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

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Regarding 10 fold cross validation

I am bit confused regarding the application of 10 fold cross validation steps. To be specific, I have made a multiple regression model (except model validation) and the model does not predict ...
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6 views

How to choose right step size for alpha in the Elastic net using glment package?

I'm using glmnet to learn different Elastic net regression.as you know, Elastic net would perform at least as good as Lasso regression. but it's not the case for me and Lasso perform better than ...
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Regression with related coefficients

I've worked out that some physical process has the form $y = ax_1 + (1-a)x_2$, and would like to perform regression to find $a$. I thought about multiple regression of $y$ on $x_1$ and $x_2$ and ...
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20 views

Finding regression coefficient only with matrix correlation

How do I find Regression coefficient if data provided is only matrix correlation table? Here is example for x1 matrix correlation. ( I also have x2,x3,x4, but only provided x1 in here) for the sake ...
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16 views

Need help with multivariate multiple regression models

I want to predict more than one dependent variable by running one model, I thought that we can use Multivariate Multiple Regression Model. But I don't know how to do it with Excel or R. Can anyone ...
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17 views

optim() for multi variable returns values on the boundary in R

I would like to use function optim() in R to minimise the target function. The two optimised parameters both have constrains. I have created a test sampel data. ...
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19 views

Simple Linear Regression - Prediction Interval and Non-constant variance

I have two questions about a simple linear regression model. I want to use test1 scores to predict test2 scores. I am using R software. x=test1, y=test2, Let's say that both tests are scored from 1 ...
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21 views

How to implement reduced-rank regression in R?

How can I fit reduced-rank regression with continuous response in R? I found the package VGAM but it only fits for discrete distributions...
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25 views

'Punishment Function' in Number of Knots in Splines?

I was considering using natural cubic splines for my prediction problem when I had a thought: In Ridge Regression, you set out to minimize the equation; \begin{equation} F(X)=\lambda\sum_i ( b^2)+ ...
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Regression - Censored Data

I am trying to create a linear regression model which will predict test scores of students based on previous test scores. x=test1, scores range from 1:100 y=test2, scores range from 2:50 I have ...
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10 views

AR(n) model with exponents

When we discuss a (time-series) model $AR(n) = \Sigma_{i=0}^n Y_{t-i} + \cdots + \epsilon_t$, we use $n$ to refer to the number of time steps back the autoregression includes. In other such models, we ...
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difference between confidence interval and prediction interval in the context of regression analysis and predictive modeling

When building prediction models, I always see the following concept 1) Confidence interval for regression model 2) Prediction interval 3) Confidence interval for predicted value I can understand ...
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Post-hoc after GLM: What does it exactly say?

Background: I have been asked to model the change of weight of a few animals undergoing experimentation via a simple GLM (General Linear Model). The data looks something like this. Note that all data ...
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What is the “pdm” stat in the “rms” R package?

I am new to the world of Regression in statistics and I have been doing a research in which I am building an ordinal logistic regression model (ORM). In order to fit my ORM model, I am using the 'orm' ...
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9 views

Model Selection with Competing risks in Cox regression

When doing cox proportional hazards regression one often has competing risks. The typical approach for this is to fit separate cox proportional hazards models for each risk, censoring the competing ...
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30 views

R adds unexpected variable to interaction model

Not sure if this is more of a programming question (in which case please move to stack overflow) or a statistical model question (in which case, please read on!) I'm exploring a data set and doing ...
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4 views

Finding an area of low variance for (robust) linear regression

In order to determine a function for a Good-Turing approximation of the number $N_r$ of distinct words that occur $r$ times in a hypothetical language corpus, I'd like to run a (log-)linear regression ...
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Comparing influence of single independent variable on two dependent variables (time series)

Scenario description: Temperature has been measured at $k+2$ different depths in a borehole. Measurements of the temperature were taken once each hour over a period of about 3 months. So observed data ...
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Trend analysis on time intervales

I am trying to do trend analysis on tweets. I am still confused. The classical model is based on computing the frequency of items, to say that the item with big number of frequency is the trending ...
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Nature of the Relationship between Predictors and Dependent in Regression

Given the interpretation of regression coefficients for continuous predictors is of the form: a one unit increase in the predictor leads to a "coefficient" unit increase in the: dependent (linear ...
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27 views

How can I create a linear regression model with some negative coefficients in R? [duplicate]

What I'm trying to do is to construct a linear model in a form like $$ Y = \beta_0X_0-\beta_1X_1+\beta_2X_2 + \beta_3 $$ where $\beta_0$, $\beta_1$ and $\beta_2$ are coefficient of predictors $X_0$, ...
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25 views

What is Nadaraya-Watson Kernel Regression Estimator for Multivariate Response?

Given a regression setting with covariates $X_{n \times m}$ and response $Y_{n \times p}$ where $p>1$, i.e the responses are vector-valued or multivariate, is there a Nadaraya-Watson estimator for ...
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58 views

Negative fitted values in OLS regression

I am running a regression where my dependent variable is a cross-section of variances. Therefore, I require my predicted values (fitted values) to be positive. However, when running a simple OLS ...
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33 views

How to perform regression with a sensitivity analysis in R

Without using non-base packages like plm, how can I perform a fixed effects regression in R with a sensitivity analysis for one or several other variables? Some ...
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18 views

How to find optimal penaltyparameter C for SVM (regression)

I am training an svm regressor using python sklearn.svm.SVR From the example given on the sklearn website, the above line of code defines my svm. ...
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58 views

Regression function of “non-regressible” data

I have some background in probability, and now trying to understand statistics, which sometimes leads to the questions of the following kind. Let $X$ and $Y$ be two random variables that represent the ...
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29 views

Bootstrap glm and extract pvalue

I am running a glm model using bootstrap, I can extract the coefficient mean and the confidence intervals for all the factors in my model. But how can I get the pvalue from there? Model: ...
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75 views

How to compute confidence bound in linear regression

In a simple linear regression problem, let $A$ be an $m\times n$ matrix of samples, $A=[x^T_1; x^T_2; ...;x^T_m]$, $w$ is the $n\times 1$ parameter vector, and $b$ is $m\times 1$ response vector. The ...
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11 views

main effects of moderating variables

I am sorry if this is very trivial and a repetition. I could not find a direct question on the website that addresses my question I am studying the relationship between X1 (independent variable) and ...
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16 views

Can I interpret a simple slope if the product is not significant?

I used Hayes' PROCESS macro to run a simple regression. The interaction product was not significant (p=0.13) however the conditional effect (simple slope) was significant (at high levels of the ...
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18 views

Estimate effect on mean of dependent variable of an increase in the independent variable in a linear regression

Suppose I have the linear regression equation: Y = B0 + B1(x) How do I find the estimated effect on mean Y of an additional 50 to x? I believe this is the multiplicative effect.
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43 views

About stepwise regression and correlation

I am trying to fit a model to some observed data with the least squares method. Now, I am at the stage where I have run a stepwise regression (traditional), with Entry level $=0.025$ and Stay level ...
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Regression Output from R [on hold]

I'm trying to regress the outcome variable "count number" on its lag and season, where 1,2,3,4 represent spring, summer, autumn and winter, respectively. However, I got some very weird output from R. ...
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Excluding Outliers and Influential Observations ($R^2$ and AIC/BIC)

I am working on a cross-sectional data set relating mortgage payments to debt-income ratios. I have some extreme outliers and experimented with excluding them from the model (some 30 observations of a ...
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17 views

One Step Ahead Forecasts Using Predict() in R

I just fit a model to a time series. I am now required to generate a 10-year extrapolation forecast of my model. My model includes a time term, a time^2 term, 12 seasonal dummies, and 4 lagged ...
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45 views

Comparison of predictive models

I am trying to compare the predictive ability of various models in predicting survival in patients. I would like to examine the predictive performance of each model using 4 tests: squared Pearson ...
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Econometric Model : [on hold]

I don't understand which model to use for "Socioeconomic factors affecting non farm labour supply for households" . I am working with Household Income and Expenditure Survey data (HIES) Bangladesh, ...
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27 views

Handling Sparse Data Frames - algorithm selection

I am new to machine learning/statistical modelling. I am trying to run a classification on a highly sparse dataset with 100 features, most of which are categorical (TRUE/FALSE) with the remaining ...
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Relation of distributions

I want to predict a distribution using multiple related distributions. One method is to use multiple regression (the model specification is that the dependent variable, yi is a combination of the ...
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8 views

Binary Logiistc regression and covariates in SPSS

When running binary logistic regression, where there is an dependent variable, multiple independent variable and covariates, where do I put the covariates in SPSS? Would they go in the covariate box ...
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R: Error with mlogit Conjoint modelling - system singularity

I am building choice models on a dates about coffee preferences. I have 5 alternatives: Brand, Cup, Price, Certification and Local Community Support. The data looks like this: ...
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32 views

The effect of the order of observations on the distribution of $\hat{\beta}$ in Linear Regression

Consider linear regression. It is known that if $Y \sim N_n\left(X\beta, \sigma^2 I_n\right)$, where $X$ is $n \times p$ of rank $p$, then $$ \hat{\beta} \sim N_p\left(\beta, ...
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29 views

$\hat{\beta}^{(M)}_i\sim \hat{\beta}^{(N)}_i$ for linear regression?

Consider an i.i.d. sample $(X_1, Y_1), \dots, (X_N, Y_N)$, where each $X_i$ and $Y_i$ are $n$-dimensional column vectors, let $M \leq N$ and denote by $\hat{\beta}^{(M)}$ and $\hat{\beta}^{(N)}$ the ...
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27 views

Linear regression with redundant features (perfect multicolinearity)

Suppose $X \sim N(0,1)$, $Z=X$, and $Y=X$. An ordinary least squares regression problem is solved: $min_{(b1,b2)} \|Y-(b1*X+b_2*Z)\|_{2}^2$ This is a strictly convex function which must have a ...
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22 views

Unstandardize the slope of standardised variables in a linear regression

If I standardize my dependent and independent variable, and run a linear regression between them, the slope estimate which I have will be standardised. The variables were standardised by subtracting ...
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22 views

ANOVA result with insignificant factors

I'm having difficulty interpreting the result I get from ANOVA. Specifically, if some of the factors I put into the model have an insignificant impact (p-value > 0.05) on the output, does it mean I ...
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51 views

What is the value of “X” in a regression equation when dealing with a time series?

I am using excel to add a polynomial trend line to a chart. The chart and the formula of the trend line are shown below. I want to add lines indicating different confidence intervals so I need to find ...
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How do residuals relate to the underlying disturbances?

In the least squares method we want to estimate the unknown parameters in the model: $$Y_j = \alpha + \beta x_j + \varepsilon_j \enspace (j=1...n)$$ Once we have done that (for some observed ...