# Reporting linear regression with Post-hoc comparisons

I have a quantitative variable (Dim: which is actually factor scores) and 2 categorical variables (Category + Region) in my dataset. I am interested in knowing if the variance explained by each categorical variable (and their interaction) is significant. Additionally I also want to know how much overall variance is explained by the model (i.e. the R squared value). After consulting materials about this topic I came to know that following 2 commands in R can fulfill my requirements.

my_lm <- lm(Dim4 ~ Category*Region, data=df)
summary(my_lm)
Anova(my_lm, type = "III")

I'm also interested in reporting whether group comparisons within each category are significantly different from each other. For this purpose, TukeyHSD has been mentioned in the reference material.

TukeyHSD(aov(my_lm), ordered=TRUE)

This command outputs the whole range of group comparisons for example:

$Category diff lwr upr p adj Tweets-Conversations 0.6843803 -0.279052730 1.647813 0.2961601 Comments-Conversations 1.6552203 0.665253423 2.645187 0.0000540$Region