# Multiple Linear Regression Output Interpretation for Categorical Variables

I'm a bit confused on interpreting the coefficient estimates for a multiple linear regression model with categorical variables and their interaction. The dependent variable is pesticide levels (DDE ng/g) in songbirds. The independent variables are Status (migrant vs resident) and location (Texas, Yucatan & Costa Rica). After running the model, I found that the interaction between status and location is significant so I created interaction plots. Here is the output from R:

summary(DDE.fit6)
##
## Call:
## lm(formula = log10(DDE) ~ Location + Status + Location * Status,
##     data = DDE.dat)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -0.79797 -0.22059 -0.02851  0.20203  1.45538
##
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)
## (Intercept)                      1.3662     0.1224  11.162  < 2e-16 ***
## LocationTexas                    0.4376     0.1324   3.306  0.00122 **
## LocationYucatan                  0.4033     0.1603   2.517  0.01304 *
## StatusResident                  -0.8308     0.1542  -5.386 3.16e-07 ***
## LocationTexas:StatusResident     1.0407     0.1770   5.880 3.14e-08 ***
## LocationYucatan:StatusResident   0.4633     0.2261   2.049  0.04247 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#**#
## Residual standard error: 0.387 on 133 degrees of freedom
## Multiple R-squared:  0.5843, Adjusted R-squared:  0.5686
## F-statistic: 37.38 on 5 and 133 DF,  p-value: < 2.2e-16**


Is the intercept the mean DDE level for Costa Rica (reference group)? Is LocationTexas the slope between Costa Rica and Texas for all groups?? Is StatusResident the slope between all migrants and residents? How do I get the coefficient estimates from the interaction plots? Thanks in advance!

Is the intercept the mean DDE level for Costa Rica (reference group)?

Nope. Costa Rica is not your reference group. You have two categorical variables. For Location, reference level is Costa Rica, for Status, reference level is Migrant. So your reference group are Migrants from Costa Rica. Intercept is mean log(DDE) in this group.

Is LocationTexas the slope between Costa Rica and Texas for all groups?

Nope. It is a difference between Costa Rica and Texas for Migrants (as this is reference group for Status). If you wish to have difference between Costa Rica and Texas for Residents, look at interaction LocationTexas:StatusResident parameter. It is 1.0407. You have to add it to LocationTexas parameter. So difference between Costa Rica and Texas for Residents is 0.4376+1.0407

Is StatusResident the slope between all migrants and residents?

Similarly, it is the difference between Costa Rica's migrants and residents.

How do I get the coefficient estimates from the interaction plots?

Look at explanation how to calculate difference between Costa Rica and Texas for Residents few lines above. On the interaction plot, you have this difference ready to read. All you need to do is to reverse the reasoning.