Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables. Also known as multivariable regression.

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Calculate Standard Error of Dependent variable using Multiple Linear Regression Output

Title says it all. I'm trying to calculate the SE of an independent variable using values from MLR. I have 5 predictors, their coefficients, their SE, t-statistics, and p-values. I also have the R^2, ...
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Problem with a covariate in multiple regression

I hope someone can help me! I am conducting a multiple regression analysis with 4 predictors selected via stepwise regression. One of them had not a bivariate correlation with my dependent variable ...
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Trying to find a proper regression model for non-negative dependent variable

I'm trying to build a regression model predicting passenger numbers on trains using a number of different variables. Originally my plan was just to do a linear regression, but the issue is the model ...
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Proof that $Var(\hat{\beta_j}) = \frac{\sigma^2}{nVar(X_j|all \space other X_i)}$ in Multiple Least Squares regression

How is it possible to prove that $Var(\hat{\beta_j}) = \frac{\sigma^2}{n \cdot Var(X_j|all \space other X_i)}$ where $j \geq 1$ (I am interested mainly in slope estimates) and $\hat{\beta_j}$ is the ...
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Non-significant regression model (MLR) with significant predictor

I'm having trouble with interpreting some results I've found. In order to test my hypotheses I've conducted four analyses. My hypotheses were: X1 positively predicts Y1 and Y2 X2 does not predict Y1 ...
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Pairwise deletion in regression

I'm conducting a research on R to study how variables like coal, wind, solar, hydro generation, demand and weather variables (independent variables) affect the energy price (dependent variable) for ...
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How to interpret interact_plot for categorical x continuous interactions

I'm wondering how to interpret interact_plot plots for categorical x continuous interactions. Here's a toy example to illustrate: ...
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How can I identify if I have enough variation in my variable to identify an impact?

My data is panel and its on employee attendance and weather. I observe employees daily attendance for about 2-3 years. So I have a panel at the daily level for each employee. I have a binary X ...
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Update an existing ordinary linear regression with new data and another covariate

I am studying a case on a topic that was studied a while ago, related to food technology. To simplify the question, let's say that there are old OLS models that relate this property ($Y$) in certain ...
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Multiple Regression Model: Find Beta 1 hat via OLS. Find Beta 2 [closed]

everyone! I'm completely new to statistics and currently learning the multiple regression model. Could anyone look through this and explain how I get to solve it. It's extemely important to me that I ...
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How to do hierarchical regression with interaction in R (see example) [closed]

I'm trying to do a hierachical regression in R like it's usually done in psychometric research.Where I first make a model with a main effect and then make a second model with an interaction effect. ...
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Multiple Regression Extreme Values in all Covariates

In multiple regression: If we have a data set with covariates having extreme values, the max value of the covariate is around 10 to 14 times the mean value of that covariate. This is occurring for all ...
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Interpreting the following multiple linear regression model

I'm having difficulties trying to interpret the coefficients of my linear model. Background: lm(encounter_rates ~ year + pland_changes + regions) I've run a ...
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Multiple regression models in R [closed]

If I have data that include: The gender variable gets the value "1" for a woman and "0" for a man. The variable hours is the average number Of weekly working hours The variable ...
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How do you determine which variables to transform in linear regression?

Are there any tips as to how to diagnose the residuals of your regression model. For example, I have a residual plot that is both skewed and non-linear. When you have many predictors, is there any ...
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Interpreting the coefficients when a ln10 transformed DV is predicted by a mixture of ln10 transformed, dummy (0 & 1 coded), and continuous IVs [duplicate]

I have a multiple regression equation that reads as follows: ln10(DV) = 0.437 + 0.394(ln10(IV_1)) + 0.061(IV_2) - 0.145(IV_3) I performed the ln10 transformations for the DV and for IV_1 to get around ...
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How would you transform a percentage dependent variable to fit a logistic regression? [duplicate]

I have a outcome variable that is a percentage (proportion). According to this, I should probably use a logistic regression: What are the issues with using percentage outcome in linear regression? My ...
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Developing Risk Scores from Cox Regression model?

A simple question on the development of risk prediction models from Cox regressions. Suppose, as an example, that I want to create a risk score for 1-year mortality in patients with cardiovascular ...
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Comparing mixed effect models using deviance statistics - comparing model 1 vs. 4 instead of 1 vs. 2, 2 vs. 3, etc

I am relatively inexperienced with mixed effect models and trying to build a model to fit my outcome of interest. I have read and followed along with chapter 4 of Singer & Willet (2003), as well ...
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Interaction of Gender and Income categorical variable

I ran the following model, with exam scores in science as my outcome variable, and parental income group divided into 5 groups and a binary gender variable with the results below: ...
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1answer
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Comparing significant differences between a linear regression on same data coded as ordinal or interval

I'm running linear regressions in R on some survey data that was delivered as Likert-scales. In R, I can code them as factors (to represent them as ordinal data) or numeric (to represent them as ...
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What is the recommend function for Ridge regression [duplicate]

The following question is an answer for why lm.ridge and glmnet results are different and how to solve that. My question is ...
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What test statistic for the hypothesis that early events affect future events?

Consider you observe a series of events occurring over time where an event's time is denoted by $t_i$ ($i=1,2,...$). That is, you observe a vector $t = (t_1, t_2, ..., t_k)$ for $k$ events. Your ...
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Should I include month of interview dummies in regression?

I have a quick question regarding dummies for a regression that I am running. I am running regressions of responses to a survey question about health on a vector of independent variables (e.g., ...
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Separate Bonferroni corrections for multiple categories

I have a study in which we are looking at healthcare costs and utilization by patients with a disease vs. healthy controls (HC), as well as by different stratifications of disease (severity, ...
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Setting up a linear regression: plant height as a function of time period and soil pH

The following is from Hoff's "A First Course in Bayesian Statistical Methods" book. The data set tplant mentioned above appears below. I am trying to use an ordinary least squares to fit a ...
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Strange, symmetric suppression between 3 IVs in multiple regression?

I have encountered an interesting phenomenon while working on some data derived from a(n admittedly badly constructed) questionnaire by a colleague, and I have no idea what to make of it ...
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Sequential Bayesian Linear Regression with Diagonal Covariance

The standard update rules for a sequential Bayesian linear regression are well-known (heck, they're even on wikipedia: https://en.wikipedia.org/wiki/Bayesian_linear_regression). However, in large ...
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Meaning of θj in equation for partial derivative of MSE

The equation to find the partial derivative of a cost function with respect to a parameter θj is given in the book Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: $$ \frac{\partial}...
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1answer
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Meaning of a varaible for calculating the partial derviative of MSE cost function

The equation to find the partial derivative of a cost function with respect to a parameter θj is given in the book 'Hands on Machine Learning with scikit-learn, ...
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Is this regression model valid X/Z = B0 + B1*X + B2*Z? [closed]

In other terms can I explain a variable with the others variables that are used to compute this variables? What are the implication for my model?
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What regression approach would suit zero-inflated data that is censored at a fuzzy threshold?

Monthly grid-cell burned area estimates are (almost) lognormally distributed, censored at a fuzzy threshold and zero-inflated. I want to predict burned area from weather etc. About 40% of the ...
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When you dummy encode for logistic regression, how do you determine the feature importance for the reference group?

Say you have an IV that can be k different categorical values, and you are trying to do logistic regression. To avoid multicollinearity, you dummy encode the IV into k-1 variables, with one of the ...
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Difference between PERMANOVA and Multiple Regression on distance Matrices

I am a newbie in statistics so the math part of these 2 tests might not be crystal clear. But it seems that they are quite similar if you try to analyze e.g. how 4 variables explain the dissimilarity ...
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Interpretation interacting dummy variables regression

Suppose I have a panel dataset with a time and cross-sectional dimension. I split the time-dimension into three intervals (Interval A, B and C). Furthermore, I split the cross-sectional dimension into ...
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1answer
74 views

Upper bound for variance of $\hat{\beta}$ in multiple linear regression

The variance of the beta estimator in an ordinary-least-squares multiple linear regression to express $Y$ as a (linear) function of $X$, $\hat{\beta}$, can be expressed as (knowing $X$ and $\sigma^2$ ...
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How to interpret regression results when there are many dummy variables, not many catergories in one dummy variable

I am confused my regression results. My data is something like this. I want to see whether the presence of these six species would have significant effects on TD. So, I make every of them be dummy ...
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1answer
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Why p-values are inconsistent when applying model on subsetted data versus using interaction terms

I have the following negative binomial GLM, where "group" is either Control or Experimental and "count" shows the number of times patient came to hospital. ...
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Which plot to check for heteroscedasticity in a multiple regression model

I have a linear model like: Reg.Model = lm(Y~X1+X2+X3, data=DF) If I want to check for the presence of heteroscedasticity using a plot, should I plot the residuals ...
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1answer
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multiple regression model with multiplication between independent variable and a dummy variable

I was asked to build a linear regression model with multiplication, in the iris dataset in R. $Sepal.Length_i = \beta_0 + \beta_1 \cdot Petal.Length_i \cdot Species_i + \epsilon_i$ now I know in R , ...
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How to compare a Linear Regression’s Coefficients with the Coefficients for its Subgroups using Standard Error?

Assume a linear regression model has been made of an item’s overall utility value, and elements like durability and color availability have statistically significant coefficients in the overall value ...
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How do I model 2 variables that both affect eachother?

I am trying to model the relationship between tourism traffic and the proportion of coral reef bleached over time. I noticed that an increase in tourism will increase the proportion of reef bleached ...
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1answer
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Moderation (interaction) - Cannot use moderation if a moderator has an effect on independent variable?

I have a following simple moderation model: $$ y = b_0 + b_1x + b_2m + b_3(x \times m) + e $$ However, previous studies have also found that $x$ has a effect on $m$: $$ m = a_0 + a_1x + u $$ If $x$ ...
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Method towards calculating 95% confidence intervals with 2 predictors

I'm trying to calculate a confidence interval for the slope of my x1 predictor. I'm given the RSS in addition to the attached info. Is my next step finding my estimated standard deviation in order to ...
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Using VIF, Interaction Effects, polynomial associations for feature selection in multiple linear regression

Is there a guide, tradition, or accepted practice on what to take into account and in what sequence between VIF, interaction effects, variable transformations and polynomial associations when ...
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What is the best method for analysing data from 10 countries, over ten years with ten variables?

I am undertaking my dissertation and I am analysing the effect FDI has on economic growth in Southeast Asian countries. I have data from ten variables for each country (10 in total) and have gathered ...
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Bayesian multivariate regression

I am trying to solve the below multivariate regression problem by building a fully Bayesian model- \begin{align*} \mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{E} \end{align*} where $\mathbf{Y} \in R^{n\...
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Interpreting coefficients of several multiple regression models

I have a dataset containing last 4 years of sales data for various categories of items. I've built one regression model for each category to explain 'the reasons' behind different performances. I've ...
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1answer
20 views

Nested models in linear regression

I am getting confused in defining if models are nested. I know the basics that the reduced model can be derived from the full model by removing terms or setting terms to 0. But what about a case like ...
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Regression coefficients residuals interdependence? [closed]

I would like to check and describe the dependence between the errors in the regressors of a regression model. Let A and B be the errors, I created the following plots: My question: Looking at the ...

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