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.