Questions tagged [multiple-regression]
Regression that includes two or more non-constant independent variables. Also known as multivariable regression.
4,581
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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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1answer
25 views
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 ...
0
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0answers
8 views
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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10 views
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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7 views
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 ...
0
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1answer
21 views
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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5 views
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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1answer
25 views
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
17 views
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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25 views
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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10 views
Two variables Hermite polynomial fit [closed]
I have a question about how to generate 2 variables Hermite poynomial fit.
We already have
$$Y \approx \sum_{r=0}^{M} \hat{\beta}_{r} \psi_{r}(X)$$
We can get $\hat{\beta_{r}}$ by the code
...
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7 views
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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9 views
Adding Predictor Variable in an Existing Model [closed]
An analyst observes a positive relationship between digital marketing expenses and online sales for a firm. However, she intuitively feels that she should add an additional predictor variable, one ...
3
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1answer
19 views
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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1answer
38 views
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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1answer
56 views
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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0answers
11 views
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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20 views
What to do when my coefficient results from a regression are extremely large? [closed]
I am investigating the relationship between M&A (mergers and acquisitions) and macroeconomic variables. I am using a China dummy variable to isolate effects in China vs other countries in the ...
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0answers
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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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2answers
51 views
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
29 views
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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39 views
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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1answer
33 views
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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1answer
17 views
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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12 views
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
68 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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15 views
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 ...
0
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1answer
18 views
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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1answer
33 views
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
20 views
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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14 views
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
39 views
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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0answers
34 views
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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0answers
13 views
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 ...
1
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1answer
19 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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0answers
23 views
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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0answers
19 views
What learnings can I take from my regression plots to improve model performance?
I am trying to predict ecommerce conversion utilizing a simple multivariate regression. In the process I am using a log transformation of conversion as my dependent variable and log transformed ...
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0answers
21 views
How do I fit a multiple linear regression where I know the relationship between some of the coefficients
I want to fit a linear regression with multiple independent variables. Say that I know that the coefficient of one variable is twice as large as the coefficient of another variable, or that one ...
1
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1answer
24 views
In multiple regression with all significant predictors, is there a way to test significance between predictors?
In multiple regression with significant predictors, is there a way to test significance between predictors?
For example let's say you have a multiple regression and you have 4 predictors that are all ...
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1answer
104 views
Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the case of multiple regression?
Consider the standard simple linear regression model:
$$
Y_i = \beta_0 + \beta_1 X_i + \epsilon_i,
$$
for $i=1,\dots,n$. In matrix-vector form this is
$$
\mathbf{Y} = \mathbf{X_n}\beta + \epsilon,
$$
...
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36 views
Multiple Regression Coefficients
In section 3.2.3 of Elements of Statistical Learning (Link), there's this statement on multiple regression coefficients on Page 54
we have shown that the $j^{th}$ multiple regression coefficient is ...
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1answer
37 views
Does AIC criterion for variable selection in the least square method require the data to be normally distributed?
I'm studying Linear Regression from the book A Modern Approach to Regression with R by Simon J. Sheather (the 2009 edition). The chapter 7 (page 228), in which different criterion for variable ...
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15 views
two groups difference with control
I'd like to test whether a binary variable, adhdCNN, differs between the two groups identified by the binary variable group, ...
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0answers
17 views
Regression output when demeaning variable
I was wondering what the exact effect is of demeaning the data in a multiple regression. That is, I would like to know the separate effect of demeaning the dependent (Y) variable and the independent (...
