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Questions tagged [r-squared]

The coefficient of determination, usually symbolized by $R^2$, is the proportion of the total response variance explained by a regression model. Can also be used for various pseudo R-squared proposed, for instance for logistic regression (and other models.)

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Model has higher (and closer to 1) $\beta$, but similar $R^2$ and correlation

I have model one which produces prediction $\hat{y_1}$, later I came up with a new model which produces prediction $\hat{y_2}$. I have ground truth $y$. The models are not regression based but they ...
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Can I use a simpler model (small R²) to get more statistically relevant results?

I am new to this kind of stuff. I am currently writing a bachelor thesis that uses data from the European Social Survey (round 7). 4 important questions that I'm using were not answered by every ...
Michael L.'s user avatar
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URGENT: I am building a Linear regression model. Yesterday my R-squared was 0.792. Today, it had dropped to 0.267. I did not change anything. Urgent [closed]

Thank you for your responses. By way of further information, I am using R-Squared because it is recommended for the project I am doing. Below are the 2 files. The one from yesterday with the 0.792 R-...
Sue's user avatar
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Estimating correlation parameter from known value of bivariate normal distribution

I want to estimate the correlation parameter $\rho$ using the following expression taken from this paper (equation 10 on page 17): $$ \hat{s}^2+\hat{\mu}^2=N_2(N^{-1}(\hat{\mu}),N^{-1}(\hat{\mu}), \...
MysteriousBrit's user avatar
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Is it appropriate to use R² on filtering data?

At work, someone has built a dashboard to identify individuals likely to have higher value of the output variable. The approach involves fitting a OLS and measuring the R² value. They attempt to ...
B_fig's user avatar
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1 vote
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Unacceptable results for adj R2

I have a dataset with 19 features. When I ran it with the Lasso algorithm. R2 for test and train was 0.69. But the value of adj r2 for test is 1.28 (above 1), and for train the value is 0.28. What is ...
Erfan Mollai's user avatar
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Higher order moments to evaluate strength of linear relationship between variables

Let $X_1,\dots,X_n$ be real random variables such that $\alpha_1X_1+\dots+\alpha_nX_n=0$ for some unknown $\alpha_1,\dots,\alpha_n$. If $n=2$, one can study the strength of linear relationship by ...
12345's user avatar
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How to improve a model with little dataset? [duplicate]

I have a dataset that has 20 features and 65 samples. I did data scaling. I also did feature selection in different ways. But this is the result. ...
Erfan Mollai's user avatar
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30 views

Adjusted R^2 or Lack of Fit

This might be a basic question, but I'll still ask, as I haven't found any proper conclusions from the forums. I'm fitting my data using the Response Surface methodology. So, ideally, the relation ...
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6 votes
2 answers
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R squared in logistic regression adjusted for number of predictors

For OLS we have an adjusted R squared which adjusts for the number of predictors included in the model. For logistic regression there are some R squared analogues (Tjur’s R squared, McFadden’s R ...
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Sum of squares of xy bigger than sum of squares for x - how can that be?

I followed this tutorial to visualize R squared. First they define the formula to calculate sums of squares: Then they apply the formula to get sums of squares of ...
LulY's user avatar
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Derive the expectation and variance of squared sample correlation: delta-method or else?

I would like to obtain the expectation and variance of the squared Pearson sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a ...
CafféSospeso's user avatar
1 vote
0 answers
26 views

Comparing Adjusted $R^2$ Between Totally Different Models

I'm curious as to what extent adjusted $R^2$ can be used to compare models. If I had two different data sets and completely different models for both data sets, could I say something like the the ...
Michael Jones's user avatar
4 votes
3 answers
124 views

Calculate $R^2$ given estimated coefficients and $N$ only

We have a simple regression equation $y=a+bx$, where $a,b$ were estimated via OLS -- we know these values. Suppose the number of observations $N=25$ is given. Is it true, that we cannot calculate $R^2$...
Vnature's user avatar
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SPSS R^2 for Negative Binomial

I am running a negative binomial regression in SPSS and wondered if there is any way to display R^2 statistics, as would be the case if binary/linear regression was conducted?
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Weighted Adjusted R2

I understand the r2 metric, being 1- (rss /tss) where rss = sum of squared residuals and tss = total sum of squares I understand how to weight this, such as when each row is a population, and some ...
Brad's user avatar
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How can I improve R2 score in my regression model? Predicting House Prices

I have trained some data on a House Pricing dataset. and I'm getting a not-so-bad R-2 score of nearly 0.5 as you can see below: I wanted to ask how can I improve this R-2 Score and get more precise ...
Nima_Ebr's user avatar
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How to evaluate an Earth system model in light of the spatial variability of observed variables?

Context My effort is to evaluate the performance of a physics-based numerical model to determine how well it simulates different state variables of a soil column (1D inside the model). The temporal ...
Alireza Amani's user avatar
9 votes
4 answers
526 views

Is p-value of R-squared and adjusted R-squared a thing?

I'm currently reading a paper which utilises a multiple regression and reports the adjusted $R^2$ with a p-value, and I'm wondering what this p-value refers to. Can you calculate p-values for adjusted ...
mrepic1123's user avatar
1 vote
3 answers
413 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-\...
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Generated regressors: using estimated value and residuals as regressors for another model when R2 is low

Consider three variables, $y, x, z$. Variable $y$ is a linear function of $x$ and $x$ has a 'part' that is driven by $z$ and another that is not. For example, the volume traded of a certain stock ($y$)...
debrah's user avatar
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3 votes
1 answer
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Ordinary Linear Regression with One Independent Variable

I am currently undertaking a project where I aim to explore the relationship between a single independent variable and a dependent variable. I have five questions that are answered on a 5-Point Likert ...
NutellaMonster's user avatar
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1 answer
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Interpret $R^2$ for a long-run equilibrium model (2 stage OLS)

I've built an error correction model using two stage OLS - first an OLS on the cointegrated I(1) variables in levels to get the cointegration coefficients, and then an ARDL in differences with the ...
Jared's user avatar
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1 answer
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How to calculate R-squared after using clogit function in R

I am trying to calculate the R-squared value of a logistic regression model using the clogit function after multiple imputations with mice package in R. Here's the ...
user avatar
1 vote
1 answer
133 views

Correct interpretation of conditional and marginal R squared in mixed effect models

I am currently running models with both random slopes and intercepts and am curious about the correct interpretation of the marginal and conditional $R^2$. From reading into them, I understand the ...
user947548's user avatar
4 votes
2 answers
172 views

Significant variable and very low R-squared [duplicate]

I'm testing if economic growth before an election is correlated with vote percentage in elections. So I have one independent variable in my model. The problem is: my independent variable is ...
Sina Alvandi's user avatar
2 votes
1 answer
39 views

Interpreting the summary() of a lm() linear model in R

I have a multiple linear regression with 4 independent variables. The summary() function returns the following: ...
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1 vote
0 answers
63 views

Equivalent of R-squared in negative binomial regression

In my study, I experiment with fixed and mixed effects negative binomial regression to my data (in R) as the response variable is a count variable. I have read somewhere that unlike in the case of ...
dysko's user avatar
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3 votes
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50 views

How do I analyze the statistical differences between the slopes and r^2 values of the trendlines for more than two groups?

I'm currently a high school senior working on an astronomy research project, and am having trouble determining if there's a special kind of statistical analysis that I need to perform on my data. I'm ...
The Bookwyrm's user avatar
1 vote
0 answers
76 views

Predicted R squared - when is it good enough?

In order to access whether I am overfitting a multilinear model, I have calculated the predicted $R^2$, based on the info found here. My question is, when is a predicted $R^2$ "good enough", ...
Bettina's user avatar
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0 answers
55 views

Is it correct to report R^2 value for simple time series trend analyses?

I am wondering if it makes sense to report an R^2 value for a simple trend analysis. For example, trends in temperature or stream flow over time. I understand that for linear regression R^2 makes ...
Mike Lavender's user avatar
3 votes
1 answer
32 views

Converting Adjusted R²

I just examined the $R^2_\text{adj}$ Formula on Wikipedia and found two ways to calculate the adjusted $R^2$. Firstly as $$R^2_\text{adj}=1-\frac{\frac{SS_\text{res}}{(n-p-1)}}{\frac{SS_\text{tot}}{(n-...
Linus's user avatar
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2 votes
1 answer
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Why Adjusted R^2 falls if I include both individual and time fixed effects?

I have a (probably simple) question on fixed effects estimation. I am trying to do baseline growth regressions of log GDP per capita against a number of covariates and, in line with the literature, I ...
last_resource's user avatar
2 votes
0 answers
95 views

A test of the difference between two r-squared?

According to Olkin and Finn (1995) and Alf and Graf (1999), the variance of the difference in r-squared is $$ var(r_1^2 - r_2^2) = a \phi a^\mathsf{T}, $$ where $a = \begin{bmatrix}2 r_{1} & -2 r_{...
Kniven's user avatar
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1 vote
1 answer
259 views

Adjusted R2 for LSTM

Background: I am working on a problem, where I am making predictions for a time-series data. I am considering two approaches: Use LSTM, predict n samples using recursive strategy (suggested e.g. in ...
Michał Panek's user avatar
7 votes
3 answers
895 views

Low R-squared for binary logistic regression model but all variables are significant

I am currently testing a binary logistic regression model (N=2000), examining the relationship between several independent variables (such as substance use -categorial-, gender-categorial-, self-...
Consuelo M. Viano Tello's user avatar
3 votes
1 answer
75 views

Out-of-sample R square is NEGATIVE [closed]

The "Out-of-sample $R^2$" is defined as: $$ R^2_{OOS} = 1 - \frac{\sum_{t=\tau}^T\left(Y_t - \hat{Y}_{t\vert t-1}\right)^2}{\sum_{t=\tau}^T\left(Y_t - \hat{\mu}_{t\vert t-1}\right)^2} $$ ...
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2 votes
1 answer
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Interpreting linear regression (Do grammar schools increase the attainment gap for disadvantaged pupils?)

On Monday The Education Policy Institute published its annual report on education in England https://epi.org.uk/annual-report-2023/. This focusses on the attainment gap between poorer pupils and their ...
inforightsjames's user avatar
1 vote
1 answer
47 views

MSPE and $R^2_{OOS}$

I've been looking at a paper for a while that I find interesting. It's essentially a comparative analysis where the authors are comparing PCA/PLS to different machine learning methods. The aim is to ...
Nbs610's user avatar
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1 vote
0 answers
35 views

Obtain the R^2 of just the top predictors identified in a LASSO/ L1 penalized regression model

I've developed a model using L1 penalized regression using tidymodels and 10-fold cross-validation, and determined the predictors that explain approximately 87% of the variance in test data. I need ...
Fredrik Nylén's user avatar
1 vote
1 answer
45 views

Significance test of an increase in adjusted R-squared between two models

I found two papers that provide their results showing the significance of an increase in adjusted R-squared between two models statistically, with p-values, to show the improvement after adding a few ...
J.K.'s user avatar
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1 vote
0 answers
41 views

Model fit / Forecast accuracy / Predictors / Explanatory power predictors (panel data)

I have the following data structure: 100 individuals (forecasters) predicted the likelihood of the outcomes of 50 events (binary outcomes, 1 or 0). For each event, each forecaster made two different ...
Marc J. Muller's user avatar
2 votes
2 answers
119 views

$R^2$ - Coefficient of Determination for Test Data

When calculating the $R^2$ value for the coefficient of determination of a linear regression model, it is well known (Wikipedia) that $SS_{Total} = SS_{Explained} + SS_{Residual}$ (1) i.e., $\sum_{i=1}...
STiGMa's user avatar
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3 votes
0 answers
130 views

How can we justfify the assumption of equal scale/variance in the definition of R-squared from Deviances in GLMs?

If we take the R-squared to be the comparison of Deviances between models (the model of interest, the saturated model, and the constant model), we can write it as (see this answer CC BY-SA 4.0): $$R_{...
Firebug's user avatar
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5 votes
1 answer
73 views

When does adding a new predictor not increase $R^2$ in OLS?

So I know that if the new predictor lies in the subspace spanned by the existing predictors, then $R^2$ will not increase. However, I recall reading that this is a sufficient condition, but not a ...
24n8's user avatar
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1 vote
0 answers
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Sample size and power calculations for multiple linear regression looking for an r squared increase [duplicate]

I want to perform a multiple regression, comparing a model with "traditional" risk factors, with a model that has two tested "novel" risk factors. I'm want to make sure that the ...
Mark Davies's user avatar
3 votes
2 answers
106 views

Is there an intuitive explanation for why $R^2 = \hat{\beta_1} * \hat{\alpha_1}$

In simple linear regression with one regressor, if you regress $y$ on $x$, i.e., $\hat{y} = \hat{\beta}_1 x + \hat{\beta}_0$ and $x$ on $y$, i.e., $\hat{x} = \hat{\alpha_1} y + \hat{\alpha_0}$, you ...
user5965026's user avatar
6 votes
2 answers
321 views

Are these two definitions of the coefficient of determination $R^2$ equal?

I want to do multiple linear regression as explained on this Wikipedia site: I am given the following data: $$ yx=(~(y_1,x_{11},\ldots,x_{1p}),\ldots, (y_n,x_{n1},\ldots,x_{np})~) $$ of $n$-many ...
mrpotato's user avatar
8 votes
1 answer
430 views

Histograms and R squared correlation

I have two sets of predictions. One prediction has an R2 = 0.57, the other R2 = 0.51 . Plotting histograms of the predictions shows that the set with R2 = 0.51 looks more accurate as compared to the ...
ggoogle userr's user avatar
0 votes
0 answers
44 views

Is it possibile to reverse engineer a partial R2 squared from a multivariate regression table?

I don't have any data, so I'm trying to extract a partial R-squared for one of the predictors from a linear multiple regression, in order to calculate the sample size for a regression study I would ...
GT87's user avatar
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