# [R] Linear Regression Question

Peter Ehlers ehlers at ucalgary.ca
Wed Oct 14 16:49:35 CEST 2009

```Alexandre,

Let me add two small points to Ted's exposition:

1. you can use the extractor function coefficients(),
or just coef() on the summary:

coef(summary(regression))

which will also give you the matrix of estimates, etc.

2. You will find that using the function str() often is

str(summary(regression))

or

str(coef(summary(regression)))

-Peter Ehlers

(Ted Harding) wrote:
> On 13-Oct-09 21:17:11, Alexandre Cohen wrote:
>> I am a student at MSc Probability and Finance at Paris 6 University/
>> Ecole Polytechnique. I am using R and I can't find an answer to the
>> following question. I will be very thankful if you can answer it.
>>
>> I have two vectors rendements_CAC40 and rendements_AlcatelLucent.
>> I use the lm function as follows, and then the sumarry function:
>>
>> regression=lm(rendements_CAC40 ~ rendements_AlcatelLucent);
>> sum=summarry(regression);
>>
>> I obtain:
>>
>> Call:
>> lm(formula = rendements_CAC40 ~ rendements_AlcatelLucent)
>>
>> Residuals:
>>       Min       1Q   Median       3Q      Max
>> -6.43940 -0.84170 -0.01124  0.76235  9.08087
>>
>> Coefficients:
>>                           Estimate Std. Error t value Pr(>|t|)
>> (Intercept)              -0.03579    0.07113  -0.503    0.615
>> rendements_AlcatelLucent  0.33951    0.01732  19.608   <2e-16 ***
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>> Residual standard error: 1.617 on 515 degrees of freedom
>> Multiple R-squared: 0.4274,   Adjusted R-squared: 0.4263
>> F-statistic: 384.5 on 1 and 515 DF,  p-value: < 2.2e-16
>>
>> I would like to access to the p-value field, but I can't find the name
>> of it, as we can see it below:
>>
>>  > names(sum)
>>   [1] "call"          "terms"         "residuals"     "coefficients"
>> "aliased"       "sigma"         "df"            "r.squared"
>>
>> I thought that I could find it in the fstatistic field, but it is not:
>>
>> sum\$fstatistic
>>     value    numdf    dendf
>> 384.4675   1.0000 515.0000
>>
>> Kind regards,
>> Alexandre Cohen
>
> Assuming you gave executed your code with "summary" correctly spelled
> (i.e. not "summarry" or "sumarry" as you have written above), then
> the information you require can be found in
>
>   sum\$coefficients
>
> which you can as well write as sum\$coef
>
> You will find that sum\$coef is an array with 4 columns ("Estimate",
> "Std. Error", "t value" and "Pr(>|t|)"), so the P-values are in the
> final column sum\$coef[,4].
>
> Emulating your calculation above with toy regression data:
>
>   X <- (0:10) ; Y <- 1.0 + 0.25*X + 2.5*rnorm(11)
>   regression <- lm(Y~X)
>   sum <- summary(regression)
>   sum
>   # Call:
>   # lm(formula = Y ~ X)
>   # Residuals:
>   #     Min      1Q  Median      3Q     Max
>   # -5.7182 -1.5383  0.2989  1.9806  3.9364
>   # Coefficients:
>   #             Estimate Std. Error t value Pr(>|t|)
>   # (Intercept)  2.10035    1.81418   1.158    0.277
>   # X           -0.03147    0.30665  -0.103    0.921
>   #
>   # Residual standard error: 3.216 on 9 degrees of freedom
>   # Multiple R-squared: 0.001169,   Adjusted R-squared: -0.1098
>   # F-statistic: 0.01053 on 1 and 9 DF,  p-value: 0.9205
>
>   sum\$coef
>   #               Estimate Std. Error    t value  Pr(>|t|)
>   # (Intercept)  2.1003505  1.8141796  1.1577412 0.2767698
>   # X           -0.0314672  0.3066523 -0.1026152 0.9205184
>
>   sum\$coef[,4]
>   # (Intercept)           X
>   #   0.2767698   0.9205184
>
> [And, by the way, although it in fact works, it is not a good idea
> to use a function name ("sum") as the name of a variable.]
>
> Hoping this helps,
> Ted.
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 14-Oct-09                                       Time: 10:53:28
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