摘要提取相关系数

Question

I am using lm() on a large data set in R . Using summary() one can get lot of details about linear regression between these two parameters.

The part I am confused with is which one is the correct parameter in the Coefficients: section of summary, to use as correlation coefficient?

Sample Data

c1 <- c(1:10)
c2 <- c(10:19)
output <- summary(lm(c1 ~ c2))

Summary

Call:
lm(formula = c1 ~ c2)

Residuals:
      Min         1Q     Median         3Q        Max 
-2.280e-15 -8.925e-16 -2.144e-16  4.221e-16  4.051e-15 

Coefficients:
             Estimate Std. Error    t value Pr(>|t|)    
(Intercept) -9.000e+00  2.902e-15 -3.101e+15   <2e-16 ***
c2           1.000e+00  1.963e-16  5.093e+15   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.783e-15 on 8 degrees of freedom
Multiple R-squared:      1, Adjusted R-squared:      1 
F-statistic: 2.594e+31 on 1 and 8 DF,  p-value: < 2.2e-16

Is this the correlation coefficient I should use?

output$coefficients[2,1]
1

Please suggest, thanks.

Answer 1

The full variance covariance matrix of the coefficient estimates is:

fm <- lm(c1 ~ c2)
vcov(fm)

and in particular sqrt(diag(vcov(fm))) equals coef(summary(fm))[, 2]

The corresponding correlation matrix is:

cov2cor(vcov(fm))

The correlation between the coefficient estimates is:

cov2cor(vcov(fm))[1, 2]