# 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 coefficients and confidence intervals when some categories have very few observations (logistic regression)

I'm fitting a logistic regression model (with multiple predictors) to data where the outcome is a success or failure. My data points are in the range of 100,000. Most of my variables are categorical, ...
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### The distribution followed by the number obtained by dividing coefficient a1 by the other coefficients a2 in multiple regression

Given the following multiple regression model. $$y\sim N(a_0+a_1x_1+a_2x_2,\sigma)$$ where $y$ is the response variable, $N(\mu,\sigma)$ is the normal distribution following the mean as $\mu$ and ...
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### Variance ratio when including irrelevant variables in a regression model

I am interested to know if there is a general formula for the ratio of the variance of regression coefficient for a predictor in a correctly specified model and a misspecified model. Specifically, let'...
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### Equality arising from coinciding of $R^2$ with slope of regression of predicted vs observed values

If I am able to interpret this correctly, then in the accepted answer to Does the slope of a regression between observed and predicted values always equal the $R^2$ of the original model? it is proven ...
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### Handling the situation: (x ~ y) == (y ~ x)

If fitting the following two models, using linear regression, produces coefficients that are essentially the same, what is the appropriate modelling technique to use? ...
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### Very similar coefficients in two different regression models [duplicate]

I have a dataset where a regression fit gives: x=1.2+0.59y y=1.2+0.64x The authors did 1), and I think that it should be ...
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1 vote
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### What is the best model for this case?

I have the following problem: A data set, which is about the soft drink consumption of people, that covers 300 subjects are available to us. Using Excel tabulations and graphing capabilities only: ...
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### calculating unstandardised betas for categorical predictors [duplicate]

I am trying to calculate the unstandardised beta for a categorical variable in a linear regression model y ~ c + βx1 where y (on the original scale) has a mean of 1000ms and a standard deviation 80 ms....
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### can i have multiple similar features derived from same properties in a dataset?

Say I am fitting a (linear) regression model to a hundred-row dataset, whose data records a series of experiments that I can hardly reproduce or further conduct to get more records, I notice that ...
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### regression coefficient language

Consider two ways of interpreting or displaying the coefficient estimates in a regression. For a small increase in X, Y decreases by the coefficient estimate amount. For a one standard deviation ...
1 vote
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### How to interpret coefficients, cross-section versus panel with fixed effects

I study the impact of a set of variables on the number of farm workers on long-term contracts. I have a panel with 8,000 geographic units and 6 years. I am particularly interested in one variable, ...
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### When testing significance between a regression coefficient of two data sets using a Z-test, how to interpret the z-value?

I am following the methods described in: Clogg, C. C., Petkova, E., & Haritou, A. (1995). Statistical methods for comparing regression coefficients between models. American Journal of Sociology, ...
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### Sampling Variance of OLS Estimators of Regression Coefficients

I am confused about whether the value of the sampling variance of the OLS estimator of a regression coefficient (e.g. slope) differs from sample to sample. Assume we have the following simple linear ...
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### Multiple linear regression slopes inconsistent with graph - why?

I am doing a multiple linear regression, with 3 categorical predictor variables (Flow, Drug, Pesticide) each with two levels (0 vs. 1). The response variable is the abundance of invertebrates. I have ...
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### How do I choose a spatial unit for fixed effects model

I have a panel dataset of 40,000 observations, that is 8,000 parishes and 5 years. When I run a fixed effects regression, using parish as a spatial unit, it shows negative adjusted R2 and rather ...
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### Fisher r-to-z transformation: comparing correlation coefficient of multiple samples

I am comparing the linearity of a regression model for two independent devices (n=10 each device group). The data is force (newtons) over time (seconds). The regression models show R^2 values of 0.9 ...
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### Multiple regression model and correlation between predictors

I am reading the Introduction to Statistical Learning in Python (ISLP) book. I am reading the below paragraph: Now suppose that the multiple regression is correct and newspaper advertising is not ...
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1 vote
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### I have a significant change in my outcome with the opposite sign in the lead period. Is this an issue?

Suppose I have a negative significant effect of a variable x on y. Also negative significant effect of the lag ie variable L1.x on y . But I get a positive sign significant effect on y in the future ...
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### Can I specify the signs on coefficients of variables in Regression models?

I have a Regression model where the coefficients of each variable need specific signs. For Example, say I have a standard OLS model: Y = β1X1 + β2X2 + … + β7X7. I want coefficients β2 and β5 to be ...
1 vote
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### Multiplicative BIASES in Log-Log regression

When we try to estimate elasticities by regression, we usually estimate the following regression model: $$ln(y) = \beta_0 + \beta_1 ln(x_1) + \dots + \epsilon$$ When we expect to have endogenous ...
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