R squared意思

"R squared" (R²) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It's a measure of goodness of fit, indicating how well the data fit the statistical model.

The value of R² ranges from 0 to 1, where:

• 0 means the model explains none of the variability of the response data around its mean.
• 1 means the model explains all the variability of the response data around its mean.

A higher R² value indicates that more of the variance in the dependent variable is explained by the independent variable(s), and thus the model fits the data better. However, it's important to note that a high R² does not necessarily mean that the model is good or useful; it depends on the context of the data and the research question being asked.

In linear regression, R² is the square of the correlation coefficient (R), which measures the strength and direction of the relationship between two variables. The correlation coefficient ranges from -1 to 1, where:

• -1 indicates a perfect negative linear relationship between the variables.
• 0 indicates no linear relationship between the variables.
• 1 indicates a perfect positive linear relationship between the variables.

In summary, R² is a useful metric for understanding how well a regression model fits the data, but it should be used in conjunction with other measures (like adjusted R², p-values, and residual analysis) to fully evaluate the model's performance and predictive ability.