# [R] summary vs anova

David Winsemius dwinsemius at comcast.net
Mon Dec 19 16:00:06 CET 2011

```On Dec 19, 2011, at 9:09 AM, Brent Pedersen wrote:

> Hi, I'm sure this is simple, but I haven't been able to find this in
> TFM,
> say I have some data in R like this (pasted here:
> http://pastebin.com/raw.php?i=sjS9Zkup):

One of the reason this is not in TFM is that these are questions that
should be available in any first course on regression textbook.

>
>    gender age smokes disease    Y
>  1 female  65   ever control 0.18
>  2 female  77  never control 0.12
>  3   male  40         state1 0.11
>  4 female  67   ever control 0.20
>  5   male  63   ever  state1 0.16
>  6 female  26  never  state1 0.13
>
> where unique(disease) == c("control", "state1", "state2")
> and unique(smokes) == c("ever", "never", "", "current")
>
> I then fit a linear model like:
>
>> model = lm(Y ~ smokes + disease + age + gender, data=df)
>
> And I want to understand the difference between:
>
>> print(summary(model))
>    Call:
>    lm(formula = Y ~ smokes + disease + age + gender, data = df)
>
>    Residuals:
>         Min       1Q   Median       3Q      Max
>    -0.22311 -0.08108 -0.03483  0.05604  0.46507
>
>    Coefficients:
>                    Estimate Std. Error t value Pr(>|t|)
>    (Intercept)    0.1206825  0.0521368   2.315   0.0211 *
>    smokescurrent  0.0150641  0.0444466   0.339   0.7348
>    smokesever     0.0498764  0.0326254   1.529   0.1271
>    smokesnever    0.0394109  0.0349142   1.129   0.2597
>    diseasestate1  0.0018739  0.0176817   0.106   0.9157
>    diseasestate2 -0.0009858  0.0178651  -0.055   0.9560
>    age            0.0002841  0.0006290   0.452   0.6518
>    gendermale     0.1164889  0.0128748   9.048   <2e-16 ***
>    ---
>    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
>    Residual standard error: 0.1257 on 397 degrees of freedom
>    Multiple R-squared: 0.1933, Adjusted R-squared: 0.1791
>    F-statistic: 13.59 on 7 and 397 DF,  p-value: 8.975e-16
>
> and:
>
>> anova(model)
>  Analysis of Variance Table
>
>  Response: Y
>             Df Sum Sq Mean Sq F value  Pr(>F)
>  smokes      3 0.1536 0.05120  3.2397 0.02215 *
>  disease     2 0.0129 0.00647  0.4096 0.66420
>  age         1 0.0431 0.04310  2.7270 0.09946 .
>  gender      1 1.2937 1.29373 81.8634 < 2e-16 ***
>  Residuals 397 6.2740 0.01580
>  ---
>  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> I understand (hopefully correctly) that anova() tests by adding each
> covariate
> to the model in order it is specified in the formula.

>
> More specific questions are:

All of which are general statistics questions which you are asked to
post in forums or lists that expect such questions ... and not to r-
help.

>
> 1) How do the p-values for smokes* in summary(model) relate to the
>   Pr(>F) for smokes in anova
> 2) what do the p-values for each of those smokes* mean exactly?
> 3) the summary above shows the values for diseasestate1 and
> diseasestate2
>   how can I get the p-value for diseasecontrol? (or, e.g.
> genderfemale)
>
>
> ^^^^^^^^^^^^^^^^^^^^^^^