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Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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5 views

Generate scenarios of multiple related parameters

Assume I have three industry datasets: interest rates, inflation and unemployment. Data contains information of last ten years and it's monthly. Now, I would like to create N possible scenarios of ...
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1answer
62 views

What do we mean by saying “Explained Variance”

I'm studying linear regression and there is a concept I can't wrap my head around. I've heard many times the expression "the independent variable explains $a$% of the variance of the dependent ...
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87 views

“Forward search” methods for outlier detection etc. in regression

I am reading Robust Diagnostic Regression Analysis by Anthony Atkinson and Marco Riani. They propose a robust "forward search" method for detecting outliers and other problematic data in regression (...
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64 views

What is the median of $y_{i}$ given $x_{i}$ for the function $y_i=\max\{0, x_{i}^{\prime}\beta + u_{i}\}$

$y_{i}$ is a kx1 matrix, $x_{i}$ is a kxk matrix, $\beta$ is a 1xk matrix of coefficients and $u_{i}$ is a kx1 matrix of error terms. $y_i=\max\{0, x_{i}^{\prime}\beta + u_{i}\}$ and $med(u_{i}|x_{i}...
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18 views

Nonlinear data to use in multiple linear regression?

I am supposed to be running a multiple linear regressions to test my hypotheses. However, when first testing the assumptions that should be met before performing a linear regression, it turns out my ...
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55 views

Calculate odds ratios and P-value for interaction across multiple separate subgroups

I'm trying to understand/replicate an adjusted logistic regression analysis where a treatment effect is estimated separately in a number (>2) of subgroups and estimating an overall P-value for ...
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1answer
50 views

Computationally verifying the equivalence of ridge regression estimates and Bayesian regression estimates

I'm trying to show that the numerical estimates of ridge regression's parameter estimates are the same as the MAP parameter estimates of a Bayesian regression model with normal prior distributions. So ...
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1answer
26 views

Omitted variable

My professor said that a regression is biased only if there is a correlation between the independent variable and the omitted variable (cov(x,u)=0). But wouldn't the omitted variable also have to be ...
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1answer
29 views

How are the condition numbers of a design matrix and its correlation matrix related?

Given a design matrix $X$ for a linear regression model, what is the relationship between the condition number of $X$ and its correlation matrix $R$? I would be interested in the case of a centered ...
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46 views

Event studies: Panel OLS vs cross sectional OLS vs FE

I'm currently working on my bachelor's thesis, where I'm investigating the effect of surprise interest rate decisions on stock prices using an event study approach similar to Bernanke and Kuttner (...
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19 views

Comparing vectors by regression coefficients

I have two vectors $Y_1$ and $Y_2$ both of which are known to be a function of observations in a design matrix $X$. Also, both $Y_1$ and $Y_2$ suffer from noise to a great extent. I am interested in ...
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R-square for regression using multiple imputation

I'm using multiple imputation to see how confidently we can apply the regression coefficients found for a sample to the whole population. Does it make sense to have an R-square for the model made ...
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Need clarification for different notations and corresponding formulas in Linear Regression

1) First of all, can anybody clarify, whether my notations correspond to the correct formula. As I found different descriptions/notations for different formulas, I tried to put these Information ...
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3answers
58 views

Is a specific mixed model within the class of models generated by lme4?

Given $i = 1, ..., n$ people, we measure a continuous response $y$, a group $g = 1, ..., G$ and a class $c = 1,2$. All members ...
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14 views

Creating a model that projects sales but adjusts for decreased traffic in a retail store

I have data for a retail shop for all of last year (well for many years but this is what I will be using) and all of this year current. The entries are the traffic (# of visitors), the sales, the ...
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20 views

Using robust regression to detect outliers

Rousseeuw and van Zomeren (1990) propose using robust regression to detect multivariate outliers, particularly in OLS regression. This approach seems to make sense (although I have not studied it in ...
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1answer
41 views

ANOVA is significant but coefficients aren't

My master thesis investigates the relation between stock raw returns and sentiment scores. To make a conclusion there is a multiple linear regression with the mean sentiment, the variance of the ...
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1answer
23 views

Derive linear regression model from the conditional distribution of Y|X

Suppose that $Y|X=x \sim N(\mu_Y + \frac{\sigma_Y(x-\mu_X)\rho}{\sigma_X}, \sigma_Y^2(1-\rho^2))$. The question asks to specify a simple regression model under this conditional distribution. A ...
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10 views

Regression coefficient convergence

Why does the term underlined in RED converge to the term underlined in GREEN? Can someone please provide a proof? Thanks in advance!
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1answer
21 views

OLS - regression: how to interpret it? [duplicate]

I'm running an OLS and was wondering if the 'Estimate' in my SPSS output is the same as the beta coefficient in a linear regression? Are there specific assumptions required to run an OLS? I have age, ...
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1answer
13 views

Get polynomial trendline from multiple graphs

I am trying to plot a trendline from multiple datasets of an experiment. This is what my graphs look like. They may not have the same range or the same X values: I usually go to google sheets and get ...
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7 views

Automated predictive model fitting with variables chosen based on accessory data frame

The Setup: I am performing an exhaustive search of multiple linear regression models with the R package leaps. The package does return vectors of certain fit statistics (i.e. BIC and r-squared). ...
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11 views

how to fit a VAR with HAC standard errors in R

I am trying to fit a vector autoregression model using library(vars) but I was not able to get it to work with HAC standard errors. ...
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0answers
9 views

R - checking colinearity of 3 categorial and 1 continuous variables

I have the following variables which are expected to influence the dependent variable kg waste: turnover (continuous), restaurant type (either D or I), operation (either P or N), owner (either M or F)...
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9 views

Could grid search result in lower score

I worked on a data set for prediction a heart disease. I used Logistic regression and got score of 0.85. To improve it I used Grid Search cross validation on the hyper parameter C and got that the ...
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Multiple regression and multiple comparisons 3 groups

I'm trying to compare the effect of an IV on my DV, where my data are separated into 3 groups. Specifically, in one group there is a significant correlation between IV and DV, but in the other two ...
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1answer
237 views

Model for spatiotemporal and discrete variables

I have a situation where I am monitoring events at 50 or so geographical sites in a town and at each of these sites, I am making measurements regarding the count of certain particles (so the ...
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10 views

between group contrasts using effect coded dummy variables in regression

I was taught a technique for doing this but can no longer figure out why this works, though using a simple data set I am able to prove it. I will go through that proof here as I think it's the ...
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1answer
30 views

Correlations - multiple observations & multiple observers

I haven't found quite this question on here. I have a data set that typically requires generalizability theory to untangle however I now face a question I believe g theory can not answer. 17 ...
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0answers
12 views

Replicating partial least squares (NIPALS) results using ordinary least squares regression in Tensorflow?

I have multivariate variables that I want to regress to a single target label. For some reason, using partial least squares regression (projected to a single component) gives much better prediction ...
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1answer
66 views

a measure for MAE (of a regression)

I'm running a grid search, in order to fine-tune a NN hyper parameters. the question is: the MAE values I get from the trainings are too close. since I have the statistical attributes of the target ...
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5 views

Deriving the sampling error to estimate prediction intervals

I have the following data, []wich, after performing linear regression, results in the following equation: [] How can I derive the sampling error to estimate prediction intervals for a new Y0 value, ...
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1answer
21 views

Regression analysis question on model selection and reduced model

I am doing a regression project on some medical data using SAS. I used forward selection, backward selection, stepwise selection, and the LASSO, and all procedures gave me the same subset of variables....
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In Regression Analysis, should variable transformations occur before or after subset selection?

I'm looking at fitting a model that has many parameters. In order to simplify the model and prevent overfitting, I am planning to use the best subset selection for variable selection. My question is, ...
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Interpretation of $det(X'X)$ in MLR

I would like to understand the interpretation of $det(X'X)$ in case of multiple regressors. $Var(x) = \sum_i^n(x_i-\bar{x})^2 = \frac{1}{n}\sum_i^nx_i^2 - \bar{x}^2 = \frac{1}{n}\sum_i^nx_i^2 - \frac{...
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2answers
25 views

Which regression should be used when both dependent and independent variables are nominal? All have multiple classes

The aim is to find which team will win the game based on head to head data. All the variables are nominal and have more than 2 classes. For now, I have coded them as dummy variables and have performed ...
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17 views

How to perform a linear mixed model with time series?

My data measures the width of plant(in cm) over the period of 5 days while taking into consideration the liquid used to treat the plants and my plants are clustered, my data look like this: ...
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21 views

Decision on instant T depends on decision on T-1

I'm trying to model decision making in a linear fashion: Lm(decision~ var1 + var2) However, i believe that decision in instant T dependant on the previous decision on T-1 with the same independants ...
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1answer
26 views

Using SVR to model simple data set

I have a fairly simple data set that I gathered from running workloads on a Hadoop Cluster. My goal is to model the running times of this application based on the feature variables of interest. The ...
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1answer
17 views

why data normalization is important for models when parameters can manage the feature weight/importance

When we study about normalization, various facts are given to explain the necessity. The most important of all is that: Normalized column if in higher range than others can have more impact on ...
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4answers
68 views

How regression trees split, when all the Features and target have only continuous values

Can anyone please explain how splitting is performed in regression trees when we only have continuous features. I have referred to different papers, but all I could find is formulas or theorems. Can ...
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18 views

Partial Least Square - choosing number of factors

I'm trying to implement PLS in R (using the package "PLS") to a time series consisting on realized variance of the S&P 500 and macroeconomic variables, however, I've notice they use cross-...
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1answer
17 views

Updating regression solutions for removing a regressor without the original dependent variable

Note: This question is analagous to the question I asked here except instead of adding a column, I am removing it. I am interested in a linear regression on the model; $Y= X\beta + \epsilon$ And I ...
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2answers
174 views

GLM: Modelling proportional data - account for variation in total sample size

When I am sampling the proportion of a sub-group of animals to the total number of animals within a sample, I can feel quite confident (after taking into account environmental factors) that I have a ...
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1answer
62 views

Updating regression solutions for a new regressor without the original dependent variable

Note: This question is analagous to the question I asked here except instead of a removing column, I am adding it. I am interested in a linear regression on the model; $Y= X\beta + \epsilon$ And I ...
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0answers
17 views

which normalization method is appropriate for regression problem?

I have a regression problem. I have 3 features: X1 is in the range (0.7 , 1.3) X2 is in the range (0.4 , 0.5) X3 is in the range (4.5 , 5.5) and Y is in the range (115 , 719) I started trying ...
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0answers
24 views

Gaussian Processes: advice on proper optimization settings for simple model?

I am trying my hand at Gaussian Processes with GPflow (basically using this basic example as my guide), and am experiencing difficulties fitting some basic periodic data which I generated. My code: <...
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18 views

Confidence interval for extrapolated value?

I have data that is modeled according to the equation: $$\tag{1} \frac{\Delta p}{L} = \frac{\mu}{k}\frac{q}{A}+\beta \rho \frac{q^2}{A^2}$$ The variables $\Delta p, L, \mu, q, A$ and $\rho$ are all ...
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1answer
86 views

Why do we need regularized logistic regression?

We use regularized Linear Regression to prevent the model from overfitting (reduce model complexity). Does the same idea hold with regularized Logistic Regression? Is regularized Logistic ...
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1answer
23 views

Alternative to GLM with non-independant observation

I would like to perform a regression to study association between 3 categorical variables and a presence/absence response variable. I was planning on using a GLM. However, my observation unit being ...