suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(ggplot2))
suppressPackageStartupMessages(library(Rcmdr))
suppressPackageStartupMessages(library(mvabund))
Problem 1
fish <- read.csv("fish.csv", header=TRUE)
fish
## density width flow temp
## 1 8 25.0 1.2 15.7
## 2 12 26.0 0.6 18.0
## 3 18 25.5 2.0 12.2
## 4 25 17.8 0.9 14.0
## 5 32 19.0 1.0 12.0
## 6 39 23.0 1.8 13.7
## 7 40 17.0 3.0 13.2
## 8 44 15.9 2.0 11.9
## 9 46 12.0 1.4 11.9
## 10 49 10.2 0.5 19.7
## 11 63 12.0 4.0 12.0
## 12 66 16.3 6.0 9.7
## 13 67 9.0 2.0 11.9
## 14 76 7.9 2.4 10.5
## 15 89 6.0 4.8 10.6
## 16 105 7.0 4.5 11.4
## 17 118 5.0 3.0 10.6
## 18 123 5.9 5.0 9.9
## 19 137 5.5 5.7 10.5
## 20 150 3.6 7.9 8.4
pairs(fish)
fish_standardized <- fish %>% mutate(
density = (density - mean(density))/sd(density),
width = (width - mean(width))/sd(width),
flow = (flow - mean(flow))/sd(flow),
temp = (temp - mean(temp))/sd(temp)
)
qqnorm(fish_standardized$density, xlab="Normal Scores", ylab="Standardized Residuals")
qqline(fish_standardized$density)
qqnorm(fish_standardized$width, xlab="Normal Scores", ylab="Standardized Residuals")
qqline(fish_standardized$width)
qqnorm(fish_standardized$flow, xlab="Normal Scores", ylab="Standardized Residuals")
qqline(fish_standardized$width)
qqnorm(fish_standardized$temp, xlab="Normal Scores", ylab="Standardized Residuals")
qqline(fish_standardized$width)
model1 <- lm(density~width+flow+temp, fish_standardized)
summary(model1)
##
## Call:
## lm(formula = density ~ width + flow + temp, data = fish_standardized)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45154 -0.17320 -0.05179 0.17136 0.52824
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.037e-16 7.099e-02 0.000 1.00000
## width -6.218e-01 9.356e-02 -6.646 5.62e-06 ***
## flow 4.377e-01 1.175e-01 3.725 0.00184 **
## temp -2.974e-03 1.113e-01 -0.027 0.97902
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3175 on 16 degrees of freedom
## Multiple R-squared: 0.9151, Adjusted R-squared: 0.8992
## F-statistic: 57.5 on 3 and 16 DF, p-value: 8.651e-09
plot(model1$fitted, resid(model1), ylab="Residuals", xlab="Fitted")
Problem 2
snails <- read.csv("snails.csv", header=TRUE)
snails
## mass diameter
## 1 31.7 51.8
## 2 29.8 46.6
## 3 23.7 41.1
## 4 17.7 50.0
## 5 21.6 44.6
## 6 10.0 38.7
## 7 13.8 37.0
## 8 3.8 24.3
## 9 23.6 47.2
## 10 36.9 55.5
## 11 21.3 44.0
## 12 11.3 33.4
## 13 13.4 35.4
## 14 22.0 42.4
## 15 39.4 49.7
## 16 20.0 48.8
## 17 33.9 59.0
## 18 26.6 43.0
## 19 6.0 27.0
## 20 0.9 16.0
## 21 12.2 34.7
## 22 7.1 33.3
## 23 9.1 34.8
## 24 26.4 47.5
pairs(snails)
model2 <- lm(mass~diameter, snails)
summary(model2)
##
## Call:
## lm(formula = mass ~ diameter, data = snails)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.9940 -1.7802 -0.5993 2.7303 11.9895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -19.5648 4.2398 -4.615 0.000134 ***
## diameter 0.9452 0.1003 9.420 3.54e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.87 on 22 degrees of freedom
## Multiple R-squared: 0.8013, Adjusted R-squared: 0.7923
## F-statistic: 88.73 on 1 and 22 DF, p-value: 3.543e-09
plot(model2$fitted, resid(model2), ylab="Residuals", xlab="Fitted")
model3 <- lm(diameter~mass, snails)
summary(model3)
##
## Call:
## lm(formula = diameter ~ mass, data = snails)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.511 -2.979 -0.107 2.364 10.246
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.7479 1.9726 12.55 1.68e-11 ***
## mass 0.8478 0.0900 9.42 3.54e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.613 on 22 degrees of freedom
## Multiple R-squared: 0.8013, Adjusted R-squared: 0.7923
## F-statistic: 88.73 on 1 and 22 DF, p-value: 3.543e-09
plot(model3$fitted, resid(model3), ylab="Residuals", xlab="Fitted")
Problem 3
voles <- read.csv("vole.csv", header=TRUE)
voles$vole <- NULL
#voles$mass <- factor(voles$mass)
pairs(voles)
# meanvar.plot(voles$rate~voles$mass)
# meanvar.plot(voles$log_rate~voles$mass)
leveneTest(rate~factor(voles$mass),voles)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 1.3364 0.2976
## 16
model4 <- lm(rate~mass,voles)
summary(model4)
##
## Call:
## lm(formula = rate ~ mass, data = voles)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.846 -18.835 -2.575 16.263 66.477
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -41.3659 19.2337 -2.151 0.0453 *
## mass 8.6493 0.8548 10.118 7.45e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28.27 on 18 degrees of freedom
## Multiple R-squared: 0.8505, Adjusted R-squared: 0.8422
## F-statistic: 102.4 on 1 and 18 DF, p-value: 7.452e-09
plot(model4$fitted, resid(model4), ylab="Residuals", xlab="Fitted")
