Log in ivan08urbieta 7 years agoPosted 7 years ago. Direct link to ivan08urbieta's post “Which parameter is then b...” Which parameter is then better to evaluate the fit of a line to a data set? the correlation coefficient (r) or the coefficient of determination (r2)? • (26 votes) Nahuel Prieto 7 years agoPosted 7 years ago. Direct link to Nahuel Prieto's post “The short answer is this:...” The short answer is this: In the case of the Least Squares Regression Line, according to traditional statistics literature, the metric you're looking for is r^2. Longer answer: If we used the MAD (mean absolute deviation) instead of the standard deviation to calculate both r and the regression line, then the line, as well as r as a metric of its effectiveness, would be more realistic, and we would not even need to square r at all. This is a very extensive subject and there are still lots of different opinions out there, so I encourage other people to complement my answer with what they think. Hope you found my answer helpful or at least interesting. Cheers! (117 votes) morecmy 5 years agoPosted 5 years ago. Direct link to morecmy's post “what's the difference bet...” what's the difference between R-squared and the total sum of squared residual? • (9 votes) Shannon Hegewald 3 years agoPosted 3 years ago. Direct link to Shannon Hegewald's post “They lost me at the squar...” They lost me at the squares • (6 votes) deka 2 years agoPosted 2 years ago. Direct link to deka's post “don't worry about them to...” don't worry about them too much (5 votes) Maryam Azmat 6 years agoPosted 6 years ago. Direct link to Maryam Azmat's post “If you have two models of...” If you have two models of a set of data, a linear model and a quadratic model, and you have worked out the R-squared value through linear regression, and are then asked to explain what the R-squared value of the quadratic model is, without using any figures, what would this explanation be? • (2 votes) Ian Pulizzotto 6 years agoPosted 6 years ago. Direct link to Ian Pulizzotto's post “A quadratic model has one...” A quadratic model has one extra parameter (the coefficient on x^2) compared to a linear model. Therefore, the quadratic model is either as accurate as, or more accurate than, the linear model for the same data. Recall that the stronger the correlation (i.e. the greater the accuracy of the model), the higher the R^2. So the R^2 for the quadratic model is greater than or equal to the R^2 for the linear model. Have a blessed, wonderful day! (5 votes) Brown Wang 7 years agoPosted 7 years ago. Direct link to Brown Wang's post “How we predict sum of squ...” How we predict sum of squares in the regression line? 347231 6 years agoPosted 6 years ago. Direct link to 347231's post “Tbh, you really cannot ge...” Tbh, you really cannot get around squaring every number. I guess if you have decimals, you could round them them off, but really,, other than that, there’s no shortcut. It is difficult to predict because the powers have to be applied to each and every number. You could always do a bit of mental math and round things off into easier numbers, but it’s not always reliable. (5 votes) Bo Stoknes 3 months agoPosted 3 months ago. Direct link to Bo Stoknes's post “Why do we square the resi...” Why do we square the residuals? I get that we need a positive value for all residuals to calculate the sum of the prediction error, but wouldn't it be easier to just calculate the sum of the absolute values of the residuals? • (3 votes) 24pearcetc 10 months agoPosted 10 months ago. Direct link to 24pearcetc's post “is there a shorter way to...” is there a shorter way to create a estimation without taking all the steps to solve the problem? is there a hack or a way to do it quickly? • (2 votes) Jose Prieto Lechuga 9 months agoPosted 9 months ago. Direct link to Jose Prieto Lechuga's post “Maybe using software like...” Maybe using software like JASP? (1 vote) Neel Kumar 6 years agoPosted 6 years ago. Direct link to Neel Kumar's post “Can I get the exact data ...” Can I get the exact data set, based on that this dot plot have been created. • (2 votes) gembaindonesia a year agoPosted a year ago. Direct link to gembaindonesia's post “Hi. I have in several cas...” Hi. I have in several cases lately observed that when you remove several obvious outliers from a data set in "one go" the R-sq actually gets lower? This is rather counter intuitive to me at least, and also when looking into the formula for how R is calculated it doesn't seem to make much sense either? Any insights into this? • (2 votes) daniella 5 months agoPosted 5 months ago. Direct link to daniella's post “The phenomenon you descri...” The phenomenon you described, where removing outliers from a dataset results in a lower R^2 value, can occur in certain cases. One possible reason is that the outliers were exerting a disproportionate influence on the correlation between the variables, causing the regression line to be biased. Removing outliers may result in a more accurate estimation of the true relationship between the variables, leading to a lower residual sum of squares and hence a lower R^2 value. Additionally, it's important to consider the nature of the outliers and the underlying data generating process to fully understand the impact of their removal on the regression analysis. (1 vote) Scott Samuel 3 years agoPosted 3 years ago. Direct link to Scott Samuel's post “how do you calculate r^2” how do you calculate r^2 • (1 vote) deka 2 years agoPosted 2 years ago. Direct link to deka's post “in case you already have ...” in case you already have r, simply do r*r yes. r^2 is nothing but a square of r(correlation coefficient) (3 votes)Want to join the conversation?
IMHO, neither r o r^2 are the best for this. In the case of r, it is calculated using the Standard Deviation, which itself is a statistic that has been long put to doubt because it squares numbers just to remove the sign and then takes a square root AFTER having added those numbers, which resembles more an Euclidean distance than a good dispersion statistic (it introduces an error to the result that is never fully removed). Here is a paper about that topic presented at the British Educational Research Association Annual Conference in 2004: https://www.leeds.ac.uk/educol/documents/00003759.htm .
they're simply a visualization of squaring numbers then summing them like 3^2 + 7^2 + 13^2 to assess how far they are from a regression line
b/r
Niels
FAQs
What is the intuitive explanation of r2? ›
R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression. 0% indicates that the model explains none of the variability of the response data around its mean.
What does R-squared mean in Khan Academy? ›In linear regression, r-squared (also called the coefficient of determination) is the proportion of variation in the response variable that is explained by the explanatory variable in the model.
Is R-squared 0.5 good? ›What qualifies as a “good” R-squared value will depend on the context. In some fields, such as the social sciences, even a relatively low R-squared value, such as 0.5, could be considered relatively strong. In other fields, the standards for a good R-squared reading can be much higher, such as 0.9 or above.
What is an acceptable R-squared level? ›A R-squared between 0.50 to 0.99 is acceptable in social science research especially when most of the explanatory variables are statistically significant.
What does R2 score tell us? ›What Does an R Squared Value Mean? An R-Squared value shows how well the model predicts the outcome of the dependent variable. R-Squared values range from 0 to 1. An R-Squared value of 0 means that the model explains or predicts 0% of the relationship between the dependent and independent variables.
What is the interpretation of R2 in words? ›You can interpret the coefficient of determination (R²) as the proportion of variance in the dependent variable that is predicted by the statistical model. Another way of thinking of it is that the R² is the proportion of variance that is shared between the independent and dependent variables.
What is R-squared explained simply? ›R-Squared (R² or the coefficient of determination) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable. In other words, r-squared shows how well the data fit the regression model (the goodness of fit).
Do you want a higher or lower R-squared? ›Higher R-squared values suggest a better fit, but it doesn't necessarily mean the model is a good predictor in an absolute sense.
What does an R2 value of 0.9 mean? ›For example, a model with an R-squared value of 0.9 means that approximately 90% of the variance in the dependent variable is explained by the independent variables. This suggests a strong relationship between the variables and indicates that the model provides a good fit to the data.
Why is R2 misleading? ›R-squared does not measure goodness of fit. It can be arbitrarily low when the model is completely correct. By making σ2 large, we drive R-squared towards 0, even when every assumption of the simple linear regression model is correct in every particular.
What if R-squared is too low? ›
A low R-squared value indicates that your independent variable is not explaining much in the variation of your dependent variable - regardless of the variable significance, this is letting you know that the identified independent variable, even though significant, is not accounting for much of the mean of your ...
How to interpret R-squared and p value? ›The greater R-square the better the model. Whereas p-value tells you about the F statistic hypothesis testing of the “fit of the intercept-only model and your model are equal”. So if the p-value is less than the significance level (usually 0.05) then your model fits the data well.
Can R-squared be too high? ›High R2 values are not always a problem. In fact, sometimes you can legitimately expect very large values. For example, if you are studying a physical process and have very precise and accurate measurements, it's possible to obtain valid R-squared values in the high 90s.
What is considered a good adjusted R-squared? ›It's common to see adjusted R-square values between 0.5 and 0.7 as a good fit. But, The minimum acceptable value of R-square and adjusted R-square depends on the specific context of the study, a higher value is better but it also depends on the research question.
What is the difference between R2 and adjusted R2? ›R-squared: This measures the variation of a regression model. R-squared either increases or remains the same when new predictors are added to the model. Adjusted R-squared: This measures the variation for a multiple regression model, and helps you determine goodness of fit.
What is the intuitive explanation of regression? ›In layman's terms, it is the process of fitting the best curve for a set of data points by reducing the distance between the actual value and predicted value (sum of squared residuals). The distance between both values is often known as error or variation or variance.
What is the concept of R2? ›Definition. The coefficient of determination, or R2 , is a measure that provides information about the goodness of fit of a model. In the context of regression it is a statistical measure of how well the regression line approximates the actual data.
What is an intuitive explanation of random variable? ›Random Variable: Simply put — a random variable is a set of possible values of a random experiment like a coin toss. In our example, the possible value of our experiment is Head or Tail.
What does R2 value mean in psychology? ›(September 2019) Click [show] for important translation instructions. In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).