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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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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, ...
Myungjin Hyun's user avatar
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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 ...
SekiTake's user avatar
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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'...
librus's user avatar
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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 ...
Paulo The Cab Driver's user avatar
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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? ...
Derek Jones's user avatar
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Is this an example of Simpsons Paradox in a regression with two independent variables?

I am doing the following regression: $$\text{home_price} \sim \alpha + \beta_1 \cdot \text{bathrooms} + \beta_1 \cdot \text{sqft_living}$$ I get the following results: $$\text{home_price}= -17581.822 ...
user2330624's user avatar
3 votes
1 answer
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What is the connection between lift and logistic regression?

I have noticed that there is an interesting connection between two (apparently different) measures. I am under a market basket analysis framework (aka frequent itemset mining, both are common names) , ...
Oscar Flores's user avatar
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1 answer
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Apartment Price dataset: Why are the coefficient signs different but not when conditioned on other values? [duplicate]

This question is similar to an open ended question a colleague asked... Given the following regression: $$\text{home_price} \sim \alpha + \beta_1 \cdot \text{sqft_living} + \beta_2 \cdot \text{...
user2330624's user avatar
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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 ...
Derek Jones's user avatar
1 vote
1 answer
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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: ...
raffaello.sanzio's user avatar
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What is the likelihood of a regression? [duplicate]

I understand linear regressions themselves have likelihoods. Is this simply the likelihood of the error? I thought it was the likelihood of the data for Y given X. In other words, $Lik(Y$~$X)=Lik(Y|...
A Friendly Fish's user avatar
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logistic regression coefficient interpretation - with / without interaction [duplicate]

In this model: ...
user654345678's user avatar
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0 answers
21 views

Interpreting log transformed variables in a regression [duplicate]

I am very confused about the interpretation of log transformed variables in a regression. For example, I have a log-level model with a B0=4.95 and B1=-1.07. So my model would be log(y)=4.95 - 1.07X. ...
mblume's user avatar
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Can Multiple Regression Output (coefficients, ratios, etc.) Be Given a Predictive Interpretation?

Generally speaking, regression output can be given a causal interpretation for typically one variable in the model (that is under the assumption of no unobserved confounding and this is not to speak ...
Brian Lookabaugh's user avatar
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Binary logistic regression: why do these two coefficients have opposing signs when they are indicators of the same outcome?

I hope someone can help me understand why this is happening. Reproducible example in R: ...
Reader 123's user avatar
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what are the consequences of re-encoding with 0 or -1?

I have a dataset of information about students and the last column is the target variable which is the final note. My goal is to make logistic regression and ordinal regression models to see whether ...
Moez Daly's user avatar
1 vote
1 answer
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Understanding linear regression output for ordinal independent variable

I'm running a linear regression on JASP with an ordinal independent variable (education level with levels 1, 2, 3) and I am wondering what is meant when the coefficient table includes different ...
elangston's user avatar
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1 answer
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Coefficient in Regression Analysis

I am running regression on two variables (independent and dependent). If the results show p-value > 0.05, it is not statistically significant. Does this mean we reject the coefficient as well? If ...
Bestmiler's user avatar
2 votes
1 answer
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Event study regression specification: interacting covariates with leads and lags

I want to create an event study regression specification for the following: $$ \ln(y_{ijt}) = \gamma \ln (x_{jt}) + \tau \ln(p_{t}) + \lambda \ln(x_{jt}) * \ln(\mbox{p}_{t}) + \epsilon_{ijt}. $$ I am ...
specfunctor's user avatar
1 vote
1 answer
50 views

Several regressions with different dependent variables

I'm working on a project where I want to compare two groups of participants based on several different metrics. Right now, I'm estimating separate regressions with different dependent variables (i.e. ...
John's user avatar
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1 vote
1 answer
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Working out/Derivation of Standard Error of Coefficient in Logistic Regression

Let's keep it simple and just go with Simple Logistic Regression where there is only 1 continuous independent variable. I.e. Log(P/1-P)=B0 + B1X1 What is the working out to derive the standard error ...
Mandem's user avatar
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Mathematical formula for interaction term in multiple regression with two predictors [duplicate]

I am trying to understand the math behind the coefficients in a multiple regression with two predictors and their interaction. I know that this can be done in matrix notation OR directly in any ...
alice123456's user avatar
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1 answer
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Manual specification of knots vs bs() for Piecewise regression

I am learning how to specify and plot piecewise regressions and have encountered a confusing situation. Namely, I have specified the knot for a piecewise regression using 2 methods: (1) manual and (2) ...
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Is an interaction term essentially interpreted as just another independent variable?

I'm trying to understand if the linear regression model interprets an interaction term as just another independent variable? This is the formula for linear regression with 2 independent variables ...
Mandem's user avatar
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4 votes
3 answers
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Cohen's d or Cohen's d-like effect size estimate for regression slope?

Can Cohen's d be calculated for the linear regression coefficient associated with a continuous predictor? If so, what is the formula? I found one question asking this already, with an answer ...
Evan's user avatar
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2 votes
1 answer
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Simple Regression Coefficient Formula for Categorical Variable?

For an indepdent numerical variable X the B1 coefficient is COV(X,Y)/Var(X). Since Categorical Variables don't have things like Means(from which things like COV and VAR are derived) how would it work ...
Mandem's user avatar
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1 answer
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Comparing regression coefficients across non-nested SEM models (Lavaan)

I had question about SEM in Lavaan which I cannot seem to get a grip on through any google forums or my old lecture slides... I wish to explain cognition using several variables (CR1/CR2, which stand ...
SEMdummy's user avatar
1 vote
2 answers
101 views

Comparing two models from the "fish" dataset

Data I'm constructing linear models using the fish dataset from this data with the following variables: res_var: response ...
OzkanGelincik's user avatar
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1 answer
104 views

Multiple Regression Coefficient Derivation in Non-Matrix Form [duplicate]

I've come across some equations on regression coefficients for multiple linear regression(Fig.1 and Fig.2) with 2 independent variables and was wondering how they were derived. FIG.1 FIG.2 I'm aware ...
Mandem's user avatar
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How does tab_model() in sjPlot report std. beta for models with log terms?

I'm using the "std2" option for tab_model(), which according to the documentation follows "Gelman's (2008) suggestion, rescaling the estimates by dividing them by two standard ...
abruh's user avatar
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4 votes
2 answers
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Interpretation of dummy-coded variable

I have a dummy variable, with 1 meaning the years in which an historical event took place and 0 meaning the years in which it didn't take place. I used 0 as the reference category. When the regression ...
brian's user avatar
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3 answers
290 views

Why define coefficient of determination as 1 - RSS/TSS?

Based on wiki, the definition of coefficient of determination is defined as $1 - RSS/TSS$, where RSS is the residual sum of squares ($\sum(y-\hat{y})^2$) and TSS is the total sum of squares ($\sum(y-\...
chichi's user avatar
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0 answers
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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....
user3919790's user avatar
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Lasso Regression Problem [duplicate]

$\operatorname*{argmin}_\beta\{\|y-X\beta\|^2 + \lambda\|\beta\|_1$, where $X$ is orthonormal. $\beta \in \mathbb R^d$. $X = [x_1,\ldots,x_n]^T$ and $y=(y_1,\ldots,y_n)^T \in \mathbb R^n$. $X^TX=I_{d\...
Harry Lofi's user avatar
5 votes
3 answers
435 views

Do autocorrelated residuals cause OLS coefficients to be biased?

I see different answers everywhere. Intuitively, I would think if residuals are autocorrelated then there is some information that you are not incorporating into your model and is a sign of a biased ...
user2330624's user avatar
5 votes
1 answer
97 views

Linear Model Equivalence regarding Latent Variables

While reading a paper (surprises in high-dimensional ridgeless least squares interpolation), I was stuck to a part of a section (5.4, page 16~18). Consider coviariates $x_i = (x_{i,1},\dots,x_{i,p}) \...
jason 1's user avatar
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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 ...
Yuuya's user avatar
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1 answer
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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 ...
Frank Swanton's user avatar
1 vote
1 answer
84 views

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, ...
Mikhail's user avatar
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4 votes
1 answer
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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, ...
jack kelly's user avatar
2 votes
1 answer
53 views

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 ...
Jingyang Zhang's user avatar
0 votes
1 answer
43 views

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 ...
blue_earth's user avatar
0 votes
1 answer
97 views

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 ...
Mikhail's user avatar
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0 answers
60 views

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 ...
Arav's user avatar
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4 votes
2 answers
81 views

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 ...
amineh's user avatar
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1 vote
0 answers
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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 ...
Sara's user avatar
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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 ...
user402101's user avatar
1 vote
0 answers
21 views

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 ...
Athaeneus's user avatar
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4 votes
2 answers
282 views

Handling non-significant beta coefficients

In our thesis, we have asked participants (consumers) about how several independent factors/variables (like price) affect the willingness to buy (the dependent factor). We have used the beta ...
Carl Berglund's user avatar
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0 answers
43 views

Variable selection based on PLS

What is the logical way to select the variables from PLS? Does choosing the feature from loadings and loading weights make sense? Loadings... Loading weights... Regression coefficients... Variable ...
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