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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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Interpreting the coefficient of the interaction between 2 (binary) endogenous variables

I have the following outcome (second-stage) equation: $$y = \beta_0 + \beta_1w + \beta_2x + \beta_3w x + \cdots$$ $y$, $w$ and $x$ are all binary. Both $w$ and $x$ are endogenous, but I have an ...
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Odds Ratio but for linear regression!

I have a linear regression model that predicts lifetime customer value. It has coefficients that tell me things like, if the customer is a VIP then they have +$100 value. However if i know that these ...
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In OLS, is autocorrelation/serial correlation still an issue when both regressor and regressand are time series data?

Suppose I am trying to figure out the slope between Jet Fuel and Brent Oil Index to hedge for price movement in Crude Oil, and say I have the following data available: Monthly Ending Price such as ...
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Mean Square of Regression Error for categorical variables while computing F statistic

Give the annova table in the image below: I need to calculate the F statistic for the null hypothesis: b2 = b3 = 0 . b2 is cofficient of cylinder and b3 is the coefficient of doors. The formula used ...
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How do I interpret a negative binomial regression with categorical predictor?

I am trying to interpret R output for a negative binomial regression. Below is my output. I'm trying to infer how much my predictor (socfrend_bin) affects my ...
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What are the effects of greater variance in the DV on regression coefficients?

I am interested in potential biases in the use of regression coefficients as dependent measures. In particular, I am currently interested in the potential confounding of regression coefficients with ...
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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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Controlling for a variable in OLS - Stratification and Reaggregation. Simple Example

In his engrossing book "Naked Statistics" Charles Wheelan begins to explain how controlling for variables works by stratifying the sample. However, he stops short of explaining the reaggregation, ...
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Comparing coefficients of two different probit models---is this “bad statistics”?

Apologies for any stupid mistakes, or if the answer to this question is trivial: I have no formal statistical training. Long story short: can we meaningfully compare coefficients of two different ...
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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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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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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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Difference in Coefficient Interpretations of Linear Probability, Logit MFX, and Probit MFX Models

I have been trying to make sense of what the difference in a LPM, Logit Marginal Effects, and Probit Marginal Effects models would be. For instance, say I ran $employment = \beta_0+\beta_1edu+\dots+...
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Interpretation of different logistic regression models to test hypotheses

I would like to test two hypotheses, but I am a little bit confused. I have a binary dependent variable z, my key variable a is ...
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R: how is the Pr(>|z|) in the results of glm.fit calculated and why?

I've been searching but I can't find anywhere an explanation of how the Pr(>|z|) column is calculated in the results of R's glm.fit function. I would really appreciate: a) an explanation so I can ...
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Proving that $ (\hat{\beta} - \beta)' (X' X) (\hat{\beta} - \beta)$ is independent with SSE

Exercise: Prove that $ \mathbf{(\hat{\beta} - \beta)' (X' X) (\hat{\beta} - \beta)}$ and SSE are independent for a Least Squares Regression Model. Attempt: Note that by $'$ I denote the transpose ...
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Interpreting intercept coefficient

I have a question in this table. is it possible to interpret the intercept coefficient in this table? why?
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Regression with log transformation of dependent variable that has negative values

I am working with a dataset that contains: a dependent variable (DV) taking both positive and negative values a binary independent variable (IV). And I'm interested in the following specification: ...
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Coefficient Significance in Regression with Arima Errors

In the R package forecast, when you run dynamic regression (regression with arima errors), the coefficients and their standard error are output, but there is no significance test available for the ...
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Regression coefficient has negative symbol but positive from the raw plot

EDIT the data is here https://www.dropbox.com/s/ufrqesp1tmeh3ll/my.data.csv?dl=0 My data consists of a crop yield value collected over multiple locations and year. This is what my data looks like: ...
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common trend test-coefficient plot

I'm doing the common trend test for DID, and want to use "coefplot" to make a coefficient plot, but I don't know how to show the last pre-treatment period(coefficient is zero) on the plot, since this ...
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Sign of coefficient in single variable logistic regression seems to contradict graphical analysis

I have a 5-level ordinal independent variable ('ACT1_2') and a Boolean output variable ('target'). ACT1_2 is a response to a survey question. When I was doing some exploratory data analysis, I graphed ...
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Coefficient interpretation in multiple regression

I have a question regarding interpretation of coefficient that I've never seen it before. Regression model : In this regression model, how can I interpret beta 1? there is partial derivative.. and ...
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Importance of regressors in time series data

Could anyone recommend bibliography or name some useful methods to analyze which (exogenous) variables are most important in determining the value of a time series? For context, I have a random time ...
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why the parameters resulted from nlme or nls are scaled??

I am doing research on applying nlme to loss reserving compartmental model but I do not understand why the parameters from the model are scaled when using nlme or nls to obtain. Below is the link to ...
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Linear regression very significant βs with multiple variables, not significant alone

Could anyone provide intuition on why for y ~ β1x1 + β2x2 + β3x3, β1 β2 and β3 can be significant in a multiple variable model (p range 7x10-3 to 8x10-4), but the βs are not significant in separate ...
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Statistical measure for linear regression with two distinct clusters of points

In the following plot, I have a linear regression of 30 points, representing 10 treatments with three replicates each. As you can see, the r-squared value is quite strong (0.83) and the p-value is ...
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General formula for standard error of the regression coefficients

Can this formula be used for calculating standard error of the regression coefficients? $$ SE(\hat{\beta}_{j})^{2} = (1 / (1 - R_{j}^{2})) * (\sigma^{2} / \sum_{i=1}^{n}(x_{ij} - \overline{x_{j}})^{2}...
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Selection of regression model for prediction and interpreting quadratic regression results

I am regressing between the body mass and eye diameter in different bat species. The relationship is non-linear (picture attached) as the eye-size cannot increase linearly with respect to body size ...
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How to calculate the multinomial logistic regression's intercept and coefficients manually?

I have a trouble on calculating the multinomial logistic regression's intercept and coefficients manually. Although I managed to get the coefficients from SPSS but I don't understand how to get them ...
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Comparing importance of predictors among different groups

The research is about understanding the importance of 3 factors on personal ratings for some restaurants. There are 3 independent variables(Food Quality, Services, Environment) and 1 dependent ...
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Fitting polynomial equation and combined effect

I have following type of data matrix. I want to find the significance of predictor (including combined effect) variables like, y=β_0+β_1 x_1+β_2 x_2+β_3 x_3+β_4 x_1^2+β_4 x_1^2+β_5 x_2^2+β_6 x_3^2+...
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Validity of Comparison of regression coefficient over time

Recently came across a study which related weight loss (DV) with number of IVs using OLS and suggested some IV might have decreasing effect over time. Sample of 50 patient, who were given different ...
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Unbiasedness and consistency

Assume the simple regression model satisfying all Gauss-Markov assumptions. Somebody suggests the estimator Why may someone consider such an estimator? Why will this estimator be consistent? Why ...
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How to derive correlation using regression without empirical proof?

I just finished learning MLE, Regression, Covariance and now in to Correlation.I want to transform logically from Regression to Correlation using Covariance. Regression: A simple regression model ...
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Converting relative effect to absolute effect in log model

I have the following model; log(daily sales) = intercept + B1*(event dummy) + error My response variable(daily sales) is basically a daily time series and 'event dummy' is an indicator variable ...
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How to interpret Negative Binomial results with dummy variables

I am working on a model that looks at how the four seasons of the year have an impact in the count of crimes from 2008 to 2017. To run the model we grouped the data by season for each year and ...
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How do I compare 5 simple linear regressions?

I'm trying to compare 5 equations of simple linear regressions. All of them have the same variables: abundance of individuals vs. year. I want to know if the slopes are significantly different from ...
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Comparing linear regression coefficient between 2 continous variables of 2 groups in SPSS

I have 2 groups A (apple N=40) and B (Banana N=40). The variable fruit is categorical. For both A and B I have 2 continuous variables (how much sunlight they got, and their color intensity). Sunlight ...
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How to comapre the same regression model run in different countries with different data? [duplicate]

I have created a regression model using macroeconomic data as predictor variables. Then I run the model separately for each country. At the end I would like to compare coefficients for each predictor ...
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Regression - a variable's mean coefficient estimate across dataset samples is reliable?

I am doing a stochastic regression on a dataset that I randomly sample to train multiple models. I'm able to achieve quite accurate predictions, but the coefficient estimates have a very large ...
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Mixed Effects Model - Some groups have a single value of x

I am working on sales of a B2B company and I have sales volumes of different customers at different price points. Some customers, however, purchased at only a single price point. I'm trying to ...
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Construct a $95\%$ confidence interval for $5\beta_4$

Construct a $95\%$ confidence interval for $5\beta_4$. If this question were about $\beta_4$ without the $5$, I would absolutely know what to do. But I have to idea how the $5$ comes into play. I can'...
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Large Prob > F in regression

On performing regression in stata, the Prob > F value I obtained is 0.1921. I understand that regression coefficients are not significant at 0.01,0.05 or 0.1% levels. Does this mean that my model is ...
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Proving proportionality between LDA and simple linear regression coefficients

For a model with a single regressor $X$ and a response $Y$ of two classes ( $y=n_k/n$ if $x$ is of class $k$, $k=1,2$), the linear discriminant will be $$\delta(x)=x'\Sigma^{-1}\hat\mu_k -\frac{1}{2}\...
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Ignoring correlation in longitudinal data (Diggle)

I am going through "Analysis of Longitudinal Data" by Diggle, but I am having trouble understanding his succinct explanation of the consequences of ignoring correlation in longitudinal data. Here is a ...
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Interpretation of Economic Significance of Coefficients in Linear Probability Model and Reversing the Dependent Variable

I have the following regression: open_regime = B1 GovernmentSupport + B2 ln(R&D Budget) + other_controls + FirmFE + TimeFE + ProjectCategoryFE where ...
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Ridge Regression problem with output

I am trying to implement ridge regression in R, but the results are wrong. $\hat\beta^{Ridge} = argmin\sum_{i=1}^N(y-\beta_0 - \sum_{j=1}^{p} x_{i,j}\beta_j)^2 + \lambda\sum_{j=1}^{p}\beta_j^2$ ...