Some clarificatins of anova() and summary ()

[sorry for the repost. I forgot to switch off formatting last time]

I have two assignment problems...

I have written this small code for regression with two regressors .

For replication purposes, it might be good to set a seed for the random
number generation.

set.seed(127)
n <- 50
x1 <- runif(n,1,10)
x2 <- x1 + rnorm(n,0,0.5)
plot(x1,x2) # x1 and x2 strongly correlated
cor(x1,x2)
y <- 3 + 0.5*x1 + 1.1*x2 + rnorm(n,0,2)
intact.lm <- lm(y ~ x1 + x2)
summary(intact.lm)
anova(intact.lm)

You should also run anova on these models:

intact21 <- lm(y~x2+x1)
intact12 <- lm(y~x1+x2)
the questions are

1.The function summary() is convenient since the result does not
depend on the order the variables
are listed in the linear model definition. It has a serious downside
though which is obvious in this case.
Are there any signficant variables left?

2. An anova(intact.lm) table shows how much the second variable
contributes to the result in
addition to the first. Is there a variable significant now?Is the
second variable significant?
Both anova and summary were in agreement that the P-value for addition  
of x2 ito a
model that already 1ncluded x1 is 0.0296. One of them uses the t  
statistic and the
other used the F statistic. I am not sure where your confusion lies.
David Winsemius

>
>
> the results i got:
>
>> summary(intact.lm)
>
> Call:
> lm(formula = y ~ x1 + x2)
>
> Residuals:
>    Min      1Q  Median      3Q     Max
> -5.5824 -1.5314 -0.1568  1.4425  5.3374
>
> Coefficients:
>            Estimate Std. Error t value Pr(>|t|)
> (Intercept)   3.4857     0.9354   3.726 0.000521 ***
> x1            0.2537     0.6117   0.415 0.680191
> x2            1.3517     0.6025   2.244 0.029608 *
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 2.34 on 47 degrees of freedom
> Multiple R-squared: 0.7483,     Adjusted R-squared: 0.7376
> F-statistic: 69.87 on 2 and 47 DF,  p-value: 8.315e-15
>
>> anova(intact.lm)
> Analysis of Variance Table
>
> Response: y
>          Df Sum Sq Mean Sq  F value   Pr(>F)
> x1         1 737.86  737.86 134.7129 2.11e-15 ***
> x2         1  27.57   27.57   5.0338  0.02961 *
> Residuals 47 257.43    5.48
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>
>
> my question is that , i cant see any "serious downside" in using
> summary (). And in the second question I am totally clueless. I need
> your help
>
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Some clarificatins of anova() and summary ()

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