Duh!  Silly me!  But my confusion persits:  What is the regression being
done?  See below....

On Sat, Dec 3, 2011 at 5:10 PM, R. Michael Weylandt <
michael.weyla...@gmail.com> wrote:

> In your code by supplying a vector M[,"e"] you are regressing "e"
> against all the variables provided in the data argument, including "e"
> itself -- this gives the very strange regression coefficients you
> observe. R has no way to know that that's somehow related to the "e"
> it sees in the data argument.
>

> In the suggested way,
>
> lm(formula = e ~ ., data = as.data.frame(M))
>
> e is regressed against everything that is not e and sensible results are
> given.
>

But still 'l1 <- lm(e~., data=df)' is not the same as 'l3 <-
lm(M[,5]~M[,1]+M[,2]+M[,3]+M[,4])'

> M <- matrix(runif(5*20), nrow=20)
> colnames(M) <- c('a', 'b', 'c', 'd', 'e')
> l1 <- lm(e~., data=df)
> summary(l1)

Call:
lm(formula = e ~ ., data = df)

Residuals:
     Min       1Q   Median       3Q      Max
-0.38343 -0.21367  0.03067  0.13757  0.49080

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.28521    0.29477   0.968    0.349
a            0.09283    0.30112   0.308    0.762
b            0.23921    0.22425   1.067    0.303
c           -0.16027    0.24154  -0.664    0.517
d            0.24025    0.20054   1.198    0.250

Residual standard error: 0.2871 on 15 degrees of freedom
Multiple R-squared: 0.1602,    Adjusted R-squared: -0.06375
F-statistic: 0.7153 on 4 and 15 DF,  p-value: 0.5943

> l3 <- lm(M[,5]~M[,1]+M[,2]+M[,3]+M[,4])
> summary(l3)

Call:
lm(formula = M[, 5] ~ M[, 1] + M[, 2] + M[, 3] + M[, 4])

Residuals:
     Min       1Q   Median       3Q      Max
-0.36355 -0.22679 -0.01202  0.18462  0.37377

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.76972    0.24501   3.142  0.00672 **
M[, 1]      -0.23830    0.24123  -0.988  0.33890
M[, 2]      -0.02046    0.21958  -0.093  0.92699
M[, 3]      -0.29518    0.22559  -1.308  0.21040
M[, 4]      -0.31545    0.24570  -1.284  0.21866
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2668 on 15 degrees of freedom
Multiple R-squared: 0.2762,    Adjusted R-squared: 0.08317
F-statistic: 1.431 on 4 and 15 DF,  p-value: 0.272

>

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