drewlee
在文章里面看到这么一句话
[quote]R2 is the usual squared multiple correlation coefficient.[/quote]
问题是R^2和相关系数有什么关系?
还有一个问题,为什么无截距项的线性模型的R2计算式子和有截距项的不一样呢?
neige
the reason why it is called R^2 is because it is R ^2, correlation ^2
I do not see there is a difference, R^2 is the proportion of variation explained by a certain predictor, it is usually a ratio of two variances
yihui
多元回归里面不是简单的叫“相关系数”,而是叫多重相关系数(复相关系数),R^2与多重相关系数就是平方关系。
drewlee
不认为另外弄出一个新名词"multiple correlation coefficient"有多大意义。
下面是Mary Sue Younger的Handbook of linear regression上面的话
[quote]
Note that it does not make sense to define a "multiple correlation coefficient" by taking the square root of r^2, primarily because no meaningful sign could be attached indicating the direction of the multiple relationships.
...
This statistic is oftern reported, even though it is a meaningless measure.
[/quote]
况且不管相不相关了。为什么有截距和无截距的两种模型要选择不同的R^2计算公式呢?
neige
ppl usually look at the sign of estimated the coefficient to determine which root to take, + or -.
I guess it is because how the coefficient can be estimated. estimation algorithm is based on regression with no intercept.In MLR, it basically orthogonalized the current variable to the previous ones, then use the residuals to do another regression without intercept to obtain the estimates....