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I am doing a multiple regression to predict average sizes of fish between areas protected from fishing and areas open to fishing. The model also takes into account habitat parameters which are the other variables (log.comp2 + rugosity). This model was the best according to AIC. log(size) transformation was used to normalize data.

mtar <- glm(log(size) ~ log.comp2 + rugosity + protection + log.comp2:protection, tar, family = "gaussian")

The output for summary(mtar) shows no significant difference for protection:

                             Estimate Std. Error t value Pr(>|t|)    
(Intercept)                  3.370952   0.022943 146.928  < 2e-16 ***
log.comp2                    0.132060   0.028386   4.652 3.48e-06 ***
rugosity                    -0.108574   0.008749 -12.410  < 2e-16 ***
protectionNo-take           -0.005873   0.023595  -0.249  0.80346    
log.comp2:protectionNo-take  0.125109   0.039544   3.164  0.00158 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.05726864)

    Null deviance: 139.63  on 2192  degrees of freedom
Residual deviance: 125.30  on 2188  degrees of freedom
AIC: -41.526

but the graph shows clear differences: enter image description here

How can I interpret this?

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  • $\begingroup$ I see no inconsistency between the output and the graphs. What specific aspect of these two bothers you? $\endgroup$
    – whuber ♦
    Commented Jan 14, 2021 at 17:29
  • $\begingroup$ Given the present and significant interaction, the main effect of protection is probably not worth interrogation $\endgroup$
    – JTH
    Commented Jan 14, 2021 at 20:23

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