Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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19 views

What statistical test should I use with count data?

In my experiment, participants are shown 4 images (A, B, C, D) that they have to rate on a 5 point scale. So my data looks like this: particpant1: A 5, B 3, C 3, D 1 p2: A 4, B 3, C 2, D 4 p3: A 4, B ...
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Multiple Regression Extreme Values in all Covariates

In multiple regression: If we have a data set with covariates having extreme values, the max value of the covariate is around 10 to 14 times the mean value of that covariate. This is occurring for all ...
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1answer
17 views

Reason for time fixed effects in regression

I'm currently doing an empirical analysis on the influence of an aging population on house prices. I have panel data with yearly observations for all 51 states of America for the years 1996-2019. When ...
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9 views

Standard Error of Estimate

In a simple regression analysis based on the least squares regression equation, I got the predicted value of 7.15 for the predictor value of 11. The sample size is 35. I computed the Standard Error of ...
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12 views

Diff-in-Diff: Time-varying treatment and Treatment affects Outcome

I would like help with the following question. I have searched the internet and I can't come to a definite DiD setup. I appreciate any help or thoughts that you might want to share. My setting/dataset ...
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38 views

How to derive EM algorithm for this regression model?

Given that $y = Xw + \epsilon$ where $y $ is $n\times 1 $, $w$ is $p\times 1$ vector and $X$ is $n \times p$ matrix of inputs $x_1, x_2, ... x_n$ each of which are $p\times 1$ vectors. Further $\...
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How do you change log-linear transformed prediction interval values for a regression back to original scale in r?

I have a simple regression model where I needed to log-transform the dependent variable because the model residuals were non-normal. Now my model is ok in that respect. So, I ran the model. But, ...
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Interpreting the following multiple linear regression model

I'm having difficulties trying to interpret the coefficients of my linear model. Background: lm(encounter_rates ~ year + pland_changes + regions) I've run a ...
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For a linear prediction model, does selective sampling to encompass the range of independent variable minimize number of samples required?

Suppose we have high confidence that $y=mx+c$ is a good model for a physical process based on previous experiments, and $m$ and $c$ vary with local/temporal conditions. We wish to predict $y$ for new ...
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How to interpret the marginal effects (MEM) of binary variables in R?

My model is binary logit regression and the dependent variable is default (whether a loan would be defaulted, if it was, it is given a value of 1). I ran logitmfx (...
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How do you prove that centering predictors doesn't affect the non-intercept terms in $\hat{\beta}$?

It's intuitive, but I'm having a hard time proving it mathematically. The claim is \begin{align} \hat{\beta} = (X^TX)^{-1}X^Ty = (L^TL)^{-1}L^Ty \end{align} where $L$ is $X$ but with all columns, ...
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For counting participants should I use linear regression or poisson regression?

I would be very grateful if anyone with a stats background might sanity checks whether my approach is correct. I am recording the prescribing of a particular drug over time. Ultimately, beyond the ...
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R's lm(), get x when y is known [duplicate]

Here is some data and a logarithmic model: df <- data.frame( x = 1:8, y = c(7.5,6,5.2,4.3,3.9,3.4,3.1,2.9) ) model <- lm(y ~ log(x), data = df) I am ...
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Panel Data Regression: Confusion about Random Effects Model

I have a panel data set covering 42 countries over a period of 14 years. My data set contains country sustainability scores (combined, economic, environmental, social) as well as the mean firm-level ...
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Interpreting (partially) overlapping time dummies

In a time series linear regression, what is the interpretation dummies that identifies two partially overlapping periods? To be clearer, I have a time series regression and my sample period goes from ...
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1answer
36 views

Applying multiple test correction for stock prices

I want to work out if there are any associations between the stock prices within two indexes, S&P 500 and FTSE 100. I plan to perform a simple regression for each pair of stocks. I've read that I ...
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20 views

Dealing with Skewed Normality for the Standardized Residuals to meet Normality Assumption (OLS)

I am required to build a OLS model. Currently, My model of log(response) against a number of predictors have fulfilled homogeneity assumption (constant variance) and low multicollinearity (based on ...
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1answer
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What are the preliminary analysis before running a logistic regression?

I have a dichotomous variable which represents if a student is accepted or not in a University. In order to do this I have about 60 variables (information of the students: gender, age, etc; their ...
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1answer
8 views

Interpretation of linear regression with covariates. Categorical variable has 3 levels

My independent variable is genotype, which has 3 levels (wild type, heterozygote and homozygote) My dependent variable is calcium concentration, which is a continuous variable. I first run a one-way ...
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1answer
20 views

How do I interpret Box-Cox-transformed linear model outputs in R? [closed]

I have a data set that was skewed, and I experimented with transformations to reduce the skew. I found a Box-Cox transformation reduced the skewness the most. It looks like this: ...
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21 views

How to model exponential time decay component with linear regression?

I was wondering if there was a way to run a regression on a formula that is not exactly a straightforward $Y=\beta X + \varepsilon$ Essentially what I have is a bunch of features $x_i$, with an ...
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10 views

Different p-values in Repeated Measures Poisson Regression and Type3 Analysis

I am working on data for 10 years that has counts of hospitalization and population size by countries. I also have other covariates that I need to control for. Using GEE Poisson regression, and ...
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37 views

Do we assume that the regressors are uncorrelated with the unobserved error $\epsilon$ for least squares?

I recall seeing sources in the past state that the Gauss-Markov assumptions assume that the regressors are uncorrelated with $\epsilon$ in order to make $E[\hat{\beta}] = \beta$. But is this ...
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How would you transform a percentage dependent variable to fit a logistic regression? [duplicate]

I have a outcome variable that is a percentage (proportion). According to this, I should probably use a logistic regression: What are the issues with using percentage outcome in linear regression? My ...
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29 views

If extrapolation is bad then how is forecasting methods statistically relevant

There are lot of articles out there that talks about why extrapolation is a bad thing to do. My question is if the above is true , how are forecasting methods like forecasting the trend based on some ...
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15 views

Chi-squared test for regression residuals

Per Cosma Shalizi, here, equation 11.2, I understood the chi-squared test for regression residuals to involve calculating: $$\sum_{i=1}^{n} \frac{(y_i - f(x_i, \theta))^2}{\sigma_i^2}$$ which will ...
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1answer
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Durbin vs. Breusch-Godfrey test for autocorrelation: which is better?

I'm being asked to justify why I use either the Durbin's alternative test for Serial Correlation or the Breusch-Godfrey test. It seems that both are relatively competent tests however there is little ...
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1answer
21 views

Developing Risk Scores from Cox Regression model?

A simple question on the development of risk prediction models from Cox regressions. Suppose, as an example, that I want to create a risk score for 1-year mortality in patients with cardiovascular ...
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9 views

Using Logistic regression in record linkage

I am curious as to how logistic regression handles string variables in a training matched data set I am aware many use Logistic regression to categorize data that includes the process of matching ...
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5 views

Comparing mixed effect models using deviance statistics - comparing model 1 vs. 4 instead of 1 vs. 2, 2 vs. 3, etc

I am relatively inexperienced with mixed effect models and trying to build a model to fit my outcome of interest. I have read and followed along with chapter 4 of Singer & Willet (2003), as well ...
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25 views

Hypothesis testing with time autocorrelated data

I have a dataset such as the following: ...
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10 views

Testing reliability of regression coefficients

If I run a logit/linear regression for the purpose of measuring marginal effects and estimating the causal impact of a specific independent variable on the dependent variable, is there a reliable way ...
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What-If Scenario Regression Modelling

I'm pondering a scenario involving some insurance data but this could be relevant in many fields. The idea is that I have a total count of some event. Let's imagine this count is the # of attorney ...
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Formulating the null hypothesis when the depended variable is a ratio involving the independent variable

I face the following simple regression model: $$ \widehat{rdexp}=\hat{\beta}_{0}+\hat{\beta}_{1}log(sales) $$ where $$ \widehat{rdexp}=\frac{RD}{sales} $$ and $RD$ is some positive number. I am having ...
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25 views

Interaction of Gender and Income categorical variable

I ran the following model, with exam scores in science as my outcome variable, and parental income group divided into 5 groups and a binary gender variable with the results below: ...
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8 views

Given a target # for the end of year, how can I calculate the probability of reaching the target given my pace at any given moment in time?

Let's say I have a target to reach 100M widgets by the end of the year. I need to monitor in real-time the probability of hitting that target. "What's the probability we'll make it today?" ...
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9 views

How to analyze dataset for an ecological study? [duplicate]

My independent variable is health care system (continuous and non normally distributed) and dependent variable are health outcomes(continuous) . This data is available for 40 cities. How should I ...
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14 views

forecasting sales using dummy variables for seasonality by week and holiday lags in excel

Hi I'm trying to create a forecast in excel that uses dummy variables for the weeks to create seasonality as well as dummy variables for certain holidays. I created 52 weeks and then had them be 1 if ...
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Forward selection metrics

When using forward selection for multiple linear regression, I've seen several metrics: (1) Using MSE - at each step, try adding each variable one at a time, see which variable reduces the MSE the ...
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5 views

Box-Cox back transformation with indicator in linear regression

I have a fitted linear regression of a Box-Cox transformed dependent variable, using an indicator variable as one of the two predictors : $$ g(Q, \lambda) = \hat{\beta_0} + \hat{\beta_1}P+ \hat{\...
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Regression modeling [closed]

I am working on a regression analysis to validate relations between investment/sales. First, I tried GLM and then Polynomial Regression Model. In both results, the conditions of regression model(...
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1answer
19 views

Time length for causal inference experiments

Let's say that I want to run a causal inference experiment, that is an experiment on historical data for an intervention that we were not able to perform a randomized controlled trial for. In the case ...
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1answer
17 views

Comparing significant differences between a linear regression on same data coded as ordinal or interval

I'm running linear regressions in R on some survey data that was delivered as Likert-scales. In R, I can code them as factors (to represent them as ordinal data) or numeric (to represent them as ...
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25 views

What is the recommend function for Ridge regression [duplicate]

The following question is an answer for why lm.ridge and glmnet results are different and how to solve that. My question is ...
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Nadaraya-Watson regression alternative for binary outcome

I am looking for pointers as to what would be the non-parametric equivalent of Nadaraya-Watson regression when modelling a binary outcome. I have been googling and ended up with Generalized Additive ...
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11 views

Improving accuracy of regression equation by using another equation [closed]

Is it possible to improve the accuracy of the regression equation by using another equation? Let me make a point more clear. Suppose we measure depth (H) and density of rocks ($ \rho $) in a certain ...
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Why should the difference between the adjusted R-square and predicted R-squared be less than 0.2? [closed]

I am building a regression model using RSM-CCD method in Design-Expert software. All the statistical parameters are OK. The difference between the adjusted R-square and predicted R-squared is less ...
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How to test the null hypothesis that two linear regression lines have the same Y value for a particular X value?

I am using ancova to test if two linear regression models are the same and it works great. I am following this tutorial: http://www.biostathandbook.com/ancova.html and I apply it in R with this ...
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Multiple linear regression while using only the explanatory variables with largest correlation (by magnitude)

I'm looking at the analysis for the red wine dataset on https://datauab.github.io/red_wine_quality/. This is a Jupyter note book, and if you go down to about In [9]:...
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Is this log-log plot that is produced in SPSS sufficient to PH?

How do you graphically test proportional hazard assumption in Cox regression in SPSS? Should I put the variable in the "block" or "Strata" in SPSS? This log-log plot is produced in ...

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