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Questions tagged [multiple-regression]

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

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Dealing with non-linear variable in multiple linear regression model

I have a multiple linear regression model which should explain the variation store price elasticities using consumer characteristics of the market area surrounding a store. Therefore, my dependent ...
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9 views

Approximate prediction interval in linear regression

Suppose we have a linear regression model of the following format : $$ y(x) = \beta_0 + \beta_1 x_1+ \beta_2x_2+\beta_3x_3+\epsilon$$ We know that the prediction interval associated with a level $\...
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37 views

Identifying treatment selection and outcomes with logistic regression

We have 300 patients who underwent either surgery or a non-surgical treatment. We listed serious complications, regardless of what treatment they received. Other descriptive measures include age, sex, ...
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25 views

$\mathbb{R}^m\to\mathbb{R}^n$ regression

The naive approach to a $\mathbb{R}^m\to\mathbb{R}^n$ regression problem is simply to solve $n$ distinct $\mathbb{R}^m\to\mathbb{R}$ regression problems. However, suppose that the output of the ...
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1answer
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Difference in results when using full dataset vs subset in lmer

I have a dataset with the number of different species across multiple years and locations. I'm interested in seeing how abundance of each species has changed over time in each place. My data looks ...
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R: multi linear regression getting NA for coefficients when using lagged values [on hold]

I'm trying to regress oil prices and gdp growth rate onto gdp growth (y). below, y is the GDP growth rate and p's are the changes in oil prices. I have up to t-4 lags of each variables. this is my r ...
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1answer
31 views

Fixed effects at industry & year level for firm-level data

Various papers that study firm-level effects include dummy variables at the industry & year level. From what I understand, calculating fixed effects requires panel data, i.e. (for firm-level data)...
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Estimate expected power on a wind turbine based on other nearby wind turbines

I'm looking for a reliable way to estimate the power that a wind turbine should be producing, based on the power that its neighbours are producing. We use this to identify turbines that are ...
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16 views

In a gamma regression, how can i interpret coefficients?

My question is pretty simple, i have done a bayesian gamma regression with an inverse link, so: $\eta_i$=$\beta_0+\beta_1x_{i1}+\dots+\beta_px_{ip}$ < using an inverse link, mu is the ...
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21 views

How to merge few types of variables to one explanatory variable

so I have a data set of bike rentals in Washington D.C. Some of my variables are factors and some are numerics and continuous. I uploaded an image of a sample of my dataset so it will be easier for ...
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26 views

multivariate linear regression without b_0 [duplicate]

I created a multivariate regression following the scheme $$y = \beta_0 + \sum^n_{i=1}\beta_i*x_i$$ and got an average deviation ofaround 5%. When I tried the regression without the $\beta_0$ I got a ...
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16 views

Can we use non-Invertibility property of a matrix to detect linearly dependent features?

In order to find whether two features (such as the size of a house in feet^2 and metert^2 ) are linearly dependent or not? One way of finding it is! you take the transpose of the feature vector and ...
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How gradient decent training will affect if we use feature-crosses or high-order polynomials?

Considering Multivariate linear regression. We use feature scaling + mean normalization(feature transformation) on our features to keep them on the same scale. If we don't do that then our contour ...
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21 views

Analyzing change over time in population - what test?

I have a very large dataset that has 3 variables I'm interested in: year, place, and observation. Every year, at the same time per year, people go out and survey different areas for fruits. They then ...
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Does the $R^2$ depend on sample size?

It's well known that adding more regressors can only improve the $R^2$. What about the number of observations? Say you have a sample of size $N$, and you draw a random subsample of size $n < N$. ...
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1answer
28 views

Data level at which the Regression should be run

So I am new to regression and I have a basic doubt: Let's say I have 100 unique products(product id) which have a lot of other features that contribute in calculating the product_price(dependent ...
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Determine the effect of each variable and interaction in regression analysis

I am studying the effect of two variables x1 and x2 on response variable y. Interaction term ...
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1answer
20 views

How should I treat categorical variables for the purpose of the “One in 10 rule”?

Hope a basic question like this is alright! To avoid overfitting, we try to maintain enough cases for the least common event per explanatory variable; people usually recommend at least 10. How should ...
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28 views

PLEASE HELP! Muliple regression table interpretation? [closed]

I'm looking for clarification as to what is happening at each step, what was found at these steps, and the conclusions of these steps.
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Comparing nested models with orthogonal predictors using the t-statistic

Imagine we have a pair of nested models. Model A includes $n$ terms. Model B includes $n+m$ terms. To assess the "value add" of ...
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24 views

Calculate $R^2$, $R^2_{adj}$, and F-statistic from $\text{R}$ model summary

I am given the full model, $M_{\tt f}$, with the regression line $$ {\tt response} = \beta_0 + \beta_1{\tt A} + \beta_2{\tt B} + \beta_2{\tt C} + \beta_4{\tt D} + \beta_5{\tt E} + \beta_6{\tt F} + ...
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2answers
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Which kind of regression should I use for my variables

I checked for related questions before posting this. I found some similar questions (like this), but I couldn't find any question that answers mine. I have two independent variables, one continuous ...
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40 views

Stationarity in a ARIMA Model with External Regressors

I have a question about when we apply an ARIMA model with external regressors. Just a quick note of my understanding on the topic, an ARIMA model with external regressors is when we apply a Regression ...
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1answer
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Interpreting aov output with lm input in R

I need help interpreting the results from an anova which was run on a lm. The data are bird counts per year by state. Here is a reference picture: Here is my code for the linear model followed by a ...
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1answer
22 views

How to test whether the association between two continuous variables varies by a third variable?

If I have two continuous variables, and want to check whether their association varies by a categorical variable (e.g. gender), is there a formal statistical test for this? I know I can create a ...
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LSTM : multi-step multidimensional multivariate multi-site timeseries forecasting [closed]

I'm working on a project in which i'm trying to do a pollution forecasting. I googled around and found that LSTM is a good candidate for this task, however, I'm still struggling at how to adapt it to ...
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17 views

Multiple Regression Effect Size, Significance, and Cohens f^2

I have a multiple regression with a continuous dependent variable, 1 continuous independent variable, and a handful of binary independent variables. The R summary is pasted below: ...
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13 views

Sigma interpretation in Bayesian Linear Model?

I have two question concerning my output of my bayesian linear regression. 1) I have all beta posterior and obviously, having used a prior for Sigma, i have a posterior for Sigma too, but what can i ...
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13 views

Effect of estimate of one variable on estimate of other variable

I have a linear equation: as Y = -4 + 5X1 + 0.9X2 +0.5X3; Suppose correlation between X1 and X2 is 0.7. Since X1 has more predictive power than X2, regression picked X1 with more weightage. X2 was ...
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24 views

Solving correlation between explanatory variables using instrumental variables

I am currently stuck on a task where I am interested in estimating the production function for agricultural output as follows: \begin{equation} y_{i} = x_{i}\beta + \alpha_i + \epsilon_{i} \end{...
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1answer
63 views

How to test Heteroskedasticity for regression model with 5 independent binary variables

I have 5 independent variables at 3 levels : 0, -1, +1 and dependent variable y at Likert scale (1 to 5) The residual vs Fitted value plot doesn't look okay. Please throw some light.
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24 views

Regression of the difference between 2 poulations in the same variable and a third variable

I want to perform a simple linear regression. I have the color indices of red flower and blue flower (E.g. red could have a number between 5 to 50 of how red it is, and blue, on the same scale, of how ...
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Trying to find whether a categorical (gender) and numeric variable (heart rate) differ between each other while controlling for Age

so I tried to use ANCOVA in R and when I was doing the diagnostics test, turns out the data is not normalized. Now I am stuck, and I do not know where to go from here. Please help. Is there a way that ...
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1answer
19 views

Modelling with a delay

Im just at the stage of looking at my data and seeing how I can model it. My data is on the cooling effect of tree shade given various measured tree variables but to make the model useful I also need ...
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42 views

using boxcox to help normalize my data

Why is it that doing a Box Cox usually reduces my adjusted R^2? Sometimes it makes my data look even worse than before. Something else I noticed is that after doing the Box Cox test, I can do it again ...
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1answer
140 views

Doing regression only with correlation matrix, means, and SDs [duplicate]

I was wondering how mathematically is it possible to run a full regression analysis between 3 predictors (x1 x2 x3) and a dependent variable (...
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1answer
42 views
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Correct approach to comparing sub-group means across multiple treatment conditions

Let's say I have an experiment where I randomly pair people up with either a male or a female player, and they play a game together. I then measure some dependent variable -- call it ...
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25 views

multiple regression transformations

I am creating a multiple regression model that tries to predict future volatility using volume and observed previous volatility. When I do the models individually, the best adjusted R^2 come from: lm(...
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0answers
19 views

Consistent estimate of $\beta$ in linear regression under multicollinearity

I am currently stuck on a task where I am interested in estimating the production function for agricultural output as follows: \begin{equation} y_{i} = x_{i}\beta + \alpha_i + \epsilon_{i} \end{...
0
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1answer
19 views

Do neural networks with binary output learn representations that are linearly separable?

Support Vector machines employ the kernel trick in order to find a space where the data is mostly linearly separable and then determine what the appropriate hyperplane. However, back in the original ...
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13 views

Should I use independent variables whose correlations with dependent variable are not significant in a linear regression model

I have performed correlation tests between my dependent and all independent variables to examine linear relationship. However, the correlation coefficients from all the tests are non-significant. What ...
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0answers
23 views

How to increase R-squared in linear rRegression by adding different terms

I am solving a question where I am supposed to increase R-squared up to 0.91, So how can I do that? There are different possibilities including transformation, adding a square term to X variable, ...
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1answer
33 views

Doubt in multiple regression

If one dependent variable is in percentage form and the other is in plain numerical form, is there a need for transformation of the variables? This is specific to multiple regression.
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14 views

BIC under linear mixed model

I know usually, we do not use Bayesian Information criterion(BIC) for model selection if we have a linear mixed model (problems involve like the sample size in the linear mixed model is not well ...
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1answer
43 views

Is this a bad residual plot?

I Have the below residual plot as result of a multiple linear regression I have fitted. I do not know how to interpret the results. Is it showing heteroscadacity? There are only about 48 observations ...
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2answers
238 views

In linear regression, why should we include quadratic terms when we are only interested in interaction terms?

Suppose I am interested in a linear regression model, for $$Y_i = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_1x_2$$, because I would like to see if an interaction between the two covariates have an ...
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2answers
97 views

conditional three-level model and repeated measures using glmer in R

I have been trying to find out the most adequate formula for my data but I found no example that reflects the structure of my data, as pictured in figure above. My data is dichotomous [correct/...
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1answer
22 views

multiple regression - interpreting the plots of the model

I'm doing a multiple regression analysis with up to 9403 observations without any prior hypothesis. The AIC and BIC variable selection both generated the same ideal model. After I ...
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0answers
15 views

What should I do in panel regression if one value is indifferent for each ID?

I'm trying to have panel regression with my dataset, but there is a problem. For each ID, one parameter is fixed (for example, gender is fixed for each ID) and it keeps coming out as NA in regression ...