# [R] Some clarificatins of anova() and summary ()

Tanmoy Talukdar tanmoy.talukdar at gmail.com
Sun Dec 14 16:20:51 CET 2008

```Why do you think that running lm() twice on those two models is going
to help me?  They are identical models and hence we get identical
results.The second question is now alright. I had some

Please tell me if you can find any "downside " in summary (). I can't find any.

i 've edited the code for that replication  issue.

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)

> summary(intact.lm)

Call:
lm(formula = y ~ x1 + x2)

Residuals:
Min      1Q  Median      3Q     Max
-3.4578 -1.1326  0.4551  1.2807  4.8241

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  3.63603    0.61944   5.870 4.23e-07 ***
x1          -0.09555    0.49114  -0.195  0.84658
x2           1.59384    0.48542   3.283  0.00194 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.807 on 47 degrees of freedom
Multiple R-squared: 0.8198,     Adjusted R-squared: 0.8121
F-statistic: 106.9 on 2 and 47 DF,  p-value: < 2.2e-16

> anova(intact.lm)
Analysis of Variance Table

Response: y
Df Sum Sq Mean Sq F value    Pr(>F)
x1         1 663.18  663.18 203.065 < 2.2e-16 ***
x2         1  35.21   35.21  10.781  0.001940 **
Residuals 47 153.49    3.27
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

On Sun, Dec 14, 2008 at 8:26 PM, David Winsemius <dwinsemius at comcast.net> wrote:
>
> On Dec 14, 2008, at 9:40 AM, Tanmoy Talukdar wrote:
>
>> [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
>>
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