Questions tagged [multiple-regression]

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

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Comparing Regression Coefficients and sub-groups

Dear Cross Validated Community, my question relates to a certain problem I have encountered in regression analysis: The models for which I am asked to conduct an analysis is this: (1) $MATH_i = ...
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Performing lack of fit test in R

I am attempting to perform LOF for my data, but I am running into an issue. I am using the package alr3 Here is a snippit of my code: ...
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Regression analysis of advertising expenditure, how to handle many zero values in predictors

I'm working to create a Media Mix Model to determine the optimal mixture of media spend across multiple channels. Trouble is the weekly data I have has many 0s. For example, TV spend will be ...
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Pooling F-Values in Multiple Regression in a Multiply Imputed Database

When working with a dataset created via multiple imputation, SPSS pools some values but not others. For example, in multiple regression, I can get coefficients, t-tests for the coefficients, t-values ...
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How to find sequential sum of squares for multiple regression using Minitab Express? [on hold]

I am in a statistical analysis course using Minitab Express (Mac). How do I find the sequential/extra sum of squares for a multiple linear regression model with subsets? This is for hypothesis ...
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Dealing with rank deficiency when multiple regressors are inherently related / a non-binary ratio

I am running a linear mixed effects model in which three of the regressor are inherently related. For sake of conceptual example: let's say I would like to see how the relative time employees arrive ...
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Test all models possibles is a good manner to choose the “best” model?

I have programmed a function in python to test all possibles linear regression models that I can do with 5 variables. I choose the "best" model in base its AIC and BIC. These models are ...
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Model (regression) stepwise function (time-varying variable) for several observations

For each observation, we have a plot like this: where the x-axis is the time and the y-axis is the value of interest. For each observation, the time of the jumps can be different, as well as the ...
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Poisson regression: Is a skewed Likert-scale dataset a valid candidate for this approach?

Goal My goal is to correctly model the effect of three independent variables (job autonomy, trait plasticity, and job complexity) on a dependent variable (job stress). Problem Having run a ...
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One main effect is positive while other is negative but interaction effect is positive in an interaction;Interpretation help [on hold]

I have three two independent variable and an one interaction of two in regression. I am using interaction effect to estimate regression. In results I have two main effects , where fcoefficient of ...
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71 views

Regression response and explanatory variables

I am a newbie to regression, and I was trying to answer the following question using this data. Is there a meaningful difference between the distribution of damage caused by hurricanes with ...
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Linear Regression : Can I use both levels and changes in the same model?

I have a linear model with 1 predictor variable in the form of: $Y = a + b_{1}*X$ Both $X$ and $Y$ are stationary variables and the fit of the model is good. I have also created 2 other models based ...
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Using ML to optimize constants of a formula for minimizing error with a real measure

I have a formula of the form P = a.X0 + b.X1 + c.X2 + X3 and Ypred = d.(1-sqrt(1-e.P)) if P is positive and -rP if P is negative. X0,X1,X2,X3 are known attributes and a,b,c,d,e are constants that I ...
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24 views

Linear Combinations of Least Square Estimator

I come across a problem about finding the least square estimator of A$\beta$, where $\beta$ is the parameter vector in linear model ($Y=X\beta+\epsilon$). My question is, would the least square ...
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Do significant coefficients in a multiple regression analysis with moderate multicollinearity mean something?

I have a multiple regression model with moderate multicollinearity (VIFs <= 3.2). One of the coefficients is significant at the 10% level. Does this mean that despite of the variance inflation, I ...
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61 views

What is acceptable R squared value in social science or psychology research? [closed]

What should be a acceptable r squared value for social science behavioral science psychology for multiple regression analysis?
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Multi modal Distribution

I have dependent monetary variable which is a lognormally distributed , i transformed it into log normally distributed using log function in R , after that mean and median has been very close. Now ...
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Regression of a discrete variable on two others, one discrete the other categorical

I have a study which pairs up two people and has them go through a sequence of processes. They are then measured according to three variables: similarity, competitive status, and trust. Similarity ...
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Can I take all variables used for correlation analysis for future multiple regression analysis?

I have sample size of 120 persons and I have 15 independent variables and 1 dependent variable. I previously used correlation analysis found 9 of them are moderately to highly correlated. I want to ...
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If I have only $(\pmb{X}'\pmb{X})^{-1}$, how can I find $\pmb{X}$ (the design matrix)?

My teacher gave me a problem, but he only give me the $(\pmb{X}'\pmb{X})^{-1}$ matrix. If I have only $(\pmb{X}'\pmb{X})^{-1}$, how can I find $\pmb{X}$ (the design matrix)? I think this is an ...
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How to correct p-values of two multiple regression models

This may be a really basic question, but I haven't found any helpful answers. Or I simply don't understand. When correcting p-values of linear regression models, which p-values are corrected? My ...
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Effect of Hydration Status on Cognitive Function - which statistical tests do I use?

I'm carrying out a study on the above. My data is normal and my independent variable has two levels (hypohydrated and euhydrated) and unequal groups (14 vs. 8). I have 5 dependent variables - CF 1, 2, ...
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Show that $\pmb{\hat{\beta}}$ and $\pmb{\hat{\sigma^2}}$ are independents and $SSRes$ and $SSR$ are independents too

I can't show that $\pmb{\hat{\beta}}$ and $\pmb{\hat{\sigma^2}}$ are independents and that $SSRes$ (residuals) and $SSR$ (regression) are independents too. I need to show this in matrix notation.
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INTERACTION REGRESSION in ols for timeseries [closed]

y=intercept + B1X +B2Z +B3Z*X + error term I have taken this interaction model USING OLS in time series. I have these two explanatory variables X and z and their INTERACTION TERM. normally people use ...
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How does R's lm algorithm handle factors [closed]

I thought they use discriminant analysis as discribed e.g. in chapter 4.4. in James et. al. "An Introduction to Statistical Learning with Applications in R". But after input from this article and ...
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Removing the effect of unknown independent variables

I have 25 years of crop yield data (Y) and Minimum Temp, Max temp, and Rainfall as X1, X2, and X3. When I do regression analysis I get a result. My question is that for the crop yield (Y), in ...
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Multivariate linear regression with missing points without imputation

I am currently trying to perform a vanilla multivariate linear regression- imagine the equations are $y_1 = a_0x_{0,1} + a_1x_{1,1}... a_nx_{n-1,1}$ $y_2 = a_0x_{0,2} + a_1x_{1,2}... a_nx_{n-1,2}$ .....
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Combining regression estimates by summing

I want to know if one can combine regression estimates from panel regressions when the new dependent variable is a sum of the dependent variables from previously estimated regressions. To be ...
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When shall I normalize/standarize the variables of a dataset? before or after subsetting a dataset?

I am using a subset of a large dataset to run panel regressions in R. Because variables range differently, I have to re-escale them (normalize/standarize). The problem is that I do not know whether I ...
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1answer
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Train predictive model with predictive variable not present in production

Assume we are receiving a continuous time-series: $$X_1 = \{x_{1,1},\ldots,x_{1,n}\} \in \mathbb{R}^n$$ $$\vdots$$ $$X_i = \{x_{i,1},\ldots,x_{i,n}\} \in \mathbb{R}^n$$ At each step $i$ (knowing all ...
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How to denote a simple slope coefficient (interaction)?

I'm using sslope in stata to test the linear relationship between x and y for different values of my moderator. The output of sslope provides me with a significance level and a coefficient. As far as ...
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Unsure how this MLE was derived from given normal distribution

I came across this mle formula in some (undocumented) code performing linear regression with input matrices $A$ and $B,$ and was wondering how it was derived. It might also be some level of ...
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How to show that VIF's are the main diagonal elements of $\mathbf{T\Lambda^{-1}T'}$?

I'm stucked in the Exercise 9.29 of Introduction to Linear Regression Analysis (5th edition), by Montgomery: 9.29) Show that if $\mathbf{X'X}$ is in correlation form, $\mathbf{\Lambda}$ is the ...
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Can you use hypothesis testing for feature selection? [closed]

How do you apply hypothesis testing to your features in a ML model and when is it sensible to Use? I have seen around that you can decide if a feature is relevant or not by looking at its significance ...
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How to interpret regression function with categorical variable?

I am trying to figure out how to interpret a regression function with no intercept and one categorical variable performed on a survey data. Each participant marks which actions, from a list of 25, ...
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Regression with non-frequent variables

I have a dataset in which I am regressing an output variable which changes daily to 4 independent variables. 3 of these variables changes on a daily frequency, but the other one changes on a quarterly ...
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1answer
62 views

Why $Cov(\pmb{y}, \pmb{\hat{y}}) = \pmb{y}^T \pmb{\hat{y}}$?

I'm trying to proof some results in Multiple Linear Regression. In matrix notation, why $Cov(\pmb{y}, \pmb{\hat{y}}) = \pmb{y}^T \pmb{\hat{y}}$?
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In a Multiple Linear Regression Model, is $Cov(\pmb{\hat{y}}, \pmb{e}) = 0$?

I'm solving the problem 3.33, from the book "Introduction to Linear Regression Analysis (5th edition)", by Montgomery and I got a doubt. 3.33) Prove that $R^2$ is the square of the correlation ...
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GLM Categorical IV Predictor vs Group by Analysis

I am modeling a continuous dependent variable with a couple of covariates (known a priori) and a variable of interest. I ran into an issue of interpretation which I'd like to clear up. When I ...
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is there a difference between E[e|x]=0 and E[e|d=1]-E[e|d=0] in continuous vs discrete case in regressions?

in the discrete case, if assignment is random, then i can express E[y|d=1]-E[y|d=0] = B + E[e|d=1]-E[e|d=0], where the expectation of the errors are the same for both groups and become zero. Where I ...
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variable transformation for percentages and zero values

I am working on socio-economic factors related to opioid mortality in North Carolina. I have three dependent variables: total age adjusted rate, white age adjusted rate, and nonwhite age adjusted ...
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nlme - multiple regression with categorical factor - proper coding?

I am certain this question has been asked several times, yet I can't seem to find the correct code or explanation. (will remove it if I find a solution) I have a rather simple design, yet I can't ...
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Can linear model automatically identify interaction form of (x1-x2)?

for linear regression $y = \beta_{1} x_{1} + \beta_{2}x_{2}$ while the true model is actually $y = \beta x_{b}$ and $x_{b} = x_{1} - x_{2} $ will a linear model automatically recover this ...
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Exact matching + multiple regression on high-dimensional treatment-control study?

I'm working on a project with healthcare data where episodes of care in the treatment and control groups must be matched to estimate average treatment effect (ATE). I have several hundred covariates ...
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Why can't I calculate the $R^2$ in some regression models if I use the method of maximum likelihood estimation?

I've modeled two regression models the first is a multiple linear regression (OLS) $$Y=\beta_0+\beta_1X_1+\cdots+\beta_nX_n+e$$ and I can get its $R^2$. The second model is a spatial autoregressive ...
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1answer
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Help need to write mathematical equation

I have created hedonic model. I understand what I am doing, but to present in a paper I need to write mathematically. Can one please help? Many thanks Log(Capital_value_psf) = Micro_Post_code + Year +...
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Can you load a dataset into Stata and keep regression estimates from a previous dataset stored? [closed]

I have a panel regression model that I am running on 6 datasets comprised of crop yields for 6 different crops. I have run multiple specifications for each crop working towards an ideal specification. ...
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How to convert orthogonal polynomials from MULTIVARIATE regression to basic polynomial equation [duplicate]

I believe the link below converts the coefficients of one x from orthogonal to monomial form, but does someone know an edit to that code that can convert the coefficients of many x's in one regression ...
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1answer
23 views

Use z-scores as measure for regression analysis/ANOVA

I want to calculate the difference between a certain value associated with a decision alternative and the value associated with the objectively correct alternative as a measure of decision accuracy in ...
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Finding the exponents of a multiple power law: is linear regression valid?

I want to fit a multiple power law equation of the form $y = {x_1}^{\alpha_1} {x_2}^{\alpha_2}$ where I have many examples of $y, x_1, x_2$. (Note there is no intercept.) Is it possible for me to ...