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The coefficient of determination, usually symbolized by $R^2$, is the proportion of the total response variance explained by a regression model.

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What does “regression of predictor onto all of the other predictors” mean?

I encountered a lot of references that talk about R squared but I can't understand what the difference is between the R squared in regression of the response on the predictors and the R squared that ...
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33 views

Proof for the coefficient of partial determination in the multiple regression model

In a multiple regression model with two predictors, the formula for the partial R squared for $Y$ and $X_2$ given $X_1$ is $R_{YX_2|X_1} = [r_{YX_2|X_1}]^2 = \frac{(r_{YX_2}-r_{X_1X_2}r_{YX_1})^2}{(...
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19 views

R2 - contribution of explanatory variables x1, x2 and x3 to the variance of the explained variable y

I wish to look at the contribution of explanatory variables x1, x2 and x3 to the variance of the explained variable y. To summarize the contribution of the explanatory variables alone to the ...
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29 views

Why are conditional and marginal pseudo R^2 the same in this example?

Here is a reproducible example: The problem is that when I calculate Pseudo R^squared for the null model it gives 0.18 to conditional R^2, the variance explained by the random factor is not 0. However ...
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21 views

Pearson and R^2 Correlation between three variables

Get it from someone else but don't quite know how to answer. If $\rho_{X,Z}=0.4$, $\rho_{Y,Z}=0.3$, what is the range of $\rho_{X,Y}$? Here $\rho$ is the Pearson correlation coefficient. We run a ...
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33 views

How do I select right features

I am working on Boston Dataset in which the aim is to predict the MEDV which is median value of owner-occupied homes in $1000s. ...
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1answer
33 views

Mediation, low R^2

I am currently working on my model in which I would like to test mediation effects. In my model following applies Y-company attractiveness X-type of application (digital vs nondigital) and M-...
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29 views

My R-square is high (60%) but many covariates are insignificant (Time series)

In my time series (37 year variable data set) regression where I have used stationary variables (Integrated of order 1) and a lagged ECM term, my $R^2$ is 60%, but only 4 (including lagged ECM term) ...
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2answers
62 views

Why is R squared zero when the best-fit line is horizontal?

Why is it so that the regression line is horizontal to the x-axis when r-squared = 0? I do understand that when r-squared = 1, estimated Y and actual Y are equal.
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29 views

Compute a measure of explained variance for hurdle models in R

I am working with a dataset df which comprises count data count and a number of categorical variables. ...
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13 views

Discussing R-squared of log-log model with a non-technical audience

I have been asked to report on the relationship between two right-skew financial variables using R-squared e.g. "market cap explain ?% of the variance in CEO compensation". The purpose of the ...
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1answer
55 views

Why is individual R-squared higher than overall R-squared?

I ran a ridge regression model on a set of data across 6 groups. As you can see, the overall R-squared is low. Because groups A and B make up the most of the data, I would think the overall R-...
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40 views

What statistics can I use to compare OLS to an ordered probit

I am trying to justify to the use of an ordered probit, my dependent variable is a survey response on a likert scale so is likely ordinal, but I wanted to provide a goodness of fit stat to back up my ...
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40 views

Calculating the Shared Variance from a Correlation Coefficient?

We often square coefficients like the R coefficient in simple/multiple linear regression or standardized factor loadings to get a percentage of variance accounted for by predictor variables. Can the ...
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28 views

OLS R-Squared Drops by 15% When Constant / Intercept is Removed?

I ran an Ordinary Least Squares model and found the constant / intercept is the more significant than all the other features. When constant is included, the R-squared is 45%, when I remove the ...
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24 views

Market modelling in R

Let's say I have data on SalesChannels(A-D), Weekstarts, Products(5 different ones), quantity sold, Price, promoperiod(true/false), Availability in Stores, and ad Spending in TV and Print and I want ...
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22 views

R2 drop in lasso: train vs test

I am using cross-validation to select best alpha(3-fold), and then applying it to test data. I am using sklearn's LassoCV. In-...
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1answer
21 views

Difference between R-Squared and Adjusted R-Squared for one Predictor

I'm currently using R-Squared and adjusted R-Squared to determine goodness of fit of a linear model. Although I understand the difference between the two, I expect that for one predictor, both the R-...
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22 views

How to compare R-squared between two regression models derived from unequal sample sizes?

I estimated the variance in an outcome variable (y) that is explained by a predictor variable (x) after adjusting for the three covariates (c1, c2 and c3). I derived a full model (y~x+c1+c2) and a ...
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31 views

Conditional and marginal R2 with mgcv

I am fitting a beta regression model with random effects using the mgcv pacakge in R. This package only provides an adjusted R-square. Is there any way to also get conditional and marginal R2 values ...
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1answer
44 views

How did R-square get its name? [duplicate]

How did R-square get its name? I understand how its calculated and interpreted, but I do not understand the r and square part of it.
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4answers
313 views

Multiple Regression, good P-value, but Low R2

I am trying to build a model in R to predict Conversion Rate. So, the model below: ...
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85 views

Is $R^2$ useless? [duplicate]

I stumbled on a discussion regarding the usefulness of $R^2$ as a metric. Where $R^2$ is defined as: $$ \frac{\sum (\hat{y} - \bar{\hat{y}})^2 } {\sum(y - \bar{y})^2 }.$$ The criticism is backed by ...
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51 views

What conclusion can I draw from this R square?

http://people.sc.fsu.edu/~jburkardt/datasets/regression/x01.txt The data records the average weight of the brain and body for a number of mammal species. There are 62 rows of data. I have a task to ...
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1answer
23 views

High value of R-squared correlation on behavioral intention while very low value of R-squared correlation on actual use of mobile shopping app

I have been working on antecedents of mobile shopping with UTAUT-2 model combined with the constructs of trust and perceived risk. I am using a sample of international students for my study. I wanted ...
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1answer
58 views

Adding a predictor reduce R squared

Currently, I am doing Poisson models with N=16,000. My study requires me to find $R^2$ for each model (using 'rsq' package). When I add P12, the $R^2$ decreased as shown below. ...
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22 views

Should I lag explanatory variables in regression with apparently strong predictive relationship?

I'm no expert when it comes to statistics (learning though) and I am working on developing a multiple linear regression model in an attempt to forecast sales revenue. I feel like I may have developed ...
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44 views

Comparing log-transformed and non-log transformed models

Suppose I have the following two models fitted with constrained linear least squares: Model 1: $Y = \beta_1X_1 + \ldots + \beta_kX_k + \varepsilon$ Model 2: $\log_{10}(Y) = \beta_1\log_{10}(X_1) + \...
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40 views

pseudo R2 as xgboost objective function

I want to use a custom objective function with xgboost: 1 - (log(y) - log(p)) / (log(y) - log(q)) y = true value, p = my probabilities, q = some other base ...
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27 views

$R^2$ value and associated significance for each predictor in regression

I would like to measure the $R^2$ value for each of the predictors in my regression analysis. I understand that I can either use the $R^2$ change in a hierarchical regression, or I can square the ...
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1answer
27 views

Different formula of coefficient of determination (R-squared)

I saw the below equation given for "Coefficient of determination" in a paper and thought it must be a typo, then I saw it in another paper too. Would anyone know what this is and how it is different ...
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27 views

variable transformation

friends, I want to use regression for prediction purposes with a sample of over 20k. I have the following results for the OLS with adj R-squared of 0.64: my first question is: can I say that the ...
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2answers
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Alternative to using $R^2$ to assign data categories?

A background to my problem: I use survey data on firms, where I want to measure the relationship between a binary variable (perceived growth barriers) and firm size. However, I cannot treat "firm size"...
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4answers
164 views

Is R-squared truly an invalid metric for non-linear models?

I have read that R-squared is invalid for non-linear models, because the relationship that SSR + SSE = SSTotal no longer holds. Can somebody explain why this is true? SSR and SSE are just the ...
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17 views

Comparing overall and conditional models

Let's say I have two regression models with 5 variables, one that is for all observations, and one that only includes values when the temperature is higher than 75 degrees. As an example I have this: ...
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154 views

R-squared for glmmTMB with beta distribution and logit link

I'm looking for a method or function for computing R² for glmmTMB models with a beta distribution and a logit link. I am interested in a ratio (%) response in a repeated measures design. I looked ...
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1answer
33 views

Find contribution of various features/input variables to the variance of the dependent variable / Attribute variance of dependent variable to features

I am working on this problem where I have 20 odd features (input variables) and two dependent variables. The objective is to find the variance structure of one of the dependent variables. More ...
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Adjusted R-squared for tree-based models

How can I use an evaluation metric like adjusted R-squared to evaluate tree-based models? It's not clear to me, since adjusted R-squared accounts for the number of predictors included in a given model,...
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2answers
56 views

Plus/Minus Model accuracy from $R^2$

I completed a linear regression for a model I was working on, and obtained that the $R^2$ value was $R^2 = 0.801$. Can one assess a $\pm$ error from this value for future predictions? I.e., if I now ...
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1answer
36 views

How to interpret these R regression coefficient results? [closed]

I'm really super new to R and am doing the most basic stuff for a beginner's statistics class. I've been staring at this question for a while and can't work out what I'm meant to do. Here's the ...
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2answers
36 views

Is it permissible to aggregate results from multiple cross sectional regressions?

Lets consider the following approach: (1) We estimate a simple linear regression model y = b0 + b1*x + error. The input data in our model estimation shall be: y = 1 month stock returns (cross ...
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1answer
23 views

Varying R-squared value

I'm new to machine learning, I have been doing a multiple linear regression (with 3 features,1 target). I'm using train_test_split module from sklearn to split the data into training and test data. ...
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1answer
111 views

Should R squared value be changing when both predictions and actual values are transformed together?

I have a regression prediction task where my outcome variable is right skewed. I performed a log transformation of the outcome variable and put it in a linear regression model. I assessed the R ...
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0answers
57 views

How to compare transformed and untransformed linear models?

I have a linear model which doesn't have any particular issues with its assumptions (diagnostics plots look well). However it has a slighly skewed response (skewness approx. 0.5) and few skew ...
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2answers
44 views

How to simulate the outcome in a simple linear regression given X and R-squared?

Suppose that we have a fixed $R^2$ and one predictor $X$, sample size = $n$. How can we simulate an outcome variable that follows a normal distribution with $\epsilon \sim N(0,1)$ so that in a simple ...
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1answer
741 views

Which is better: r-squared or adjusted r-squared?

I just started to learn about the following statistical measures, r-squared and adjusted r-squared and was wondering why can't we use adjusted r-squared for every regression model considering the ...
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1answer
195 views

R-squared in linear probability model

Is R-squared a relevant measure to evaluate goodness of fit in linear probability model? I suspect there may be an issue given that the model predicts probabilities (i.e. between 0 and 1, and even ...
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0answers
16 views

Averaging R2 between different sized test sets

I'm testing a model using different tests sets. In fact, I'm mimicking cross validation but since my data is correlated I used data from individual years as test sets instead of assigning my data ...
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1answer
66 views

why does adding new variables to a regression model keep R squared unchanged

I have linear regression model clustered on both firm and data. when I add two more variables to the regression model, one of the newly added variable is significant, but the R squared remains the ...
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1answer
247 views

Multiple Correlation Coefficient with three or more independent variables

The formula for the multiple coefficient of correlation of two independent variables ($x_1$ and $x_2$) and an dependent variables ($y$) is this: What is the formula for three ($x_1$, $x_2$, $x_3$) or ...