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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 
## -1.30323 -0.33671 -0.06455  0.13681  2.73429 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 386.55002  150.10432   2.575   0.0203 *
## Year         -0.19201    0.07468  -2.571   0.0205 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8181 on 16 degrees of freedom
## Multiple R-squared:  0.2924, Adjusted R-squared:  0.2481 
## F-statistic: 6.611 on 1 and 16 DF,  p-value: 0.02051

Linear model fit for Fished Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.fished)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2750 -0.5682 -0.0875  0.2692  2.6729 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 608.06015  135.15160   4.499 0.000117 ***
## Year         -0.30209    0.06724  -4.493 0.000119 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8968 on 27 degrees of freedom
## Multiple R-squared:  0.4278, Adjusted R-squared:  0.4066 
## F-statistic: 20.18 on 1 and 27 DF,  p-value: 0.0001191

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  19.89  19.890  26.290 6.32e-06 ***
## Zone         1   0.71   0.712   0.941    0.337    
## Residuals   44  33.29   0.757                     
## ---
## 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  19.89018  0.71222  33.28929
## Deg. of Freedom        1        1        44
## 
## Residual standard error: 0.869813
## 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.