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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 
## -18.9299  -6.7662  -0.7426   5.4136  19.4385 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 5658.2095  1712.2556   3.305  0.00394 **
## Year          -2.8058     0.8517  -3.294  0.00403 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.94 on 18 degrees of freedom
## Multiple R-squared:  0.3762, Adjusted R-squared:  0.3415 
## F-statistic: 10.85 on 1 and 18 DF,  p-value: 0.00403

Linear model fit for Fished Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.fished)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -29.80 -13.40  -0.21  11.30  50.49 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 10295.540   2429.301   4.238 0.000198 ***
## Year           -5.108      1.208  -4.227 0.000204 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.02 on 30 degrees of freedom
## Multiple R-squared:  0.3733, Adjusted R-squared:  0.3524 
## F-statistic: 17.87 on 1 and 30 DF,  p-value: 0.0002039

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   7330    7330  26.546 4.58e-06 ***
## Zone         1   1089    1089   3.945   0.0526 .  
## Residuals   49  13530     276                     
## ---
## 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   7329.872  1089.423 13530.074
## Deg. of Freedom         1         1        49
## 
## Residual standard error: 16.61698
## 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.