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.