# Questions tagged [regression-coefficients]

The parameters of a regression model. Most commonly, the values by which the independent variables will be multiplied to get the predicted value of the dependent variable.

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### Comparing Groups in a linear regression with an interaction term

I have the below equation: $$y_{ij} = b_0 + b_1X_{ij} + b_2Z_{ij} + b_3XZ_{ij} + \gamma H_{ij} + \delta S_{ij} + \mu_{ij} + e_{ij},$$ where $b_1X_{ij}$ is a dichotomous variable, indicating whether ...
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### standardizing(scaling) Linear Regression with continuous and categorical independent variables

I have a dataframe with a ctm, dependent continuous var, ctp, independent continuous var and day, factor with 10 levels. And I'm trying to run the linear model below in R. ...
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### Trying to show $E[\hat \beta_1 | \mathbf{X}] = \beta_1$ directly from the definition of $\hat \beta_1$?

Suppose we have the standard simple linear regression model: $$Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i,$$ with $E[\varepsilon_i|X_i] = 0$ and $\text{Var}[\varepsilon_i|X_i] = \sigma^2$. I'm ...
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### Interview question: patterns in residuals in “handmade” regression model

I was asked this during an interview, I am not sure my answers make sense. Q: You have got $n$ features $x_1,..,x_n$ for each observation $y$. You build a linear regression model by estimating the ...
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### What methods can I use to quantify the impact of multiple variables on a response variable?

Suppose I have observations for both the predictors ${x_1,x_2,...,x_p}$ and the response $y$, what I am interested in is the controls of these predictors on the response $y$. There are several cases ...
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### Market Mix Modeling using Random Forest

I am trying to build a random forest-based market mix model, wherein I want to calculate the contribution of each of my X variables towards the target. Typical MMM problem statement, but here am not ...
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### How to choose initial $\theta$ (intercept and $\beta$s) in simple linear regression? [closed]

I have the sales of items from January 2013 to October 2015. I just want to predict the total sales for the next month. Just for the sake of learning, I would like to transform it into a multiple ...
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### Determine what equation is being modelled with linear regression?

I am performing linear regression using the equation $x^{*}=(A^TA)^{-1}A^Tb$, from: $Ax=b$ → $A^TAx^{*}=A^Tb$ → $(A^TA)^{-1}A^TAx^{*}=(A^TA)^{-1}A^Tb$ → $x^{*}=(A^TA)^{-1}A^Tb$ I am trying to model an ...
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### In logistic regression, is there an official term for the value you get when you multiply feature values with coefficients?

I am currently calling it the effect, so I can report on the impact of the feature values for each observation. But is there an official term for it? That is, to understand why someone is getting a ...
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### Regression coefficient for a logged dependent variable

I am running into a puzzling econometric issue. Here is my data set-up and the model: I am using a two way fixed effects model on a panel data of states. For regression results, I take natural log of ...
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### How to prove the following linear regression properties? [duplicate]

Why is it that the below are true? $\sum_{i=1}^n \hat{y}_ie_i= 0$ so far, I have, for the above: $\sum_{i=1}^n (\hat{y_i})(y_i-\hat{y_i})=0$ = $\sum_{i=1}^n \hat{y_i} y_i- \hat{y_i}^2$ so does the ...
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### How do we use linear regression in which response variable is related to the regressors in a nonlinear fashion? [duplicate]

"This is called a multiple linear regression model because more than one regressor is involved. The adjective linear is employed to indicate that the model is linear in the parameters β 0 , β 1 , ...
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### Compare two effect sizes

I want to ask whether two effect sizes (B1 and B2) are different than one another. Both B1 and B2 are derived from a Spearman correlation, and I can extract the SE and confidence intervals. I ...
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### Coefficient of $Y$ on $X$ and Coefficient of $X$ on $Y$ [duplicate]

Under what circumstances the coefficients from simple linear regression of $Y$ on $X$ is equal to that of $X$ on $Y$? Will it hold when the standard deviations of $X$ and $Y$ are the same? I would ...
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### Appropriate way to report multiple linear regression in APA

I have a significant result for linear regression: When I control for age and sex, the main coefficient of interest is no longer significant: What is the appropriate way to write in APA format the ...
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### How to interpret normalized coefficients in logistic regression?

I trained a logistic regression model with 5 features per sample. Before training, I normalized the range of my features into [0,1] (MinMax scaler). After training, I received the following ...
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### Least square estimator for regression with errors depending on observed values

Consider the following model: $y_i = \beta x_i + \epsilon_i x_i$ where $y_i$, i = 1,2,3...n are observed; $x_i$, i = 1,2...n are known positive constants and $\beta$ is an unknown parameter. There ...
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### Should the treatment effect coefficient in a difference-in-difference model be consistent with graph trend?

I am running a difference-in-difference regression and the coefficient of the interaction term (treat*post) is negative, so I concluded that the effect of the treatment was negative on the outcome ...
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### Response variable (a percentile) is uniform and identically distributed but not independent?

Imagine the following problem: $(X,U,Y)$ is drawn from one of $n$ groups where X are the explanatory variables and $U$ is some quantity (a ratio if that’s relevant). The response variable $Y$ is the ...
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### Multiply beta coefficients from two different models

I have a count outcome with a heavy right skew that is modeled with a negative binomial. I have a continuous mediator that is modeled with OLS. We're attempting a method of causal mediation analyses ...
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### ARCH coefficient in GARCH models

Is anyone knows to interpret ARCH Coefficient in GARCH Models ? I tried to find what is ARCH Coefficient means. Some says it's for detecting Spillover effect, Some says Volatility Clustering or ...
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### Testing equality of coefficients from two different regressions / distribution of test statistic

There was a question posed on how to test for differences between regression parameters from two different regressions. If $\beta_1$ and $\beta_2$ are the two coefficients from two respective ...
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### What to report in cross validated elastic net regression?

Let's assume I want to construct a regression model to predict a specific outcome variable but I don't have enough data to do a proper train-test set split (n = 200). I have 7 predictor variables (...
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### How do you check whether heteroscedastic-consistent estimators fix your error variance problem?

I am running an OLS regression, and have non-constant error variance (residuals vs fitted looks like a fan opening up to the right). I have tried a number of power transformation but they seem to make ...