[R] Could the Odds represent weight in Generalized Linear Model?

Wed Jan 31 10:20:05 CET 2018

Dear Lenny,

\beta_1 is the log odds ratio for age. If you want the odds ratio,
then you need to calculate it.

It looks like some reading up on glm won't harm you.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx op inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no
more than asking him to perform a post-mortem examination: he may be
able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does
not ensure that a reasonable answer can be extracted from a given body
of data. ~ John Tukey
///////////////////////////////////////////////////////////////////////////////////////////

2018-01-30 15:46 GMT+01:00 contact retour-client
<retour.client.contact op gmail.com>:
> Dear Thierry,
>
> Thanks a lot for this answer,
>
> I mean i want to obtain such model Behavior1 = β0+β1*Age , the purpose is to
> obtain  β1. I want to be sure that the odds value could be the  β1. Or how
> to calculate it ?
>
> Thanks again for your precious help.
>
> Lenny
>
> Garanti sans virus. www.avg.com
>
> 2018-01-30 15:37 GMT+01:00 Thierry Onkelinx <thierry.onkelinx op inbo.be>:
>>
>> Dear Lenny,
>>
>> You can do this by using Age as an offset factor.
>>
>> dataset$wAge <- dataset$Age * 1.02
>> glm(cbind(Yes,No) ~ offset(wAge) + Times + Type, family=binomial, data =
>> dataset)
>>
>> Best regards,
>>
>>
>>
>>
>> ir. Thierry Onkelinx
>> Statisticus / Statistician
>>
>> Vlaamse Overheid / Government of Flanders
>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
>> FOREST
>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
>> thierry.onkelinx op inbo.be
>> Havenlaan 88 bus 73, 1000 Brussel
>> www.inbo.be
>>
>>
>> ///////////////////////////////////////////////////////////////////////////////////////////
>> To call in the statistician after the experiment is done may be no more
>> than asking him to perform a post-mortem examination: he may be able to say
>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner
>> The combination of some data and an aching desire for an answer does not
>> ensure that a reasonable answer can be extracted from a given body of data.
>> ~ John Tukey
>>
>> ///////////////////////////////////////////////////////////////////////////////////////////
>>
>>
>>
>> 2018-01-30 11:14 GMT+01:00 contact retour-client
>> <retour.client.contact op gmail.com>:
>>>
>>> Hello all,
>>>
>>>
>>> I'm sorry if my question seems basic.
>>>
>>> Im studying a responses (Yes,No) in a survey and, thanks to GLM I obtain
>>> the following relation with my variables : (Yes,No)~ β0 + Age We note
>>> this
>>> this certain type of (Yes,No) response is linked to age (p<0.05 in glm) .
>>>
>>> After that we calculated :
>>>
>>> model1=glm(cbind(Yes,No) ~ Age + Times + Type, family=binomial)
>>> summary(model1)
>>> exp(model1$coefficients)
>>>
>>> exp(model1$coefficients)(Intercept)         Age       Times TypeRegular
>>>  0.01659381  1.02546748  1.01544154  1.70056425
>>>
>>> The odds of answering 'Yes' is multiplied with 1.02 for each additional
>>> year of age.
>>>
>>> My questions is :
>>>
>>> (1) it is possible to add to my model, (Yes,No)~ β0 + Age, the weight of
>>> the variable Age. Is it in fact the odd value ? Here is an example : is
>>> it
>>> ok to formulate my model as that (Yes,No)~ β0 + 1.02* Age: here 1.02 is
>>> what I call weight of age, in other words, I want to quantify its impact
>>> in
>>> the model.
>>>
>>> (2)suppose I want to model (Yes,No)~ β0 + Type with type a categorical
>>> data. odd value of TypeRegular is 1.70056425. But in my model it is
>>> simply
>>> Type that include Regular and Irregular. How to adapt this value to Type
>>> ?
>>>
>>> My data
>>>
>>> res=structure(list(Age = c(10, 14, 14, 15, 16, 16, 16, 17, 17, 17, 17,
>>> 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 20,
>>> 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22,
>>> 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23,
>>> 23, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26,
>>> 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27,
>>> 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29,
>>> 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31,
>>> 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33,
>>> 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35,
>>> 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37,
>>> 37, 37, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38,
>>> 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40,
>>> 40, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42,
>>> 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43,
>>> 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45,
>>> 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47,
>>> 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 49, 49, 50,
>>> 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50,
>>> 51, 51, 51, 51, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 52, 52, 52,
>>> 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53,
>>> 53, 54, 54, 54, 54, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 55, 55,
>>> 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56,
>>> 57, 57, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 58, 58, 59,
>>> 59, 59, 59, 59, 59, 60, 60, 60, 60, 60, 60, 60, 61, 62, 62, 62, 62,
>>> 63, 64, 64, 65, 65, 67, 74), Times = c(6L, 6L, 16L, 6L, 9L, 23L, 33L,
>>> 6L, 14L, 17L, 36L, 4L, 9L, 15L, 20L, 26L, 28L, 30L, 33L, 6L, 11L, 14L,
>>> 20L, 26L, 28L, 30L, 32L, 4L, 4L, 6L, 9L, 17L, 26L, 28L, 30L, 33L, 44L,
>>> 47L, 4L, 6L, 23L, 26L, 32L, 4L, 9L, 11L, 11L, 14L, 14L, 15L, 17L, 18L,
>>> 20L, 23L, 26L, 36L, 44L, 50L, 4L, 9L, 28L, 30L, 32L, 4L, 17L, 23L, 4L,
>>> 6L, 9L, 9L, 11L, 14L, 25L, 33L, 33L, 51L, 4L, 6L, 14L, 17L, 18L, 26L,
>>> 28L, 30L, 32L, 33L, 44L, 50L, 6L, 9L, 9L, 11L, 14L, 17L, 22L, 23L,
>>> 30L, 4L, 9L, 11L, 14L, 15L, 20L, 23L, 28L, 29L, 36L, 39L, 43L, 51L,
>>> 58L, 14L, 20L, 23L, 26L, 28L, 36L, 51L, 4L, 6L, 9L, 16L, 17L, 18L,
>>> 23L, 33L, 37L, 51L, 9L, 11L, 14L, 18L, 23L, 26L, 28L, 58L, 9L, 17L,
>>> 33L, 36L, 37L, 58L, 4L, 6L, 9L, 9L, 11L, 17L, 20L, 26L, 28L, 32L, 33L,
>>> 47L, 4L, 6L, 9L, 15L, 23L, 28L, 4L, 9L, 9L, 15L, 17L, 18L, 20L, 23L,
>>> 28L, 30L, 30L, 4L, 6L, 6L, 9L, 17L, 18L, 33L, 36L, 4L, 6L, 11L, 14L,
>>> 15L, 17L, 23L, 26L, 28L, 36L, 4L, 6L, 9L, 11L, 17L, 18L, 23L, 25L,
>>> 28L, 30L, 6L, 9L, 11L, 14L, 14L, 17L, 20L, 23L, 28L, 35L, 44L, 4L, 6L,
>>> 9L, 14L, 17L, 44L, 6L, 9L, 14L, 17L, 22L, 26L, 28L, 29L, 33L, 36L,
>>> 50L, 4L, 6L, 6L, 17L, 20L, 23L, 28L, 30L, 36L, 51L, 58L, 4L, 9L, 9L,
>>> 14L, 15L, 17L, 23L, 26L, 28L, 30L, 36L, 38L, 6L, 6L, 9L, 17L, 23L,
>>> 26L, 28L, 43L, 44L, 4L, 15L, 17L, 17L, 25L, 26L, 28L, 36L, 44L, 51L,
>>> 58L, 6L, 9L, 16L, 25L, 28L, 32L, 44L, 58L, 4L, 9L, 17L, 28L, 30L, 36L,
>>> 43L, 44L, 6L, 11L, 14L, 16L, 26L, 30L, 44L, 15L, 20L, 23L, 26L, 28L,
>>> 52L, 4L, 6L, 9L, 9L, 11L, 14L, 16L, 17L, 20L, 23L, 26L, 28L, 30L, 33L,
>>> 35L, 37L, 50L, 51L, 6L, 9L, 14L, 17L, 18L, 18L, 26L, 44L, 50L, 9L,
>>> 14L, 14L, 15L, 18L, 20L, 23L, 28L, 33L, 36L, 43L, 44L, 50L, 4L, 9L,
>>> 11L, 14L, 18L, 26L, 28L, 29L, 30L, 32L, 43L, 44L, 52L, 6L, 9L, 20L,
>>> 23L, 28L, 30L, 33L, 36L, 43L, 4L, 9L, 11L, 14L, 16L, 20L, 23L, 26L,
>>> 28L, 36L, 50L, 51L, 4L, 6L, 9L, 14L, 18L, 23L, 26L, 30L, 36L, 43L,
>>> 44L, 52L, 6L, 9L, 17L, 18L, 23L, 26L, 28L, 30L, 35L, 9L, 14L, 20L,
>>> 32L, 33L, 36L, 44L, 6L, 9L, 23L, 25L, 36L, 51L, 9L, 17L, 17L, 18L,
>>> 20L, 33L, 58L, 9L, 23L, 26L, 28L, 36L, 6L, 20L, 28L, 20L, 23L, 4L,
>>> 15L), Type = c("Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Irregular", "Regular", "Irregular", "Irregular",
>>> "Irregular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Irregular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Irregular", "Regular", "Regular",
>>> "Irregular", "Regular", "Irregular", "Regular", "Regular", "Regular",
>>> "Irregular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Irregular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Irregular",
>>> "Regular", "Regular", "Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Irregular", "Regular", "Irregular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Irregular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Irregular", "Regular", "Irregular",
>>> "Regular", "Regular", "Irregular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Irregular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Irregular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Irregular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Irregular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Irregular", "Regular", "Irregular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Irregular", "Irregular", "Irregular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Irregular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Irregular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Regular", "Regular", "Regular",
>>> "Irregular", "Regular", "Regular", "Regular", "Irregular", "Regular",
>>> "Regular", "Regular", "Regular", "Irregular", "Regular", "Regular",
>>> "Regular", "Regular", "Regular", "Irregular", "Regular", "Regular",
>>> "Regular", "Irregular", "Regular", "Regular"), Yes = c(0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L,
>>> 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L,
>>> 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 0L,
>>> 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L,
>>> 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L,
>>> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
>>> 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), No = c(1L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
>>> 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 0L, 1L, 1L, 1L, 1L,
>>> 2L, 1L, 1L, 1L, 1L, 1L, 3L, 0L, 1L, 1L, 1L, 1L, 1L, 5L, 1L, 1L, 1L,
>>> 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 3L, 1L, 2L, 1L, 1L,
>>> 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
>>> 3L, 1L, 2L, 2L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 0L, 1L, 1L, 1L, 2L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L,
>>> 1L, 1L, 3L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 2L, 1L, 1L, 1L, 1L, 0L, 0L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 5L, 1L, 1L, 0L, 3L,
>>> 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 3L, 2L, 1L, 2L, 0L, 1L, 1L, 1L, 0L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 0L, 1L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 0L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L,
>>> 0L, 1L, 1L, 1L, 0L, 1L, 2L, 1L, 1L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>>> 1L, 1L, 0L, 0L, 1L, 1L, 1L, 2L, 1L, 1L, 0L, 1L, 2L, 1L, 2L, 1L, 1L,
>>> 1L, 2L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L,
>>> 1L, 1L, 1L, 1L, 3L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L,
>>> 1L, 1L, 0L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 0L, 2L, 4L, 1L, 3L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>>> 2L, 2L, 2L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>>> 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L)),
>>> .Names = c("Age", "Times", "Type", "Yes", "No"), row.names = c(NA,
>>> -426L), class = "data.frame")
>>>
>>> Thansk a lot for your help.
>>>
>>>
>>> Lenny
>>>
>>>
>>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>>> Garanti
>>> sans virus. www.avg.com
>>>
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