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

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How to determine the sign of R underlying R-squared?

So we know that: $$ R^{2}=\frac{SSR}{SSTO} $$ If we want to know the value of $R$, how do we know what the proper sign is?
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14 views

Relation between R2 and the covariate correlation matrix (multidimensional case)

Following the post : Relation between $R^2$ and the covariate correlation matrix Does it exist a formula for N>3 when N is the number of covariates ? Many thanks
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34 views

Relation between $R^2$ and the covariate correlation matrix

I'm quite new to Statistics and I'm facing a problem. Is there any relation between $R^2$ and the correlation matrix of the covariates? A short example is (case with 2 covariates) : A7 ~ A1 + A2 ...
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22 views

Adjusted R-squared: number of terms or independent variables?

When applying a multiple linear regression, does the adjusted R-squared value depend on the number of independent variables in the model or the number of terms? Specifically, I'm concerned that adding ...
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24 views

Explanation of the formula for calculating adjusted R squared of linear model

The classcial formula for calculating the adjusted $R^2$ of a linear model is as follows: $$R^2_{adj} = 1 - ((n-1)/(n-p-1)) \times (1-R^2)$$ where $n$ is the sample size and $p$ is the number of ...
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14 views

ANOVA: Why residuals are uncorrelated with group means?

If I want to compare group means $\bar Y_1, \bar Y_2, \dots, \bar Y_L$ of a numeric variable $Y$ across the $L$ levels $x_1, \dots, x_L$ of a categorical variable $X$ in terms of R-squared, then I can ...
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60 views

Large sample with low R² and high RMSE; or Small aggregated sample with high R² and low RMSE?

I have 45 independent variables and 50 (US) state controls. I have a sample of about 100,000 county-level observations. With this sample, I run my regression (observations weighted by population) and ...
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32 views

Goodness of fit between actual values and non-linear model

I was wanting to get a goodness of fit similar to R^2 for a model I'm evaluating. The output of the model is one of 8 numbers based on environmental characteristics. This is not a linear model, so ...
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30 views

Which one to compromise between MAPE and Adj R square in multiple regression

I'm trying to forecast sales of a product based on the other variables like Competitor sales, Fuel Price and CPI (Consumer Price Index). The below given output (based on 1 to 44 months) gives me the ...
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16 views

log transformation decreased model fit?

I just wondered why logged income (independent variable) decreased my model fit for OLS regression. My income distribution is skewed to the right and I am trying to transform the data. I separately ...
0
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1answer
34 views

comparing $R^2$ across two data sets

I have a set of covariates that characterize the type of experience a worker has (industry experience, general management experience, etc), and I am regressing compensation on these measures of ...
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25 views

Comparing R2 between Different Samples

Good Evening All, I'm looking to directly compare the variance explained by the same regression model (same IVs, DV) between two different samples. The way I'm conceptualizing it is like Fisher's ...
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1answer
22 views

Exponential equation fitting

I have two variables: y= head (0.5,0.10,0.15,0.25,0.34) and x= instar (1, 2, 3, 4,5). How fitting my data on exponential growth in R? I need p-value fitting, F (is possible?), R^2 and degree freedom. ...
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1answer
54 views

Show that $\sqrt{ESS} \leq \sqrt{ESS_{A}}+\sqrt{ESS_{\bar{A}}}$ where ESS=Explained sum of squares

Suppose we have a dependent variable $Y$ with mean zero and set of regressors which we divide into two sets, $A$ and $\bar{A}$. Let $ESS$ denote the explained sum of squares (ESS) from regressing $Y$ ...
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47 views

Comparing two R square. Are they statistically different?

What is a correct way to compare two $R^2$? I have dependent variable $Y$ and $X_1, X_2, X_3, X_4.$ I run two regression models, namely with $X_1$, $X_2$ and $X_3$, $X_4$. Both $R^2$ values are close. ...
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26 views

r linear regression mistakenly giving me r2 value of 1 [duplicate]

I'm using R to create a linear regression model from survey data about public sentiment for a new technology. I am encountering a problem where the addition of a new explanatory variable raises the ...
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1answer
627 views

Regressions. Why a and b explains more than a+b?

So I have sample of 1987 observations. I'm checking how accounting measures can explain stock returns. If I do a regression of stock returns on CFO (cash flow) and Accruals, I get $R^2= 0.075$. But if ...
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21 views

How to calculate PRESS and $R^2_{predicted}$ in Stata automatically [migrated]

So I have two models and I want to calculate these statistics. Is there any package to calculate them in Stata? PRESS statistic (wiki) And, if I am not mistaken. $$ R^2_{predicted} = 1 - ...
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28 views

Assesing the explanatory power of predictors, interactions and combination of terms

I have a model with 5 basic predictors and all interactions between the predictors themselves. Something like (I'm simplifying here, in reality I have many more variables): ...
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1answer
83 views

Is there any difference between $r^2$ and $R^2$?

The correlation coefficient is usually written with a capital $R$ but sometimes not. I wonder if there really is a difference between $r^2$ and $R^2$? Can $r$ mean something other than a correlation ...
0
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1answer
34 views

Why does adding more terms into a linear model always increase the r-squared value?

Many statistics textbooks state that adding more terms into a linear model always reduces the sum of squares and in turn increases the r-squared value. This has led to the use of the adjusted ...
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1answer
38 views

Do you think I should apply a transformation to my independent variables?

I have done a simple linear regression on my two standardized independent variables and standardized dpendent variable. In the residual plot there is a distinct quadratic pattern left after the two ...
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1answer
57 views

What if a transformed variable yields more normal and less heteroskedastic residuals but lower $R^2$?

I am trying to decide whether to use a square root transformed dependent variable in multiple linear regression. Transforming $y$ leads to more normally distributed residuals and also to less ...
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306 views

Interesting derivation of R squared

Years ago I found this identity through experimentation playing with data and transformations. After explaining it to my statistics professor he came in the next class with a one-page proof using ...
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312 views

What is the distribution of $R^2$ in linear regression under the null hypothesis? Why is its mode not at zero when $k>3$?

What is the distribution of the coefficient of determination, or R squared, $R^2$, in linear univariate multiple regression under the null hypothesis $H_0:\beta=0$? How does it depend on the number ...
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63 views

What measure of effect size in ANOVA has mode at zero under the null (unlike $\eta^2$ that does not)?

I encountered a weird effect when computing eta squared in ANOVA. Here is a short simulation to demonstrate it. I simulate $k$ groups with $n=10$ each, with all values drawn from standard normal ...
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1answer
100 views

Model uncertainty (model averaging) and R-Squared (R2)

Is it possible to calculate r-squared for an "average model"? Lets say I have 4 different response variables that I want to model to a set (or subset) of 4 independent variables. I'd then like to ...
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1answer
115 views

Partitioning explained variance to fixed effects by comparing r squared (R2) between linear mixed models

Lets say I have 2 linear mixed models. One is simply a subset of the other. The first contains terms for 2 fixed effects and a random intercept. One of the fixed effects, "x1" I know, a priori, ...
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1answer
90 views

A way to compute significance of R-squared change across models in a path model, or specifically lavaan?

I have a straightforward path model with a single endogenous variable and multiple observed predictors - in other words, a regression. (I'm doing it as a path model to be able to easily test ...
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31 views

McFadden's Pseudo R² - Comparability across different datasets

Several authors in applied research papers claim that McFadden's Pseudo R² cannot be used for comparing models that are based on different datasets. I have searched some ...
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31 views

Why is it possible that the White test and the special case of the White test can give different values of $R^2$

In the textbook I am using (Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge, 5e), it is implied that the $R^2$ from the regression of residual-squared on all independent ...
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1answer
46 views

Which regression model to choose? [duplicate]

I have two models, one lm(y ~ x1 + x2 + 0) which gives me a close to 0.90 something $R^2$ and another model lm(y ~ x1 + x2) ...
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37 views

optim() for multi variable returns values on the boundary in R

I would like to use function optim() in R to minimise the target function. The two optimised parameters both have constrains. I have created a test sampel data. ...
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26 views

Excluding Outliers and Influential Observations ($R^2$ and AIC/BIC)

I am working on a cross-sectional data set relating mortgage payments to debt-income ratios. I have some extreme outliers and experimented with excluding them from the model (some 30 observations of a ...
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232 views

Is there an elegant/insightful way to understand this linear regression identity for multiple $R^2$?

In linear regression I have come across a delightful result that if we fit the model $$E[Y] = \beta_1 X_1 + \beta_2 X_2 + c,$$ then, if we standardize and centre the $Y$, $X_1$ and $X_2$ data, ...
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56 views

Measure of explained variance for Poisson GLM (log-link function)

I am looking for an appropriate measure of the "explained variance" of a Poisson GLM (using a log-link function). I have found a number of different resources (both on this site and elsewhere) that ...
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25 views

Regression variable conversion

There is a question that I cannot solve. They may be solved by variance and covariance but I couldn't. So I thought there should be another way to solve. Question: A researcher has a sample of 43 ...
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1answer
46 views

Good Literature about Problems with R squared

A question from a newbie. Recently, I was told that R squared or adjusted R squared can not used as a criteria to select a good regression model (model selection) due to, for example, overfitting . I ...
3
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1answer
141 views

Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$

I am interested in the geometric meaning of the multiple correlation $R$ and coefficient of determination $R^2$ in the regression $y_i = \beta_1 + \beta_2 x_{2,i} + \dots + \beta_k x_{k,i} + ...
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87 views

R-squared for elastic net

How is the R-squared calculated for an elastic net? How about LASSO? Should be different from OLS, or not? Edit: The main problem is as follows: We have all kinds of fruits like $f_1, f_2, ..., fn$ ...
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48 views

R-squared adj. in multiple linear regression of 75% = high correlation?

I have a response column and a column of categorical predictors (around 25 categories) and I get with minitab linear regression analysis a R-sqr adjusted of 75%. ...
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34 views

How do we calculate the $R^2$ statistic for a mixed model with one random intercept only?

I have read in previous posts that for mixed models with random intercepts only, the statistic for $R^2$ is $$R^2 = \frac{\text{V of intercept only model} − \text{V of full model}}{\text{V of ...
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17 views

Why is the R-Square of PROC CALIS a period

I am running PROC CALIS on some data and everything seems to work correctly, except the R-Square table has a . (period) for the R-Square of one of the measured dependent variables. Why would this be? ...
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87 views

Test of between groups difference in r-squared value in linear regression

Running a linear regression with one continuous IV (sleep) and one categorical IV (gender). Have run a split-file analysis and there appears to be a difference between genders in r-squared. How would ...
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44 views

$R^2$ (coefficient of determination) and linearity in multiple linear regression

For simple linear regression (SLR), in order for $R^2$ (the coefficient of determination) to be a meaningful measure, it must be true that $X$ and $Y$ are linearly correlated. Specifically, $R^2=r^2$, ...
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Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum?

Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum? Is there an easy mathematical explanation to this as $r^2$ is squared and don't add ...
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33 views

Model Averaging

Good Afternoon, I am working on model averaging of data collected about bird species and habitat vegetation. I have been using the MuMIn package in R and have taken a subset of all possible models ...
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118 views

Assessing strength of instrument

I want to use a risk score (RS) as an instrument for an exposure on a clinical outcome. However, I wont have access to data on the outcome for some time, and wish to examine whether this risk score ...
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22 views

Distinguishing between different notions of $R^2$

What is the distinction between $R^2_{pop}$ – the population R-squared $R^2_{out}$ – the out-of-sample R-squared $R^2_{c.v.}$ – the squared population cross-validity coefficient ? These ...
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54 views

Regression model for ordinal dependent variable and catogrical independent variables

If I'm using R, which regression model should I use for my dataset? (I need to get the R-squared value.) I have 1 dependent variable and 6 independent variables as follows: 1 dependent variable: ...