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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 
## -3.2751 -1.3345  0.3004  1.0217  3.8312 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -816.5131   375.4574  -2.175   0.0450 *
## Year           0.4079     0.1868   2.184   0.0442 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.046 on 16 degrees of freedom
## Multiple R-squared:  0.2296, Adjusted R-squared:  0.1815 
## F-statistic: 4.769 on 1 and 16 DF,  p-value: 0.04422

Linear model fit for Fished Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.fished)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.4512 -3.1962 -2.3146 -0.7926 23.7572 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -863.8974   923.4928  -0.935    0.358
## Year           0.4317     0.4595   0.940    0.356
## 
## Residual standard error: 6.128 on 27 degrees of freedom
## Multiple R-squared:  0.03166,    Adjusted R-squared:  -0.004202 
## F-statistic: 0.8828 on 1 and 27 DF,  p-value: 0.3558

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   52.8   52.79   2.149  0.150
## Zone         1    2.2    2.25   0.092  0.764
## Residuals   44 1080.8   24.56
## Call:
##    aov(formula = Mean ~ Year + Zone, data = spp)
## 
## Terms:
##                      Year      Zone Residuals
## Sum of Squares    52.7939    2.2477 1080.8309
## Deg. of Freedom         1         1        44
## 
## Residual standard error: 4.956242
## 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.