Statistics 简明教程
Statistics - Adjusted R-Squared
R 平方表示线性回归模型的独立变量 (X) 解释的因变量 (Y) 中的变化比例。调整后的 R 平方根据模型中独立变量的数量来调整该统计数据。${R^2}$ 显示项（数据点）与曲线或直线拟合的程度。调整后的 ${R^2}$ 也表示项与曲线或直线拟合的程度，但也对模型中的项的数量进行调整。如果你向模型中添加越来越多的无用变量，调整后的 r 平方就会降低。如果你添加更多有用的变量，调整后的 r 平方就会提高。
R-squared measures the proportion of the variation in your dependent variable (Y) explained by your independent variables (X) for a linear regression model. Adjusted R-squared adjusts the statistic based on the number of independent variables in the model.${R^2}$ shows how well terms (data points) fit a curve or line. Adjusted ${R^2}$ also indicates how well terms fit a curve or line, but adjusts for the number of terms in a model. If you add more and more useless variables to a model, adjusted r-squared will decrease. If you add more useful variables, adjusted r-squared will increase.
调整后的 ${R^2}$ 始终小于或等于 ${R^2}$。只有在使用样本时才需要 ${R^2}$。换句话说，当你拥有整个人群数据时，就不需要 ${R^2}$。
Adjusted ${R_{adj}^2}$ will always be less than or equal to ${R^2}$. You only need ${R^2}$ when working with samples. In other words, ${R^2}$ isn’t necessary when you have data from an entire population.
Formula
其中——
Where −
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${n}$ = the number of points in your data sample.
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${k}$ = the number of independent regressors, i.e. the number of variables in your model, excluding the constant.
Example
Problem Statement −
Problem Statement −
一个基金的样本 R 平方值接近 0.5，而且它肯定提供了经过风险调整后的较高的回报，5 个预测变量的样本量为 50。找出调整后的 R 平方值。
A fund has a sample R-squared value close to 0.5 and it is doubtlessly offering higher risk adjusted returns with the sample size of 50 for 5 predictors. Find Adjusted R square value.
Solution −
Solution −
样本量 = 50 预测变量的数量 = 5 样本 R 平方 = 0.5。将这些值代入等式中，
Sample size = 50 Number of predictor = 5 Sample R - square = 0.5.Substitute the qualities in the equation,