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Comparison of the regression slopes by means of an ANCOVA.

Plot of the linear model fit for both Zones

Linear model fit for Reserve Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.reserve)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.52530 -0.80100  0.01721  0.74799  1.74001 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 302.18359  190.28078   1.588    0.132
## Year         -0.14949    0.09467  -1.579    0.134
## 
## Residual standard error: 1.037 on 16 degrees of freedom
## Multiple R-squared:  0.1348, Adjusted R-squared:  0.08077 
## F-statistic: 2.494 on 1 and 16 DF,  p-value: 0.1339

Linear model fit for Fished Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.fished)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.4014 -1.5720 -0.5264  0.9072  5.5708 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) 491.1738   332.7326   1.476    0.151
## Year         -0.2431     0.1655  -1.468    0.154
## 
## Residual standard error: 2.208 on 27 degrees of freedom
## Multiple R-squared:  0.07394,    Adjusted R-squared:  0.03964 
## F-statistic: 2.156 on 1 and 27 DF,  p-value: 0.1536

ANCOVA model, the “Mean abundnace” is modeled as the dependent variable with “Zone (Fished or Reserve)” as the factor and Year as the covariate. The summary of the results show a significant effect of Year, but no significant interaction. These results suggest that the slope of the regression between Year-mean at both Fished and Reserve areas is similar.

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Year         1  12.85  12.854   3.785 0.0581 .
## Zone         1   9.24   9.243   2.721 0.1061  
## Residuals   44 149.44   3.396                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Call:
##    aov(formula = Mean ~ Year + Zone, data = spp)
## 
## Terms:
##                      Year      Zone Residuals
## Sum of Squares   12.85366   9.24273 149.43987
## Deg. of Freedom         1         1        44
## 
## Residual standard error: 1.842922
## Estimated effects may be unbalanced

Compare the residuals

Standard model validation graphs are (i) residuals versus fitted values to verify homogeneity, (ii) a QQ-plot or histogram of the residuals for normality, and (iii) residuals versus each explanatory variable to check independence and (iv) Residuals versus Year

Reserves, Fished.