>
> Use `lm` the way it is designed to be used, with a data argument:
>
> > l2 <- lm(e~. , data=as.data.frame(M))
> > summary(l2)
>
> Call:
> lm(formula = e ~ ., data = as.data.frame(M))
>
>
And what is the regression being done in this case?  How are the
independent  variables used?

It looks like M[,5]~M[,1]+M[,2]+M[,3]+M[,4] as those are the
coefficients.   But the results are different when I do that explicitly:

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

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

Residuals:
       Min         1Q     Median         3Q        Max
-9.580e-17 -3.360e-17 -8.596e-18  9.114e-18  2.032e-16

Coefficients:
              Estimate Std. Error    t value Pr(>|t|)
(Intercept) -7.505e-17  7.158e-17 -1.048e+00    0.312
a           -1.653e-17  7.117e-17 -2.320e-01    0.820
b           -5.042e-17  5.480e-17 -9.200e-01    0.373
c            4.236e-17  5.774e-17  7.340e-01    0.475
d           -3.878e-17  4.946e-17 -7.840e-01    0.446
e            1.000e+00  6.083e-17  1.644e+16   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.763e-17 on 14 degrees of freedom
Multiple R-squared:     1,    Adjusted R-squared:     1
F-statistic: 6.435e+31 on 5 and 14 DF,  p-value: < 2.2e-16

> 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
-0.49398 -0.14203  0.01588  0.14157  0.31335

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.6681     0.1859   3.594  0.00266 **
M[, 1]       -0.1767     0.2419  -0.730  0.47644
M[, 2]       -0.3874     0.2135  -1.814  0.08970 .
M[, 3]        0.3695     0.2180   1.695  0.11078
M[, 4]        0.1361     0.2366   0.575  0.57360
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2449 on 15 degrees of freedom
Multiple R-squared: 0.2988,    Adjusted R-squared: 0.1119
F-statistic: 1.598 on 4 and 15 DF,  p-value: 0.2261


cheers
Worik

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