Means of different groups in ANCOVA with 2 factors R - r

Question

I am currently studying the influence of different traits on the shell volume of a snail.
I have a dataframe, where each line represents a given individual, and several columns with all its attributes (length, shell volume, sex, infection).
I made the ANCOVA: mod=aov(log(volume) ~ infection*sex*log(length)).
I got this:
Df Sum Sq Mean Sq F value Pr(>F)
inf 1 4.896 4.896 258.126 <2e-16 ***
sex 1 3.653 3.653 192.564 <2e-16 ***
log(length) 1 14.556 14.556 767.335 <2e-16 ***
inf:sex 1 0.028 0.028 1.472 0.227
inf:log(length) 1 0.020 0.020 1.064 0.304
sex:log(length) 1 0.001 0.001 0.076 0.783
inf:sex:log(length) 1 0.010 0.010 0.522 0.471
Residuals 174 3.301 0.019
So significant effects of sex, infection and length, but no interaction terms.
Since there are no interactions, I would like to know, for a given sex, whether the intercept of log(volume) = f(log(length)) is bigger for infected individuals or uninfected individuals.
I tried to use summary.lm(mod), which gave me this:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.42806 0.15429 -2.774 0.00613 **
infmic -0.54963 0.40895 -1.344 0.18070
sexM -0.11542 0.35508 -0.325 0.74554
log(length) 2.41915 0.11144 21.709 < 2e-16 ***
infmic:sexM 0.52459 0.63956 0.820 0.41320
infmic:log(length) 0.43215 0.33717 1.282 0.20166
sexM:log(length) 0.04207 0.28113 0.150 0.88122
infmic:sexM:log(length) -0.38222 0.52920 -0.722 0.47110
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1377 on 174 degrees of freedom
Multiple R-squared: 0.8753, Adjusted R-squared: 0.8703
F-statistic: 174.5 on 7 and 174 DF, p-value: < 2.2e-16
But I have trouble interpreting the results, and still don't see how to conclude.
I also have "few" other questions:
Why aren't sex and infection significant in the lm output?
I know it is not significant here,but how to interpret the lines about the interaction terms?
What I think is that infmic:sexM represents the change in the slope of log(volume)=f(log(length)) for infected males compared with uninfected females. Then, would infmic:length be the change of slope between infected females and uninfected females? And sexM:length the change between uninfected males and uninfected females? Is this true?
And what does the triple interaction term represent?
Thanks a lot!

Answer 1

EDIT: I found part of the answer.
Let's split the data in 4 groups (F-NI, F-I, M-NI, M-I), and look for the equation of the regression line log(volume) = f(log(length)) for each of these groups. Here, the coefficients are the ones given by the function summary.lm(mod)
The equations are:
For non-infected females:log(volume) = (Intercept) + log(length)
For infected females:log(volume) = (Intercept) + infmic + log(length) + infmic:log(length)
For non-infected males:log(volume) = (Intercept) + sexM + log(length) + sexM:log(length)
For infected males:log(volume) = (Intercept) + infmic + sexM + infmic:sexM + log(length) + infmic:log(length) + sexM:log(length) + infmic:sexM:log(length)
For each equation, the slope is the part that starts with log(length), and the intercept is the part before.
It might be obvious for some of you, but I really didn't understand what each coefficient represented at first, so I prefer to put it here!
Alice