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
## -6.9519 -2.2287 -0.4805 0.8539 6.7038
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 901.5581 659.7956 1.366 0.191
## Year -0.4452 0.3283 -1.356 0.194
##
## Residual standard error: 3.596 on 16 degrees of freedom
## Multiple R-squared: 0.1031, Adjusted R-squared: 0.04706
## F-statistic: 1.84 on 1 and 16 DF, p-value: 0.1938
Linear model fit for Fished Areas
##
## Call:
## lm(formula = Mean ~ Year, data = spp.fished)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.002 -5.186 -1.501 4.129 31.104
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2767.546 1477.353 1.873 0.0719 .
## Year -1.372 0.735 -1.867 0.0728 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.803 on 27 degrees of freedom
## Multiple R-squared: 0.1143, Adjusted R-squared: 0.08154
## F-statistic: 3.486 on 1 and 27 DF, p-value: 0.0728
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 1 301.2 301.19 4.629 0.037 *
## Zone 1 74.9 74.90 1.151 0.289
## Residuals 44 2863.0 65.07
## ---
## 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 301.1878 74.8988 2862.9649
## Deg. of Freedom 1 1 44
##
## Residual standard error: 8.066436
## 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.