# Further analysis of significant interaction between a covariate and independent variable

I am studying to see if there are differences in mussel feeding ability (CR) based on 10 different food types (Taxa) and water source (Treatment) using the covariates shell length (SL) and Initial food concentration (lin <-I log transformed it).

wayancova<-aov(sqrt(CR)~SL+Treatment+lin*Taxa,data=blanks,na.action=na.omit)

Df Sum Sq Mean Sq F value  Pr(>F)
SL            1   4.61   4.608   4.286 0.03991 *
Treatment     1   1.46   1.463   1.360 0.24506
lin           1   3.05   3.045   2.832 0.09419 .
Taxa          9  16.37   1.818   1.691 0.09422 .
lin:Taxa      9  28.61   3.179   2.956 0.00271 **
Residuals   174 187.08   1.075

I do not have an interaction between Treatment and the other factors because they were found to not have a significant interaction so I turned it into an additive model. I had a significant interaction between the covariate Initial concentration and independent variable Taxa (which suggests it is an unequal slopes model).

My advisor now wants me to find which of these interactions are significantly different from each other. I ran a linear regression for each taxa

CentricCR<-lm(sqrt(CR)~SL+log(Initial),data=LRcentric)

I am now attempting to use this code to compare the lsmeans of the interaction, but am very uncertain if this is the right coding.

leastsquare<-lsmeans(wayancova,pairwise ~ **Taxa:lin**, adjust = "tukey")
leastsquare\$contrasts
cld(leastsquare)

I suppose my questions would be, is this the correct approach and methodology to interpreting an ANCOVA, and will my lsmeans coding answer which slopes are different?