Questions tagged [regression]

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

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7 views

How to check if parameters from non-linear curve fits on two datasets are statistically significant?

I have two datasets. They measure a physical response Y (in a certain sample) with increasing concentrations (X) of a certain molecule (dose response). I fit my datasets to a model known as one site ...
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11 views

Can I regress overlapping independent variables?

give cash coupon give non-cash coupon Brand B Item A Item B Non-Brand B Item C Item D give cash coupon ratio= (item A Sales volume + item C Sales volume)/ total sales Brand B sales ratio = (item A ...
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Is there any valid way to compare two lmer models based on two differnt datasets?

I am a Master's student and currently analyzing a 2 datasets with reading times as dependent variables. For the first dataset, I used a blocked presentation of the linguistic and visual stimuli, while ...
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Very high information value - what does it mean?

Hey I used iv function from scorecard package to calculate Information Value of my independent variables. What suprised me is ...
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29 views

How does the slope change when I add a constant to the logarithm in a linear regression?

I have a regression as follows: ln(y + 5) = A + B*ln(x + 5) The addition of the number 5 in both logarithms is done simply because there are negative numbers in both variables, but I would like to ...
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If ε or error rate is normally distributed $N(0, σ^2 )$, why is y also $Y ∼ N(µ, σ^2 )$?

I have the following notes which describe a basic height model: If Y has some distribution with mean µ and variance $σ^2$: E(Y) = µ, Var(Y) = $σ^2$ then this can be written: Y = µ + ε i.e. Data = ...
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Least Squares Etimates of Simple Linear Regression with Three Level Categorical Variable

For a simple linear regression model with a binary categorical variable: $$y_i = \beta_0 + \beta_1 x_i + \epsilon_i.$$ The least squares estimate are: $$\hat{\beta}_0 = \bar{y}_0 \; \text{and} \; \hat{...
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1answer
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What should I do if only 1 covariate violate the proportionality assumption in Cox PH?

Can I still use Cox PH model? or I will have to find a non-PH model? What are the available models that can be used here? Schoenfeld residuals (using ...
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Why getting very high values for MSE/MAE/MAPE when R2 score is very good

I am applying different regression models (RF, Knn, etc) on some well-known datasets (bike sharing, diabetics, etc). The value of R2 is very good. From the R2 score,...
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Estimating Time to failure when there is no failure pattern

Assume I have data from some sensors and the goal is to estimate the failure time, however, some sensors never fail, and the question is what label to assign to those sensors. For example, consider: ...
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Why to put variance around the mean line to the definition of $R^2$? By what is this particular choice dictated?

Suppose we have a linear regression and we calculate $R^2 = 0.81$. That means $81\text %$ less variance around the regression line than mean line, since $R^2 = \frac{\mathrm{Var\ (mean\ line) - Var\ (...
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224 views

Use of expression "statistically significantly predicts" based on in-sample analysis

Suppose one estimates a linear time series model $$ y_t=\beta_0+\beta_1 x_{t-1}+\varepsilon_t $$ and finds that $\hat\beta_1>0$ and the $p$-value associated with $\hat\beta_1$ is lower than the ...
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84 views

Logistic regression Wald statistic

I have to do a logistic regression analysis. I'm attempting to understand which variables I am taking out of a model. I am doing a simple hypothesis test to understand whether I should keep an ...
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1answer
256 views

Fit error-in-variables polynomial regression using mle2 (R)

I need to fit a polynomial regression that accounts for measurement errors. I found out how to do it with a mcmc model (using RJags) and I would like to do it with a Maximum Likelihood Estimator (...
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Interpretation of regression coefficients with multiple categorical predictors

This question has an UPDATE further below added after the answer below. There is a nice answer HERE regarding how to interpret regression coefficients when predictors each consist of two categories in ...
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146 views

Beta regression fitted values

I have a beta regression model in R, have generated predicted (fitted) values based on my data, and plotted lines of those fitted values on a scatter plot of the actual data. I'm most used to GLMMs, ...
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Looking for associations between variables of different years

I am new to statistics so I hope the question has at least some sense, I have a database with 400 firms for which i have observations of multiple variables per year, and I have ten years. Now, I would ...
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regression and causation

In the Chen and Pearl (2013) article there are several critics about econometrics textbooks. Currently I try to understand more about it. In particular the Authors written (pag 4, footnote 5): From ...
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Minimizing $L_1$ norm with underdetermined linear least-squares constraint [duplicate]

I have some complex-valued time-series data, $y \in \mathbb{C}^n$ - a noisy sparse signal (a signal that is sparse in the Fourier domain and additive Gaussian white noise) So, we have $y = A x + \...
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Simple Linear Regression with Three Level Categorical Variable

Let the following regression equation: $$Y_i = \beta_0 + \beta_1 X_i + \epsilon_i,$$ where $X_i$ is a dummy variable. By setting $X_1$, $X_0$, $Y_1$ and $Y_0$ the variables $X$ and $Y$ when $1$ or $0$ ...
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Find cumulant function for structure measure [closed]

I have an exercise about exponential family with structure measure $\nu=m_{[-1,1]}$ being the Lebesgue measure restricted to the interval $[-1,1]$. I have to compute cumulant function $\kappa$ and ...
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Show that the weights in IWLS algorithm are always 1

I have a data for fire insurance with a model with the responce variable Y claim size and there are two potential predictor. I have to fit the linear additive model $$E(log Y_i)=\beta_0+\beta x_{i,grp}...
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384 views

Is a time trend a substitute for first differencing?

I am doing a macroeconomic analysis involving BOP, investment ratio, GDP growth rates, and CPI inflation as dependent variables. My independent variables are other macro variables. When I test for ...
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1answer
176 views

Do I accept or reject the null hypothesis?

M1 : Y ∼ β0 + β1x1 + β2x2 M2 : Y ∼ β0 + β1x1 anova(M1,M2) shows a p-value of 0.0001, so we prefer M1 at significance level 0.05. Would that be correct? I thought that if .0001<.05, I should reject ...
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What type of regression/predictive modelling should I do? ( more like should i learn to approach)

I have a score based outcome column that is based on other variables. For example: MatchStatus1 MatchStatus2 Score 50 50 35 Above is just a simplified version of the datasets where the score was ...
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Analytical expression of a CatBoost regression model in R

When adjusting a multiparametric regression model, an analytical expression that characterizes the fitted model (e.g., in a linear multiparametric regression, the equation is $\hat\beta= \hat\beta_o+\...
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1answer
686 views

Difference between regression between groups vs across all subjects (continuum)?

I'd like to understand this better in terms of drawbacks and suitability. For example, if my data includes investigating differences between 2 patient groups and a control group (3 groups in total), ...
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relationship between expectation of a ratio of random variables and a ratio of expectation of random variables [duplicate]

I know that in general for random variables $X$ and a function $g$ $E[g(X)]\ne g[E(X)]$. I would like to know when the following holds $E_Z\Big[\frac{cov(X,Y|Z)}{var(X|Z)}\Big] = \frac{E_Z[cov(X,Y|Z)]}...
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1answer
24 views

data transformation for regression

I'm trying to perform LASSO regression on a dataset, and the following 2 photos show the histograms of 8 attributes. I'd like to transform them in some way to improve the model. Data transformation is ...
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1answer
677 views

Linear Regression in Python using gradient descent

(cross-posted from data-science StackExchange)(someone recommended that this community is more appropriate for my problem) I am trying to implement a simple multivariate linear regression model ...
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1answer
29 views

estimation method in GAM model

I created a GAM model with semiparametric with parametric and nonparametric covariates. In the parametric regression model there is an estimation method to determine the value of the beta coefficient. ...
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1answer
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Backsolve error with summary.rq on heteroscedastic data

Hello I am having some troubles in R when I try to make a summary of a quantile regression with my data. When I try this: ...
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Variance of a linear estimator

There is a theorem (here, Theorem 3.2.) which says: Let $x_i \sim p_i(\mu_i, \sigma_i^2)$ for $1 \leq i \leq n$ be a set of pairwise uncorrelated random variables. Consider the linear estimator $y_{n,...
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How to determine the best sample size for fitting a linear regression for ranked data?

I have an ordered database of $N$ city sizes (population), I would like to estimate with OLS the following (http://pages.stern.nyu.edu/~xgabaix/papers/rank.pdf Gabaix and Ibragimov, 2011): $$ \ln(i-1/...
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Regression Method for Non-Normal Data [closed]

I'm trying to figure out what is the most appropriate data analysis method for my study. My data distribution is non-normal and I have one independent variable (degree of co-creation) and two ...
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1answer
168 views

Predicting using GLS

I have GLS regression coefficients of the 'best' model from four different islands in my study system. I would like to compare how the 'best' model from island 1 predicts the response variable on ...
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2answers
465 views

Linear regression on Olympic data - How consistent are the effects over time?

I have performed a linear regression to predict Olympic medal count from Population and GDP for year 2008, 2012 and 2016 I have been asked to explain how consistent the effects of Population and GDP ...
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1answer
2k views

Which index is preferred in GAM, "R-sq" or "Deviance explained"?

I use mgcv package in R to build a Generalized Additive Model. When looking at results of (e.g., summary()), there are two ...
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1answer
169 views

Linear regression - confidence interval for expected difference in $Y$ with respect to unknown values of $X$

Suppose I am given all of the necessary parameters about some linear model, but not the data itself. Namely, I am given $\hat{\beta}_1,\hat{\beta_0},\bar X, S_e, r^2$, etc. Also, I know that $X_1,\...
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linear regression/ANOVA with a covariate measured on a different set of objects

CV has helped me many times but it's my first question as I am struggling to find the right type of analysis for my problem. I have a continuous response variable measured in several groups and my aim ...
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4answers
189 views

Show $J(I-H) = 0$

This is in multiple linear regression. Given $m, n \in \mathbb{N}$ and matrices $X \in \mathbb{R}^{m \times (n+1)} (m > n + 1), H = X(X'X)^{-1}X' \in \mathbb{R}^{m\times m}$, the hat matrix, $, I = ...
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1answer
28 views

Simple Linear Regression Question Confusion

By using this site I found the two linear regression models that the question asked. The equations came out to be: $$US=60.495+18.550x$$ $$China =-2.08+18.296x$$ A follow-up question asked me to find &...
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1answer
58 views

Regression stats question

I am currently focusing on developing a way to predict the onset of sexual maturity in lake sturgeon by using the elemental composition in the fin ray. Lake sturgeon spawn later in life (females ...
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2answers
104 views

How to reduce RMS error value in regression analysis & predictions - feature engineering, model selection

There's this dataset containing the metadata of Twitch's top 1,000 streamers of 2020. You can have the details here. I am currently participating in a challenge to predict the values for Followers ...
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1answer
312 views

Factor with only one item from EFA

I did an EFA and I recovered 4 factors but one factor has only one item with a loading of 1.00 and the lowest proportion of variance of all the factors. Further, this factor with a single item is very ...
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How to solve least absolute deviation by simplex method?

Here is the least absolute deviation problem under concerned: $ \underset{\textbf{w}}{\arg\min} L(w)=\sum_{i=1}^{n}|y_{i}-\textbf{w}^T\textbf{x}|$. I know it can be rearranged as LP problem in ...
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27 views

Regression coefficients while minimizing absolute error

I understand that we like working with square error instead of absolute error because it makes the calculus easy. But I was wondering about the parameters of Linear Regression minimized for absolute ...
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1answer
30 views

Difference-in-differences - Binary data

I am working on an exercise using conversion rate data on a travel website. The conversion rate is defined as the number of users in a given time period that make a purchase. There are two groups, A ...
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1answer
946 views

SSR computation for multiple linear regression on book by Douglas

`I am reading the book "Introduction to linear regression analysis" 5th by Douglas. In the chapter 3 for the multiple linear regression for model $y = X\beta+\epsilon$, it computed $SSR = \hat{\beta}'...
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1answer
952 views

Dealing with imbalanced/zero-inflated training examples for regression

I am trying to predict the rainfall in a desert with a regression model. However, as you might expect, most of my training examples have zeroed labels. I have two questions: a. What is an appropriate ...

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