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.