Also known as coefficient of determination, multiple R-squared is the proportion of the variation in dependent variable that can be explained by the independent variables. It provides a measure of how well observed outcomes are replicated by the model.
Published in Chapter:
US Medical Expense Analysis Through Frequency and Severity Bootstrapping and Regression Model
Fangjun Li (University of Connecticut, USA) and Gao Niu (Bryant University, USA)
Copyright: © 2022|Pages: 31
DOI: 10.4018/978-1-7998-8455-2.ch007
Abstract
For the purpose of control health expenditures, there are some papers investigating the characteristics of patients who may incur high expenditures. However fewer papers are found which are based on the overall medical conditions, so this chapter was to find a relationship among the prevalence of medical conditions, utilization of healthcare services, and average expenses per person. The authors used bootstrapping simulation for data preprocessing and then used linear regression and random forest methods to train several models. The metrics root mean square error (RMSE), mean absolute percent error (MAPE), mean absolute error (MAE) all showed that the selected linear regression model performs slightly better than the selected random forest regression model, and the linear model used medical conditions, type of services, and their interaction terms as predictors.
FAQs
Also known as coefficient of determination, multiple R-squared is the proportion of the variation in dependent variable that can be explained by the independent variables. It provides a measure of how well observed outcomes are replicated by the model.
What is the difference between adjusted R-squared and multiple R-squared? ›
While R-squared tends to increase as more variables are added to the model (even if they don't improve the model significantly), Adjusted R-squared penalizes the addition of unnecessary variables. It considers the number of predictors in the model and adjusts R-squared accordingly.
What do multiple R values indicate? ›
Multiple R: The correlation coefficient between the observed and predicted values. It ranges in value from 0 to 1. A small value indicates that there is little or no linear relationship between the dependent variable and the independent variables.
What does a low multiple R-squared mean? ›
A low R-squared basically means that your model does do not include all [random] variables that are associated with the outcome. That is not necessarily a problem as long as the omitted variables are not correlated with your predictors.
Should multiple R-squared be high or low? ›
R-squared measures the goodness of fit of a regression model. Hence, a higher R-squared indicates the model is a good fit, while a lower R-squared indicates the model is not a good fit.
Do I use multiple or adjusted R-squared? ›
The fundamental point is that when you add predictors to your model, the multiple Rsquared will always increase, as a predictor will always explain some portion of the variance. Adjusted Rsquared controls against this increase, and adds penalties for the number of predictors in the model.
What does adjusted R-squared tell us in multiple regression? ›
Summary. The adjusted R-squared is a modified version of R-squared that adjusts for predictors that are not significant in a regression model. Compared to a model with additional input variables, a lower adjusted R-squared indicates that the additional input variables are not adding value to the model.
What is a good R-squared value for correlation? ›
It depends on how reliable your measures are, how independent they are from each other, and the relationship between the independent and dependent variables. In the social sciences, an r squared in the range of . 4 to . 5 is fairly strong, other things being equal.
What is 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 does the multiple R statistic of the regression output represent? ›
The Multiple R-squared value is most often used for simple linear regression (one predictor). It tells us what percentage of the variation within our dependent variable that the independent variable is explaining. In other words, it's another method to determine how well our model is fitting the data.
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 ...
What does R-squared tell us in multiple regression? ›
R-squared measures the strength of the relationship between your model and the dependent variable on a convenient 0 – 100% scale.
What is a good R-squared value for multiple regression? ›
Estimating the multivariate regression model using the data set below and using the ordinary least square regression method yields an of R-squared of 0.106. A model with a R-squared that is between 0.10 and 0.50 is good provided that some or most of the explanatory variables are statistically significant.
