R- Analysis of homogeneity of slopes

Question

I´d like to analyse the effect of a treatment (treatment : Factor w/ 2 levels "ambient","elevated") in tree diameter increment. Tree diameter is influenced by tree size. To do so, I performed the following lm:

Call:
lm(formula = BAI2013 ~ diameterJul12 * treatment, data = bandNA)

Residuals:
     Min       1Q   Median       3Q      Max 
-16.6493  -3.1740  -0.3767   3.3631  22.7267 

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)                     -20.49357    2.12883  -9.627  < 2e-16 ***
diameterJul12                     1.24194    0.08876  13.992  < 2e-16 ***
treatmentelevated                10.72336    3.45783   3.101 0.002295 ** 
diameterJul12:treatmentelevated  -0.54953    0.14795  -3.714 0.000285 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.461 on 153 degrees of freedom
Multiple R-squared:  0.6035,    Adjusted R-squared:  0.5958 
F-statistic: 77.63 on 3 and 153 DF,  p-value: < 2.2e-16

How can I interpret the results? I need to figure out whether the slope of BAI~diameter is steeper for elevated trees than for ambient. Thanks

Answer 1

The maximum likelihood fitted model is

BAI2013 = 1.24194 * diameterJul12 + 10.72336 * treatmentelevated - 0.54953 * diameterJul12 * treatmentelevated - 20.49357

Here treatmentelevated is a binary variable which is 1 for "elevated". All terms have significant p-values (these come from Wald statistics) suggesting they should be kept in the model. The interaction term is negative suggesting the slope of BAI~diameter is less steep (by 0.54953) in the elevated treatment group.