# [R] Question about linear models

David Winsemius dwinsemius at comcast.net
Wed Nov 19 06:03:03 CET 2008

```Er, ...  the log transform is more like using larger units (giving
smaller numerical values.)

On Nov 18, 2008, at 11:55 PM, David Winsemius wrote:

> You can always inflate the SS by using smaller units, which is what
> your log transformation is doing. What is important for inference
> is the ratios of those sums of squares. The rest of your homework is
> something you will need to complete yourself.
>
> http://www.ugr.es/~falvarez/relaMetodos2.pdf    ..... see Question 9
> see Question 47
>
> --
> David Winsemius, MD
> Heritage Labs
>
>
> On Nov 18, 2008, at 11:44 PM, Ricardo Ríos wrote:
>
>> Hi wizards,
>>
>> I have the following model:
>>
>> x<-c(20.79, 22.40, 23.15, 23.89, 24.02, 25.14, 28.49, 29.04, 29.88,
>> 30.06)
>> y <- c(194.5, 197.9, 199.4, 200.9, 201.4, 203.6, 209.5, 210.7,
>> 211.9, 212.2)
>> model1 <- lm( y ~ x )
>> anova(model1)
>>
>>        Df Sum Sq Mean Sq F value    Pr(>F)
>> x          1 368.87  368.87  4384.6 3.011e-12 ***
>> Residuals  8   0.67    0.08
>>
>>
>> But, I have realized the following transformation:
>>
>> lnx <- log(x)
>> lny <- log(y)
>> model2 <- lm( lny ~ lnx )
>> anova(model2)
>>
>> Response: lny
>>        Df    Sum Sq   Mean Sq F value    Pr(>F)
>> lnx        1 0.0088620 0.0088620   27234 2.034e-15 ***
>> Residuals  8 0.0000026 0.0000003
>>
>>
>>
>> The second model has a Sum of square Residuals very small
>>
>> I have analyzed the following graph:
>>
>> plot( model1\$fitted.values, model1\$residuals)
>> plot( model2\$fitted.values, model2\$residuals)
>>
>>
>> I have observed that maybe the first model has a specification error.
>> is that correct? Which model is the best?
>>
>> anything.
>>
>>
>>
>> --
>> http://ricardorios.wordpress.com/
>>
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