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Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables.

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Can I use predictor variable in percentages in multiple linear regression?

The situation is as follows: Outcome variable is numeric, and values are indicating salary of a subject. And I have 3 independent variables: Age (in years) Experience (in years) Skill in percentages (...
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LME/Multiple regression with many predictors and limited DV range

For a single-case patient study (case profile), I have 20 IVs such as medication intake, amount of sleep etc; and one DV representing the severity of the symptom reported by the patient in each of k=...
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Different error weighting for positive and negative residuals for OLS?

For OLS-estimators in multivariate regression analysis, it logically doesn't matter whether an error is positive or negative. I was wondering if in some situations it might make sense to weight a ...
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8 views

Including or excluding a variable and what about the p-values when VIF = 5.2?

I'm writing my master thesis and run into a question about multicollinearity. I have two interaction effects which have a high VIF (5.2, 4.8). Both are interaction effects between categorical ...
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1answer
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Can i use an independent variable in % units in a probit regression

I want to do a probit regression and one explanatory variable is given in % units. Do i have to transform it in decimal units or can i use it in % units in my probit regression?
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A question about the Least Squares Estimation: what motivates its definition in the general case?

Let $Y_{1},Y_{2},\ldots,Y_{n}$ be independent random variables with expected values $\mu_{1},\mu_{2},\ldots,\mu_{n}$, respectively. Suppose that the $\mu_{i}$'s are functions of the parameter vector ...
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Partial Collinearity in Regression

I had a doubt about the effect of multi-colinearity in regression analysis. I understand if two variables are co-related we cannot disentangle the effects of one from the other on the target variable ...
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How do I classify multiple time series into different buckets?

I have 60 different time series, denoted $\{y_{i,t}\}_{i=1}^{60}$. So $i$ denotes the time series in question, and $t$ obviously denotes the time period from $t=1$ to $t=T$, where $t \in \mathbb{N}_{+}...
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Ordinal categorical predictor in multiple regression

I have an ordinal predictor (family income), which has 4 levels: 1- Below $2000 2- $2000 - $3999 3- $4000 - $5999 4- $6000 - $7999 So each level is an increase ...
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53 views

Multiple linear regression: am I interpreting the methodology right?

This is a follow-up question to 1 and 2. So we have the normal linear model \begin{align*} \textbf{Y} = \textbf{X}\beta + \epsilon \end{align*} where $\epsilon\sim\mathcal{N}(\textbf{0},\sigma^{2}\...
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13 views

What is most important in building a regression model? [duplicate]

When I build a regression model, which is considered most important: removing insignificant variables, checking jfor multicollinearity and removing those variables that contribute to it, multiple R-...
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51 views

Why do we need to determine the distribution of $\textbf{Y}$ in the multiple linear regression problem?

Once again, here I am. Given the multiple linear regression model \begin{align*} \textbf{Y} = \textbf{X}\beta + \epsilon \end{align*} where $\epsilon\sim\mathcal{N}(\textbf{0},\sigma^{2}\textbf{I})$ ...
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74 views

Why is this linear regression false?

Context I'm working with real physical datas such as Temperature, Humidity, etc. My aim is to create a Linear Regression $F()$ about physical effect. It is known that : (image from youtube : https://...
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5 views

Statistical significant difference between two regressed models with use of confidence intervals

I wonder how to decide if two regression models are significantly different at a location X. Here is an artificial example, $\hat{Y}=a+b\cdot X+c\cdot X^2$. The graph shows the (artificial) measured ...
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What kind of kernel is used by statsmodels.nonparametric.kernel_regression.KernelReg?

I am doing multivariate nonparametric kernel regression using the Python function as mentioned in the title. The documentation can be found here: https://www.statsmodels.org/stable/generated/...
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1answer
31 views

Testing whether two categorical variables have identical coefficients

I am currently doing an exercise question asking me to construct a model to test whether the coefficients of two categorical variables ($X_2$ and $X_3$) are same in R. Specifically, these two ...
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1answer
30 views

Question about the Multiple Linear Regression: why and how does it work?

I know this question is quite simple and maybe quite naive as well, but I would like to get some help. The general linear model can be expressed as \begin{align*} \textbf{Y} = \textbf{X}\beta + \...
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Goodness of Fit in linear regression - to me this is not a [duplicate]

The link that is supposed to answer my question neither mentions $R^{2}$ nor GoF. At least I do not see it. What is the name and the formula to calculate the GoF in that link? Both should exist for a ...
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37 views

Estimating errors in a least square linear regression

Suppose I have a linear model of the form: $$\mathbb A \mathbf x = \mathbf y$$ where $\mathbf x\in\mathbb R^p$ is a vector of parameters, $\mathbb A\in\mathbb R^{n\times p}$ a known matrix, and $\...
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1answer
35 views

How to calculate the coefficient of a dummy variable reference category?

I am currently building a regression model with numerous continuous, categorical (employing dummies) and interaction variables. I understand we must use k-1 dummies with one variable becoming the ...
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How can I fit a multiple linear regression model in R if the value for beta coefficient of each predictor is given? [closed]

I've got an exercise question asking me to fit a multiple linear regression model in R when the values of coefficients are given. I don't know how to do it. specifically, I have 5 predictors in my ...
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2answers
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Adjusted R2 for model with only one independent variable?

Adjusted R2 is said to be more unbiased than ordinary R2 as it takes the number of explanatory variables into account. Can adjusted R2 be used in a model with only an intercept and one independent ...
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Partailling out approach in multiple linear regression [duplicate]

Assume I run the following regression: $$ sales = \beta_{0} + \beta_{1} price + \beta_{2}advert + \beta_{3}advert^2 $$ Now I regress sales, price, and advertising separately on advertising_squared ...
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Is the prediction with and without mean normalisation different in Collaborative Filtering?

In case of Collaborative Filtering: Given an output matrix I wish to learn parameters $\Theta$ (Parameter Vector) and X (Feature Vector). Now if I mean normalise the output matrix the values of $\...
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1answer
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What is the computational cost of gradient descent vs linear regression?

I know the computational costs for the closed form of linear regression is $O(n^3)$, but I can't find a similar cost comparison to gradient descent. There are some similar questions here with people "...
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Assumption multiple regression: normality of residuals

I want to run a multiple regression analysis for a given dataset in SPSS. However, the dataset violates the assumption of normality of residuals, as depicted in the picture. The values for the ...
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5 views

Relative Change Model

In a toy experiment meant to generate data for a pedagogic multiple regression example,7 types of gummi bear with different composition of ingredients (covariates: price, protein and carbohydrate per ...
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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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4answers
890 views

Control variables and other independent variables

I'm trying to do a multiple-regression analysis in Stata. I'm new to this subject, so I need someone to explain it to me in "simple words". I did an multiple-regression analysis: my control ...
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13 views

Appropriate model for cross sectional study of firms [closed]

I am conducting a cross-sectional study of 99 UK firms in 2017. I aim to find a positive/negative effect between a board characteristic (diversity) and performance variables (i.e. ROA, ROA, EBITDA, ...
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1answer
22 views

How to overcome Coefficients: (4 not defined because of singularities) [duplicate]

Stats is not my strong point but trying to run a regression. I'm aware that it happens because some of these variables are perfectly collinear. However, I do not know how to fix this? Any help would ...
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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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18 views

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
37 views

Interpretation of p-values in multiple regression output

I have data from a survey where I collected demographic information and quiz scores from college students. I ran backward model selection to determine which of my variables affect knowledge. My best ...
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6 views

Regress in two variables against basis functions when one of them might be “sparse”

I'm tasked with the problem of fitting a series of functional forms $\{f_t(S,K)\}$ along the time axis. At each time $t=0,1,\cdots,T$, there are $N_t$ samples $$(F_{t,i}, S_{t,i}, K_{t,i}),\quad i=1,2,...
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48 views

Control variables not significant

Study: The impact of satisfaction and loyalty on image dependent variable: loyalty independent variables: satisfaction, destination image control variables: age, sex, nationality, number of visits I ...
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1answer
15 views

How to compute residuals in multiple linear regression model

The residual can be seen as the distance between the observed data and the predicted data In an a simple regression model (i.e. $x\in \mathbb{R}^{n\times m}$, $m = 1$, $y \in \mathbb{R}$) we have $\...
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0answers
13 views

Using coeftest results in predict.lm() in R [closed]

I am analyzing a dataset in which the variance of the error term in my regression is not constant for all observations. For this, I re-built the model, estimating heteroskedasticity-robust (Huber-...
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25 views

Summarize regression results on different datasets

I have 20 datasets (extracted from 20 different software systems) and fit a logistic regression model on each of them. On every dataset, the model was the same (same dependent variable and the same ...
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18 views

Multiple linear regression with dependent as a dummy predictor

I have a model $Y = \alpha + \beta_1X_1 + \beta_2X_2$. $Y$ has a bimodal normal(ish) distribution, so I'm looking to see if the relationship between the predictors and the response is different for ...
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1answer
49 views

Using GAM outside statistical modelling software (in-datatabase, outside R)

Question to advanced users, math pros/programists. Can you help me understand this explanation how to use GAM outside R? As I understand very vaguely, a matrix of parameters is being exported and ...
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0answers
22 views

Finding inverse of $X'X$ in the case of two regressors [duplicate]

Variance of OLS etimator in matrix form look like this: $Var(\hat{\beta_j})=\sigma^2(X'X^{-1})$ I'm struggling to derive inverse matrix for the case with two independent variables. $X'X$ $=$ $\...
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0answers
8 views

How to interpret the predicted gender difference in interaction [duplicate]

In my model: Gender=Male, school =education, position =lecturer (ref categories) Model: Score (y) =4.215 + 0.646(logcitations) + 0.299(female) + 1.457 (Seniorlecturer) + 1.804 (AssProf) + 2.620 (...
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Complementary log-log or log-log transformation when combining estimates from multiple imputation after cox regression

Can anyone give me an argument for or against using the complementary log-log transformation as opposed to the log-log transformation on survival estimates after cox regression in multiple imputation ...
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32 views

What's the difference between loadings from partial least squares (PLS) regression and beta coefficients from multiple linear regression?

I have a set of independent variables (X1, X2, ..., X10) and I have run a PLS to find a combination of the X1, X2, ..., X10 that best predicts an outcome Y (a single-variable outcome). As a result, I ...
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34 views

Logistic regression - binary to continuous - how to interpret?

Given data with a binary outcome, i.e.: $0$ = no event, $1$ = event which can be modeled with logistic regression, how then do we understand the following logic: ...
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7 views

Negative coefficient in model caused by weak multicollinearity

I performed multiple regression and obtained the following model: Q = (0.33495)P + (-76.89321)G + (6.31424)P・G - 3.36334 P = precipitation; G = groundwater; Q = stream discharge The coefficient of (...
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15 views

Multivariate Generalized Least Squares

I'd like to use the generalized least squares (GLS) in the multivariate version. I have a response variable $\boldsymbol{Y}$ with dimension $n \times m$, where $n$ indicates the number of observations ...
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0answers
41 views

Cross-Validation on a multiple linear regression model, negative values?

I'm trying to demonstrate that, using a linear model with too many predictors, that the correlation can be artificially inflated, and that k-fold cross validation can expose overfitting. To do this, ...