mixed models help?! - simple question from a simple mind

I have a stunningly simple data set and, unfortunately, an equally simple mind when it comes to stats. This is how my data are set up: I asked people to sit small exams on different days of the week ...
273 views

### To find significant differences between means using repeated measures GLM

I am new in using SPSS and stuck with General Linear Model [which is just linear model] procedure. I have 8 cognition variables like latency, thigmotaxis, spatial, quadrant, nt quadrant, proximity, ...
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### Differences in power in regression versus mean of a ratio

I've been futzing around with the following example, and feel that there must be a good explanation or reference that I am blindly missing. Supposer you have a linear relationship between two ...
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### The effects of seasonality, etc [on hold]

How are trend, seasonality, cycle and irregular components treated in a linear regression model and a ARIMA model?
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### Least squares robust to outliers

I have sparse overdefined system of linear equations. For example I have n variables, m equations(m>n) and k equations from m are "bad" equations that represent outliers. Is there any methods to ...
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### What is $\rho$ in case of $Cov(X,Y) = \rho \cdot SD(Y) \cdot SD(X)$ if we have to undertake meta-analysis of sample-correaltions? [duplicate]

$\rho$ has been interpreted by Mathai and Rathie in their book as linear correlation. What is the correct interpretation when the covariance equals $\rho$ multiplied by the standard deviation $X$ ...
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### What is the meaning of Mean Sq for for quantitative variables in AOV?

In an open course, Mean Sq was explained using a factor variable. Suppose your linear model is y = b0 + b1*I{x == A} + b2*I{x == B} where A, B are Factor ...
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### Big coefficient difference between logit/probit and linear probability model

Setting: Large N, short T panel dataset. Very few 1's (probably 1 percent), most zeroes. I estimate a logistic regression and find a negative significant coefficient on the IV of interest. ...
763 views

### Updating linear regression efficiently when adding observations and/or predictors in R

I would be interested in finding ways in R for efficiently updating a linear model when an observation or a predictor is added. biglm has an updating capability when adding observations, but my data ...
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### Flat maximum effect?

I've seen this referred to in relation to model selection but haven't come across a definitive description of it. What the flat maximum effect?
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### R's stats::aov and nlme::lme produce conflicting results

I want to use both anova and linear models to test the assumption that my some of my categories have different means than the rest. I am using stats::aov for anova and nlme::lme for linear modelling. ...
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### Interpretation of intercept in Helmert coding

I have a general, presumably simple, question, but I couldn't find a conclusive answer so far. Assume I have a simple case of a General Linear Model with one categorical predictor variable, that has ...
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### Linear/Non-linear Regression - SPSS

Hopefully somebody will be able to shed some light on my SPSS problems! I have been given 65 values. 57 of these data values are quarterly results and 8 are the holdback data to be used. I have to ...
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### Programmatically check if two classes are linear separable

How to programmatically check if two classes are linear separable? (only yes/no answer) Maybe I can train linear SVM on data(use parameters to overfit) and then run test on same data and if accuracy ...
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### Strange linearity test for ANCOVA

There is an easy way to test the linearity hypothesis for a simple regression model $y \sim {\cal N}(\alpha+\beta x,\sigma^2)$: calling $H_0$ this model, perform a test against the ANOVA model $H_1$ ...
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### Likelihood ratio test to compare two predictions

I have two predictions from two different types of methods. "predictedHousePrices1" is a continuous variable and the output of a prediction from a RandomForest model, "predictedHousePrices2" is the ...
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### symmetry of linear regression

Consider the following linear regressions on two sets of data x and y (of same length) y=ax x=by As you know, the usual optimisation by OLS is usually not giving (at all!) b=1/a This is because ...
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### Comparing linear models

My Linear Models professor said that it is possible sometimes to obtain two different linear models for the same data, such that the models cannot be compared to determine which is better. How can ...
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### What's the value of ANOVA/LME?

I have some data I want to analyze, for which I was curious whether one or more conditions lead to measurements significantly different from the rest. I started out by making a table of t-test ...
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### Line of best fit (Linear regression) over vertical line

I want to get a line of the best fit which is a line that passes as close as possible to a set of points defined by coordinates point_i = (X_i, Y_i). When I apply linear regression, I have a special ...
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### anova, t-test, linear models: run on individual data points or per-person means?

The format of my studies is testing 10 individuals in 5 conditions 100 times per condition (this is a behavioral test) - resulting in around 5000 raw data points. I am currently using 3 statistical ...
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### Determine presence of “plateau” phase with lme4

I am trying to determine whether the data depicted in the following figure shows a plateau phase for higher scramblings. As I have often been encouraged to use linear models instead of anova - I ...
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### R linear models - category IDs as strings or ints

I am trying to fit a linear model (lme4::lmer()) to my data in R. I would like to look at a number of things, including "scrambling" of visual stimuli and ...
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### Inequality of elements of hat matrix

We have a linear model \begin{align} Y=X\beta + \varepsilon \end{align} where $X$ is $n \times p$ ($n > p$) matrix of full rank. All assumptions of linear model hold. I have to prove inequality ...
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### Comparing means for 2 sets of (paired?) data

N patients with N samples from site A and N from site B (before and after treatment). In both sites we find 1-4 microbes, which are tested for antimicrobial susceptibility to obtain MIC values. I ...
19k views

### What is the difference between linear regression and logistic regression?

What is the difference between linear regression and logistic regression? When would you use each?
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### Does full subset selection regression model building suffer from the same handicaps as stepwise regression?

Let's assume $p$ potential predictor variables $X_1,...,X_p$ and a single dependent variable $Y$. Now I evaluate the performance of all possible linear models considering all possible combinations of ...
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### In case of multi-time series data, does the significant linear model gives there is something more?

I have total of 9 time series data. I'm basically using 8 variables as my X and 1 variable as Y. I've tried VAR model today but I don't see ANYTHING. However, when I do linear regression, all of the ...
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### Looking for the 'Elbow' in data

Subitization is the rapid, accurate enumeration of low-numerosity displays, distinguished from counting by a sharp non-linearity in the plot of response times. Below is a representative plot, from ...
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### Does stand-alone dummy variables in linear regression models make sense?

Dummy (or binary) variables ($X_2$) can be used in linear regression models to help explaining a possible group effect that a continuous predictor variable ($X_1$) might present in explaining the ...
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### Scikit linear model predictions not matching

I'm using scikits linear model for modelling two input variables and one output variable. I suspect that the two input variables have a quadratic relationship with the output variable. So I created ...
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### Repeated measures ANOVA: Mauchly's test undefined

I'm doing a two-way between-within ANOVA in SPSS. I have two groups with 9 subjects each (so total = 18), and 24 levels of one repeated measure. I understand why Mauchly's test of Sphericity has no ...
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### From half-circle to linear model

this is kinda homeworkish so I don't want a full solution I just want some input. I have this data set And I want to transform the data (with a rbf Kernel?) in order to be able to do a simple ...
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### Linear regression with independent variables with varying proportions

I am looking to do a linear regression on two independent variables that will be present in varying proportions. For example trying to do a linear regression on $Y$ which is payment behavior (payback ...
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### Fit a regression line by using MATLAB

I have the following data ...
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### What are typically encountered condition numbers in social science?

As part of my thesis, I'm proving (or attempting to prove...) a few asymptotic results. Because these results depend on the condition number, I'd like to have some idea about the typical sizes of a ...
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### Guidelines for splitting positively-skewed DV for Linear Modeling?

I am creating a multiple Linear Regression model using a Dependent variable which is extremely positively-skewed: My skewness statistic is 27.610, std. deviation is 2832.139, range of values from 0 - ...
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### GLS regression versus linear mixed models in R

I am looking for papers in the management area that discuss more on the use of linear mixed models in R. Yet all I am getting the results where most, if not all, use GLS regression technique. Would ...
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### Two simple or one complex model, BIC and likelihood

I have a set of data points with a total number of Nt. I know a priori that the data comes from two distinct processes (distributions). I am trying to find the optimal model parameters together with ...
4k views

### How to calculate the difference of two slopes?

Is there a method to understand if two lines are (more or less) parallel? I have two lines generated from linear regressions and I would like to understand if they are parallel. In other words, I ...
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### Distinction between linear and nonlinear model

I have read some explanations about the properties of linear vs nonlinear models, but still I am sometimes not sure if a model on hand is a linear or a nonlinear one. For example, is the following ...
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### Best way to visually present relationships from a multivariate linear model

I have a linear model with about 6 predictors and I'm going to be presenting the estimates, f values, p values, etc. However, I was wondering what would be the best visual plot to represent the ...
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I have bootstrapped a linear model in PROC GLM. Now I want to construct CI's around the parameter estimates. For binary variables, it's straightforward: drop the reference category where the ...
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### How to retrieve adjusted values for a predictor variable in a linear model in R

Using R and ggplot, I would like to plot my output variable with one of my predictor variables adjusted for the other variables in the model. (I'm asking this question here, because I don't actually ...
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### Selecting PCA components which separate groups

I frequently use to diagnose my multivariate data using PCA (omics data with hundreds of thousands of variables and dozens or hundreds of samples). The data often come from experiments with several ...
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### Prediction and credible interval

I am wondering if prediction interval and credible interval evaluate the same thing. For instance with a linear regression, when you estimate the prediction interval of a fitted values, you estimate ...
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### Troublesome residual plot from linear mixed model

I have fitted the following linear mixed model based on the results of an economic game: lmer(TotalScore~perOOgivenP+Game+(1|Subject),REML=T,data=mdl1table)->m1 ...
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### Error with lm, common R mistake

I'm taking a class on R and I cannot get the professors code to work. I am trying to do a simple linear model and I run this code: ...
### Show that the cross-product term $\hat y'r$ from $y'y$ is 0 [duplicate]
Show that the cross-product term \hat $y'r$ from $y'y$ is 0. I see that $y'y = ( \hat y + r)'( \hat y + r) = \hat y' \hat y + \hat y'r + r' \hat y + r'r$ But not sure what identity can be used here ...
### Different $B_0$ after setting the independent variable columns to factors?
I'm currently working with a dataset in R and my $B_0$ result is different when I run linear regression with & without converting the data into factors. And I want to understand what I'm doing ...