Analysis of possum
bodyweight data
poss <- possum
poss$region <- factor(poss$Location)
levels(poss$region) <- c("W.A", "S.A", "N.T", "QuL", "NSW", "Vic", "Tas")
colnames(poss)<-c("y","z","Location", "x")
head(poss)
## y z Location x
## 1 3.5 89.0 1 W.A
## 2 3.3 91.5 1 W.A
## 3 3.5 95.5 1 W.A
## 4 3.1 92.0 1 W.A
## 5 2.8 85.5 1 W.A
## 6 3.0 90.5 1 W.A
# Draw side by side boxplots
boxplot(y~x, data=poss, col=2:8, xlab="region", ylab="Weight")
![](data:image/png;base64,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)
# Obtain scatter plot
# Start with a skeleton plot
plot(poss$z, poss$y, type="n", xlab="Length", ylab="Weight")
# Add points for the seven regions
for (i in 1:7) {
points(poss$z[poss$Location==i],poss$y[poss$Location==i],type="p", pch=as.character(i), col=i)
}
## Add legends
legend(x=76, y=4.2, legend=paste(as.character(1:7), levels(poss$x)), lty=1:7, col=1:7)
![](data:image/png;base64,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)
# Start modelling
#Fit the model with interaction.
poss.lm1<-lm(y~z+x+z:x,data=poss)
summary(poss.lm1)
##
## Call:
## lm(formula = y ~ z + x + z:x, data = poss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.67953 -0.15793 0.01999 0.14591 0.78255
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.5842639 1.5008154 -2.388 0.0191 *
## z 0.0748795 0.0167202 4.478 2.27e-05 ***
## xS.A 0.3283443 2.3839136 0.138 0.8908
## xN.T 6.0527549 3.3898871 1.786 0.0777 .
## xQuL -5.9670098 4.5482536 -1.312 0.1930
## xNSW -2.4035332 2.7983463 -0.859 0.3927
## xVic 0.8984502 2.4135144 0.372 0.7106
## xTas -0.1263706 2.4142962 -0.052 0.9584
## z:xS.A -0.0031036 0.0280484 -0.111 0.9121
## z:xN.T -0.0675469 0.0383301 -1.762 0.0815 .
## z:xQuL 0.0663129 0.0494622 1.341 0.1835
## z:xNSW 0.0256881 0.0318912 0.805 0.4227
## z:xVic -0.0141738 0.0279034 -0.508 0.6128
## z:xTas -0.0003129 0.0276672 -0.011 0.9910
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2828 on 87 degrees of freedom
## Multiple R-squared: 0.6731, Adjusted R-squared: 0.6243
## F-statistic: 13.78 on 13 and 87 DF, p-value: 4.8e-16
plot(poss$z, poss$y,type="n", xlab="Length", ylab="Weight")
for (i in 1:7) {
lines(poss$z[poss$Location==i],poss.lm1$fit[poss$Location==i],type="l",
lty=i, col=i, lwd=1.8)
points(poss$z[poss$Location==i],poss$y[poss$Location==i],type="p",
pch=as.character(i), col=i)
}
poss.lm0 <- lm(y~z,data=poss)
abline(poss.lm0, lwd=3, col=9)
# Has drawn the seven parallel regression lines
legend(x=76, y=4.2, legend=paste(as.character(1:7), levels(poss$x)),
lty=1:7, col=1:7)
![](data:image/png;base64,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)
n <- length(possum$Body_Weight)
# Wrong model since Location is not a numeric covariate
wrong.lm <- lm(Body_Weight~Location, data=possum)
summary(wrong.lm)
##
## Call:
## lm(formula = Body_Weight ~ Location, data = possum)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.20753 -0.21060 0.01309 0.21309 1.35124
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.16630 0.07740 40.910 < 2e-16 ***
## Location -0.07939 0.01801 -4.409 2.64e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4239 on 99 degrees of freedom
## Multiple R-squared: 0.1641, Adjusted R-squared: 0.1557
## F-statistic: 19.44 on 1 and 99 DF, p-value: 2.643e-05
nis <- table(possum$Location)
meanwts <- tapply(possum$Body_Weight, possum$Location, mean)
varwts <- tapply(possum$Body_Weight, possum$Location, var)
datasums <- data.frame(nis=nis, mean=meanwts, var=varwts)
datasums <- data.frame(nis=nis, mean=meanwts, var=varwts)
modelss <- sum(datasums[,2] * (meanwts - mean(meanwts))^2)
residss <- sum( (datasums[,2] - 1) * varwts)
fvalue <- (modelss/6) / (residss/94)
fcritical <- qf(0.95, df1= 6, df2=94)
x <- seq(from=0, to=12, length=200)
y <- df(x, df1=6, df2=94)
plot(x, y, type="l", xlab="", ylab="Density of F(6, 94)", col=4)
abline(v=fcritical, lty=3, col=3)
abline(v=fvalue, lty=2, col=2)
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)
pvalue <- 1-pf(fvalue, df1=6, df2=94)
### Doing the above in R
# Convert the Location column to a factor
possum$Location <- as.factor(possum$Location)
summary(possum) # Now Location is a factor
## Body_Weight Length Location
## Min. :1.80 Min. :75.00 1:33
## 1st Qu.:2.60 1st Qu.:84.00 2:12
## Median :2.80 Median :88.00 3: 7
## Mean :2.88 Mean :87.16 4: 6
## 3rd Qu.:3.20 3rd Qu.:90.00 5:13
## Max. :4.20 Max. :96.50 6:13
## 7:17
# Put the identifiability constraint:
options(contrasts=c("contr.treatment", "contr.poly"))
colnames(possum) <- c("y", "z", "x")
# Fit model M1
possum.lm1 <- lm(y~x, data=possum)
summary(possum.lm1)
##
## Call:
## lm(formula = y ~ x, data = possum)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.84167 -0.23333 0.01765 0.21765 0.96667
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.13333 0.06402 48.943 < 2e-16 ***
## x2 -0.49167 0.12397 -3.966 0.000143 ***
## x3 -0.01905 0.15304 -0.124 0.901214
## x4 0.33333 0.16322 2.042 0.043929 *
## x5 -0.37949 0.12043 -3.151 0.002182 **
## x6 -0.68718 0.12043 -5.706 1.34e-07 ***
## x7 -0.45098 0.10979 -4.108 8.53e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3678 on 94 degrees of freedom
## Multiple R-squared: 0.4026, Adjusted R-squared: 0.3644
## F-statistic: 10.56 on 6 and 94 DF, p-value: 6.204e-09
anova(possum.lm1)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 6 8.5667 1.42778 10.556 6.204e-09 ***
## Residuals 94 12.7137 0.13525
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
possum.lm2 <- lm(y~z, data=poss)
summary(possum.lm2)
##
## Call:
## lm(formula = y ~ z, data = poss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.77843 -0.19072 -0.02632 0.20928 0.82708
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.284148 0.633108 -6.767 9.36e-10 ***
## z 0.082202 0.007256 11.329 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3059 on 99 degrees of freedom
## Multiple R-squared: 0.5646, Adjusted R-squared: 0.5602
## F-statistic: 128.4 on 1 and 99 DF, p-value: < 2.2e-16
anova(possum.lm2)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## z 1 12.0139 12.0139 128.35 < 2.2e-16 ***
## Residuals 99 9.2665 0.0936
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Include both location and length but no interaction
possum.lm3 <- lm(y~x+z, data=poss)
summary(possum.lm3)
##
## Call:
## lm(formula = y ~ x + z, data = poss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.67242 -0.19970 0.01845 0.17516 0.78209
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.390403 0.816320 -4.153 7.27e-05 ***
## xS.A 0.057028 0.117868 0.484 0.62964
## xN.T 0.100261 0.119312 0.840 0.40288
## xQuL 0.152418 0.128260 1.188 0.23772
## xNSW -0.176672 0.096536 -1.830 0.07044 .
## xVic -0.310958 0.104334 -2.980 0.00367 **
## xTas -0.161791 0.092289 -1.753 0.08288 .
## z 0.072719 0.009083 8.006 3.29e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2845 on 93 degrees of freedom
## Multiple R-squared: 0.6463, Adjusted R-squared: 0.6197
## F-statistic: 24.28 on 7 and 93 DF, p-value: < 2.2e-16
anova(possum.lm3)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 6 8.5667 1.4278 17.643 1.521e-13 ***
## z 1 5.1876 5.1876 64.102 3.287e-12 ***
## Residuals 93 7.5262 0.0809
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Include interaction effect
possum.lm4 <- lm(y~x+z+x:z, data=poss)
summary(possum.lm4)
##
## Call:
## lm(formula = y ~ x + z + x:z, data = poss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.67953 -0.15793 0.01999 0.14591 0.78255
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.5842639 1.5008154 -2.388 0.0191 *
## xS.A 0.3283443 2.3839136 0.138 0.8908
## xN.T 6.0527549 3.3898871 1.786 0.0777 .
## xQuL -5.9670098 4.5482536 -1.312 0.1930
## xNSW -2.4035332 2.7983463 -0.859 0.3927
## xVic 0.8984502 2.4135144 0.372 0.7106
## xTas -0.1263706 2.4142962 -0.052 0.9584
## z 0.0748795 0.0167202 4.478 2.27e-05 ***
## xS.A:z -0.0031036 0.0280484 -0.111 0.9121
## xN.T:z -0.0675469 0.0383301 -1.762 0.0815 .
## xQuL:z 0.0663129 0.0494622 1.341 0.1835
## xNSW:z 0.0256881 0.0318912 0.805 0.4227
## xVic:z -0.0141738 0.0279034 -0.508 0.6128
## xTas:z -0.0003129 0.0276672 -0.011 0.9910
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2828 on 87 degrees of freedom
## Multiple R-squared: 0.6731, Adjusted R-squared: 0.6243
## F-statistic: 13.78 on 13 and 87 DF, p-value: 4.8e-16
anova(possum.lm4)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 6 8.5667 1.4278 17.8561 2.194e-13 ***
## z 1 5.1876 5.1876 64.8768 3.833e-12 ***
## x:z 6 0.5696 0.0949 1.1873 0.3206
## Residuals 87 6.9565 0.0800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(possum.lm2, possum.lm3)
## Analysis of Variance Table
##
## Model 1: y ~ z
## Model 2: y ~ x + z
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 99 9.2665
## 2 93 7.5262 6 1.7404 3.5842 0.003065 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Check the diagnostics for M3
plot(possum.lm3$fit, possum.lm3$res,xlab="Fitted values",ylab="Residuals",
main="Anscombe plot")
abline(h=0)
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)
qqnorm(possum.lm3$res,main="Normal probability plot")
qqline(possum.lm3$res)
![](data:image/png;base64,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)
Analysis of gas mileage
data
summary(gasmileage)
## mileage model
## Min. :22.00 Length:11
## 1st Qu.:24.00 Class :character
## Median :27.00 Mode :character
## Mean :26.55
## 3rd Qu.:28.50
## Max. :32.00
y <- c(22, 26, 28, 24, 29, 29, 32, 28, 23, 24)
xx <- c(1,1,2,2,2,3,3,3,4,4)
# Plot the observations
plot(xx, y, col="red", pch="*", xlab="Model", ylab="Mileage")
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAHgCAIAAAD17khjAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAgAElEQVR4nO3daVhUV4LG8VNSWKKgAWUTtCM0iqKtEZeASgbQeWxENA/o2IIGN9C0LK2oiWNMqwRiFOhAjEuMS4xRW02I66QNbaKxjcrEiWnzoOIKokhAEVlCF9Z8qG6GIaKlYt1bh//vU3FOLe/lHnyrblVdNQaDQQAAALm0UjoAAABofhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJKRVOoD5zJ079+uvv1Y6BQCgBbGxsdm1a5ezs7P5H7oFFfzf/va32bNn9+nTR+kgAICW4ne/+11xcTEF/8x5e3v7+voqnQIA0FLY2Ngo9dAqeg++rq7u8uXLNTU1jcZramqKi4sViQQAgIVSRcHr9frFixfb2dl5eHg4ODgsWLCgrq6ufnbHjh0uLi4KxgMAwOKo4hB9RkZGampqQkKCn5/fsWPH0tPTS0pKNmzYoHQuAAAslSoKfv369fPmzUtJSRFChIeH+/r6RkVFjR07NiwsTOloAABYJFUcor9+/frQoUPrf4yMjIyKikpMTPzl+/EAAMAUqij4Xr165eTkNBxJS0urrKxMSkpSKhIAABZNFYfoJ02aFB8fr9frQ0NDAwICdDqdk5PTxo0bw8LCKioqXF1dlQ4IoGXLyhKFhWL5cqVzAI9BFQUfFxdXXl6+YsWKzMzM/Px8T09PIURISEh2dnZsbGxRUZHSAQG0VHl5Ii1N6HSirEwkJIiICDFsmNKZAJOoouCFEIsWLZo/f35hYaGbm1v9YGho6NWrV48cOXLhwgVT7iQ/P3/9+vVNzZ47d+7GjRvNkBVAy+HsLIYMEQsXiooKsWKF8PJSOhBgKrUUvBCidevWHh4eDUeqqqratm0bFBQUFBRkyj20adPG3t6+qdmqqioOBgB4PPb2wtZWuLmJzp1FdbXgnBywHGop+EOHDn3yySdVVVVhYWGRkZFpaWmrV6++ePFily5dFi1aFBMTY8qduLu7L1iwoKnZ5ORknU7XfJEBtAwuLmLzZuHgIE6eVDoK8BhUUfA7d+4cP368t7e3k5PTjBkzcnNzV61aNXv2bB8fn+PHj8+aNat9+/YTJkxQOiaAFqn+S7ycmQMWRRUFn5qaOnXq1PXr12s0moMHD4aEhMyfP3/58uVCiGnTpnXo0CE9PZ2CBwDAdKr4Hvz58+fHjRun0WiEECNHjtTpdH5+fvWzI0aMyMvLUy4dAACWRxUF36lTp/oK12g077zzTt++fetnb9y40fCj9QAA4JFUcYh+zJgxixcv7tixo7+/v6enZ3x8vHHcYDCcOnVq2bJlwcHByiYEAMCyqOIV/FtvvTVmzJhXXnll+vTpDcdDQ0MHDx7s6uqanp6uVDYAACyRKgre1tZ2y5Ytt2/fXrduXcPxKVOmHDhw4KuvvrKzs1MqGwAAlkgVh+iNOnTo0KFDh4YjERERSoUBAMCiqeIVPAAAaF4UPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkpFU6QGO1tbV37961srKyt7dXOgsAAJZKLa/gCwoK/vM//9PDw6NNmzaOjo4ODg5t2rTx8vJ6/fXXL1++rHQ6AAAsjCpewZ8+fXro0KEdO3YMDQ319vZ2cHAwGAx37tw5f/78n//857Vr1x4+fLhv375KxwQAwGKoouDnzJnz0ksv7d6928bGptFURkbG5MmTk5KSDh06pEg2AAAskSoO0X/33XfTpk37ZbsLIbRa7auvvpqbm2v+VAAAWC5VFHz37t3/+te/NjWbk5PTo0cPc+YBAMDSqeIQ/WuvvTZu3LjLly9HRET07NnT3t5eo9EY34PPzs7+/PPPd+zYoXRGAAAsiSoKPjw8fO/evWlpadOmTWs4rtFoAgMD9+7d+9vf/lapbAAAWCJVFLwQYtSoUaNGjbp9+3ZRUdGNGzeEEM7Ozm5ubg4ODqbfyU8//ZSdnX3//v0Hzur1er1e3zxxAQBQN7UUvJG9vb29vb2Pj4/xx6qqqse6+c2bN0+dOtXUbF1dXU1NzVPlAwDAQqil4A8dOvTJJ59UVVWFhYVFRkampaWtXr364sWLXbp0WbRoUUxMjCl30rt377Vr1zY1+8knn9ja2jZfZAAA1EsVBb9z587x48d7e3s7OTnNmDEjNzd31apVs2fP9vHxOX78+KxZs9q3bz9hwgSlYwIAYDFUUfCpqalTp05dv369RqM5ePBgSEjI/Pnzly9fLoSYNm1ahw4d0tPTKXgAAEyniu/Bnz9/fty4cRqNRggxcuRInU7n5+dXPztixIi8vDzl0gEAYHlUUfCdOnWqr3CNRvPOO+80PPP8jRs33NzcFIoGAIBFUsUh+jFjxixevLhjx47+/v6enp7x8fHGcYPBcOrUqWXLlgUHByubEAAAy6KKV/BvvfXWmDFjXnnllenTpzccDw0NHTx4sKura3p6ulLZAACwRKooeFtb2y1btty+fXvdunUNx6dMmXLgwIGvvvrKzs5OqWwAAFgiVRyiN+rQoUOHDh0ajkRERCgVBgAAi6aKV/AAAKB5UfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4wQVaWWLBA6RBQDgsAFoiCBx4qL0/MmCHOnRMFBSIhQRw9qnQgmBcLABaLggceytlZDBkiPv1U7N0revYUXl5KB4J5sQBgsbRKBwDUzd5e2NoKNzfRubOorhYuLkoHgnmxAGCxKHjgUVxcxObNwsFBnDypdBQogQUAy0TBA48ydOg/L4SFKZoDCmEBwDLxHjwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEhIvQV///79/Pz8f/zjH0oHAQDA8qil4Pfv3z9u3LjRo0dv2rRJCLFu3TonJycvL6/27du/9dZbBoNB6YAAAFgSrdIBhBBi586d48ePHzhwoKOjY0xMzKlTpz766KMFCxYMGDDg2LFjS5YscXV1nTp1qtIxAQCwGKoo+NTU1FmzZr3//vtCiDVr1syaNSs1NfW1114TQowcObKuru69996j4AEAMJ0qDtGfO3cuNDTUeDkiIkIIMWzYsPrZgICA8+fPK5MMAADLpIqCd3Nz+/vf/268fPHiRSFEfn5+/ez58+e7dOmiTDIAACyTKg7RT5069c0337xx44a9vf26desGDhy4cOHCzp079+/f/9ixY0uXLp05c6bSGQEAsCSqKPikpKTKysoNGzb84x//CA8Pz8zMfPXVV//93//dODtq1KiFCxcqmxAtXVaWKCwUy5crnQMKYQHAAmlU+w20vLy8U6dO9ejRY9CgQSbepLa29ocffmhqNiAg4N13350+fXozBUTLkJcn0tKETifKyoSjo4iIEA0+IAL5sQDwdPr27btly5bf/OY35n/oR7+CLygoKC8v792797OOUldXd+3aNVdX1zZt2gghvL29vb29hRA1NTXl5eXOzs6PvIdTp04lJCQ0Nfvzzz/fvn27GQOjRXB2FkOGiIULRUWFWLFCeHkpHQjmxQKAxXpYwX/xxRfR0dE3b94UQhgMhuHDh48ZMyYuLq7ZQ+j1+qVLl65cubK6utrGxiYuLi4lJcXKyso4u2PHjujoaFOONAwZMiQ3N7epWTs7O3t7+2YLjRbC3l7Y2go3N9G5s6iuFi4uSgeCebEAYLGaLPiPP/54ypQpU6dOHTZs2KRJk4QQ/v7+CQkJOp0uJiameUNkZGSkpqYmJCT4+fkdO3YsPT29pKRkw4YNzfsowBNycRGbNwsHB3HypNJRoAQWACxTkwWfmpoaFxeXnp5eWlpqHFm6dGlNTU1WVlazF/z69evnzZuXkpIihAgPD/f19Y2Kiho7dmxYWFjzPhDwJIYO/ecFFmTLxAKAZWrye/BXrlwZMWJEo8HAwMDLly83e4jr168Prf8TEiIyMjIqKioxMbGmpqbZHwsAgJagyYL39vY+ceJEo8Hc3FxPT89mD9GrV6+cnJyGI2lpaZWVlUlJSc3+WAAAtARNHqKPi4uLiYnRarXBwcFCiJKSkr179yYnJ7/99tvNHmLSpEnx8fF6vT40NDQgIECn0zk5OW3cuDEsLKyiosLV1bXZHxEAALk1WfDR0dEVFRVLlix54403hBBOTk46nW7OnDmJiYnNHiIuLq68vHzFihWZmZn5+fnGgwQhISHZ2dmxsbFFRUXN/ogAAMjtESe6qaysPHv27JUrVxwdHfv06dOpU6dnF6W2trawsNDNzU2n09UP6vX6I0eOXLhwITY29inv387OLiMjgxPdAADMRr0numnXrt2gQYNMP5fc02jdurWHh0ejQa1WGxQUFBQUZIYAAABIo8mCf/nll3852KpVK1tb2x49ekyZMoW3xgEAUK0mP0X//PPPHzx4cN++fUVFRXq9/ubNm/v37z9x4kRxcfEHH3zQrVu3v/zlL+YMCgAATNdkwbdp08bHx+fq1asnTpzYu3fv8ePHr1275u7uPnny5EuXLi1cuDA+Pt6cQQEAgOmaLPitW7ca/1P2+hEXF5fXX389OTlZo9HMnj37/Pnz9+7dM0tIAADweJoseI1GU1ZW1miwtLTU+B+ylZWVGQwG1f5XswAAtHBNfsguMjJywYIFtra2o0ePtrW1vXfv3v79++fNmzdlypRr164lJib279/fzs7OnFkBAICJmiz4ZcuW3bt3Lzo6ura21sbGprq62srKavr06ampqRs2bPjhhx+ys7PNGRQAAJiuyYK3srLKzMx8/fXXT506VVBQ4OLi0r9//27dugkhIiMjY2JiNBqNGXMCAIDH8IgT3bi6ujb8P1tLS0szMzOXLFnyjFMBAICn0mTBGwyGbdu2ff/99/fv368f/PHHH7/99lsKHgAAlXvYe/Bvvvlmjx49Ll265Ojo2LVr16tXr969e3f16tXmzAcAAJ5Ak1+T27RpU2JiYl5e3vvvv9+vX7/jx49fvHjRx8fHwcHBnPkAAMATaLLgi4qKjP8TvK+v7/fffy+EsLGxWbhw4bJly8yXDgAAPJEmC97d3f38+fNCiF//+tdFRUUlJSVCCAcHh7Nnz5ovHQAAeCJNFvyoUaOSk5PXrl1rZ2fXp0+fP/7xjxcvXszKynJ3dzdnPgAA8AQe9iG7wsLCQ4cOxcbGrlq1Kigo6P3337e2tt66das58wEAgCfQZMG3b99+9+7dxstDhw4tLi7Ozc3t3r37r371K3NlAwAAT+gRJ7oRQhQUFJSXl/fu3XvEiBFmCAQAAJ5ek+/BCyG++OILV1fXrl279unTRwgxfPjwrKwscwUDAABPrsmC//jjj0NDQ8PCwrZs2WIc8ff3T0hIWLdunbmyAQCAJ9TkIfrU1NS4uLj09PTS0lLjyNKlS2tqarKysmJiYswVDwAAPIkmX8FfuXLll2+6BwYGXr58+RlHAgAAT6vJgvf29j5x4kSjwdzcXE9Pz2ccCQAAPK0mD9HHxcXFxMRotVrjCWtLSkr27t2bnJz89ttvmzEeAAB4Ek0WfHR0dEVFxZIlS9544w0hhJOTk06nmzNnTmJiohnjAQCAJ/Gw78HHxcVNnTr17NmzV65ccXR07NOnT6dOncyWDAAAPLFHnOimXbt2gwYNGjRokHnSAACAZtG44FetWvXI2/z+979/NmEAAEDzaFzwf/zjHx95GwoeAACVa1zwxv/3HQAAWLSHnYseAABYqMav4D/88MNf/epXw4cP//DDD5u6zbRp055xKgAA8FQaF3xiYmJoaOjw4cOTkpKaug0FDwCAyjUu+IqKCuOF27dvmz0MAABoHo0L/uzZs4+8jY+Pz7MJAwAAmkfjgu/du/cjb2MwGJ5NGAAA0DwaF7xWq9Xr9X379o2IiBg2bJhW+4hT3QEAABVq3N/FxcV79uzZvXt3cnJy+/btX3755fDw8MDAQGtrazMnu3PnTklJiaenZ6tWfJcPAIDH07g7HRwcoqOj9+7dW1JS8u6775aWlr788svOzs5TpkzZv3//zz///IxyfPzxx/7+/j/88IMQori4ePTo0fb29t27d3/uuefefffdZ/SgAADIqskXx3Z2dr/73e927dpVUlKyfv362traiRMnOjk5RUVFNXuIzMzMSZMmabVaJycnIcTkyZNPnz69evXqgwcPzpw5MykpacuWLc3+oAAASExj4ifmfvrpp+3bt7/55ptlZWXN/iE7Dw+PCRMmpKSkCCGKi4tdXFyOHDkybNgw4+zrr7/+xRdffPfdd0/5KHZ2dhkZGdOnT3/auAAAmKZv375btmz5zW9+Y/6HfsTb2yUlJevWrRsxYoSLi0tqaurEiRO//vrrZg9x9+7dAQMG1D+iEKJ///71swEBAfn5+c3+oAAASOzBBX/r1q01a9YEBwe7urouXbq0V69eX331VUFBQVZWVkBAQLOHGDZs2IcfflhbWyuE8Pb2trOz+/bbb+tnjx492qtXr2Z/UAAAJNb4U/SrV6/euXPnkSNHOnfuHB4evmzZMj8/P41G80xDpKamvvTSS76+vpMnTx44cOCCBQsmT56cnJzcrVu3v/zlLytXrvzoo4+eaQAAACTT+D14Y5f37dt38ODBTX0/bfXq1c2e48KFCxkZGTt27CgrK2s47uPjs3jx4vHjxz/9QzzVe/BZWaKwUCxf/vQxAAAth4LvwTd+Bd+vXz/jhZMnT5ozh5eX1/vvv//uu+8WFhYWFxeXlZXZ29u7uLh069bNnDEeIC9PpKUJnU6UlYmEBBERIf716T8AAFSrccGfPn1akRxCiLq6usLCQldX10alXlNTU15e7uzs/Mh7OHz4cFBQ0EOu0OjwgEmcncWQIWLhQlFRIVasEF5ej30PAACYnSpOEqfX6xcvXmxnZ+fh4eHg4LBgwYK6urr62R07dri4uJhyP4GBgYam2draOjg4PHY4e3thayvc3ERQkKiuFqYlAQBAWao41XxGRkZqampCQoKfn9+xY8fS09NLSko2bNigdK5/cXERmzcLBwdh3rctAAB4Yqoo+PXr18+bN894opvw8HBfX9+oqKixY8eGhYUpHU0IIcTQof+8oJI8AAA8iioO0V+/fn1ofYkKERkZGRUVlZiYWFNTo2AqAAAslyoKvlevXjk5OQ1H0tLSKisrk5KSlIoEAIBFU8Uh+kmTJsXHx+v1+tDQ0ICAAJ1O5+TktHHjxrCwsIqKCldXV6UDAgBgYVRR8HFxceXl5StWrMjMzMzPz/f09BRChISEZGdnx8bGFhUVKR0QAAALo4pD9EKIRYsWlZSUXLx40d3dvX4wNDT06tWrOTk5a9asUTAbAAAWRxWv4I1at27t4eHRaFCr1QYFBT389DUAAKARtbyCBwAAzYiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACSk6oL//PPPS0pKlE4BAIDlUXXBjx079syZM0qnAADA8miVDiCEEJ999tmnn376wKnU1NRNmzYJIbZs2WLWTAAAWDJVFLxOp/v000+rqqp8fX2tra0bThUVFVVWVioVDAAAC6WKgg8JCfnuu+8iIyOtrKw2b97cvXt347hGo8nKygoODlY2HgAAFkct78H36NHj+PHjgYGBvr6+a9asUToOAACWTS0FL4SwtrZ+++239+3bl5KSEhIScvPmTaUTAf+SlSUWLFA6BAAlWOyfv4oK3uill146c+ZM+/bt+/Tpo3QWQIi8PDFjhjh3ThQUiIQEcfSo0oEAmIuF//mr4j34Rp577rnt27dv3779xIkTXbp0Mf2G33zzTWJiYlOzVVVVt2/fbo6AaEmcncWQIWLhQlFRIVasEF5eSgcCYC4W/uevooKvq6u7du2aq6trmzZthBATJkyYMGGCEKKmpqa8vNzZ2fmR9zB48OAPPvjg/v37D5wNCAiwt7dv3syQn729sLUVbm6ic2dRXS1cXJQOBMBcLPzPXxUFr9frly5dunLlyurqahsbm7i4uJSUFCsrK+Psjh07oqOjDQbDI+/H2tr6hRdeaGq2VSvVvR8By+DiIjZvFg4O4uRJpaMAMC9L/vNXRcFnZGSkpqYmJCT4+fkdO3YsPT29pKRkw4YNSucChBBCDB36zwthYYrmAGB2lvznr4qCX79+/bx581JSUoQQ4eHhvr6+UVFRY8eODbPAXygAAGqgiqPW169fH1r/LEmIyMjIqKioxMTEmpoaBVMBAGC5VFHwvXr1ysnJaTiSlpZWWVmZlJSkVCQAACyaKg7RT5o0KT4+Xq/Xh4aGBgQE6HQ6JyenjRs3hoWFVVRUuLq6Kh0QAAALo4qCj4uLKy8vX7FiRWZmZn5+vqenpxAiJCQkOzs7Nja2qKhI6YAAAFgYVRyiF0IsWrSopKTk4sWL7u7u9YOhoaFXr17Nycnh7PQAADwWVbyCN2rdurWHh0ejQa1WGxQUFBQUpEgkAAAslFpewQMAgGZEwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AQNOyssSCBUqHeBIUPAAAD5KXJ2bMEOfOiYICkZAgjh5VOtDjoeABAHgQZ2cxZIj49FOxd6/o2VN4eSkd6PFolQ4AAIAq2dsLW1vh5iY6dxbV1cLFRelAj4eCBwCgCS4uYvNm4eAgTp5UOspjo+ABAGjC0KH/vBAWpmiOJ8F78AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACamo4Ovq6i5fvlxTU9NovKampri4WJFIAABYKFUUvF6vX7x4sZ2dnYeHh4ODw4IFC+rq6upnd+zY4eLiomA8AAAsjlbpAEIIkZGRkZqampCQ4Ofnd+zYsfT09JKSkg0bNiidCwAAS6WKgl+/fv28efNSUlKEEOHh4b6+vlFRUWPHjg0LC1M6GgAAFkkVh+ivX78+dOjQ+h8jIyOjoqISExN/+X48AAAwhSoKvlevXjk5OQ1H0tLSKisrk5KSlIoEAIBFU8Uh+kmTJsXHx+v1+tDQ0ICAAJ1O5+TktHHjxrCwsIqKCldXV6UDCpGVJQoLxfLlSucAAMAkqij4uLi48vLyFStWZGZm5ufne3p6CiFCQkKys7NjY2OLioqUDJeXJ9LShE4nyspEQoKIiBDDhimZBwAAE6ii4IUQixYtmj9/fmFhoZubW/1gaGjo1atXjxw5cuHCBVPu5MyZM8nJyU3N/vzzz/fu3XvsZM7OYsgQsXChqKgQK1YIL6/HvgcAAMxOLQUvhLCystJoNAaDoeGgVqv19/f38fEx5R7c3d3HjRvX1OyJEyf69u372LHs7YWtrXBzE507i+pqwTfyAQCWQBUFr9frly5dunLlyurqahsbm7i4uJSUFCsrK+Psjh07oqOjGxX/Azk4ODyk4NPT021sbJ4kn4uL2LxZODiIkyef5OYAAJidKgpe7Se6qf8KH9/LBwBYCFUUPCe6AQCgeanie/Cc6AYAgOalioLnRDcAADQvVRyit4AT3QAAYFFUUfCqPtENAAAWSBWH6IUQixYtKikpuXjxoru7e/2g8UQ3OTk5a9asUTAbAAAWRxWv4I1at27t4eHRaFCr1QYFBQUFBSkSCQAAC6WigjeDzz///MyZM09ww59++unIkSOOjo7NHslSXL9+veFZhFua0tLStm3bPuGJkixfbW1teXk561/pFIph/VtbWwcEBDzZzUtLS5s3j+laUMFPmzbt1KlTZWVlT3Db8+fP5+bmdunSpdlTWYpz5855eXm1aqWW93TMrKioqF27dh06dFA6iDLu3bt3+/Zt1j/rX8SFV7AAAAxaSURBVOkgyrh37151dXW7du2e7Obh4eHPP/98syYyVeNzv+OB9u7d+8EHH+zZs0fpIIpp27ZtaWlpi30K/8orrwQHB0+ePFnpIMpg/bP+Wf+WuP5b6BNSAADkRsEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBW8Sa2trrbYFnRTol1q3bt1iz/IhhNBqtdbW1kqnUAzrn/XP+lc6xZPgRDcmqaurq6ioeO6555QOopjS0tKOHTsqnUIxd+/etbGxabH/xrH+Wf+sf0tc/xQ8AAASarkHnQAAkBgFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBP8CXX365Z8+eh1xh9+7dgwYNeu6554KCgv7nf/7HbMHM5uG/gc8++0zz/82YMcOc8Z6d995778UXX7Szs/P29l65cqVer3/g1WRdAKZsvsR7/969e3/4wx88PDxsbW0HDBiwa9eupq4p5QIwcfMlXgD1Dhw48NlnnzU1a0l734D/r66ubtCgQUlJSU1dYd++fRqNZtasWTt37hw5cmS7du2uXbtmzoTP2iN/AytXrnRyclrTwFdffWXOhM/IsmXLhBBz5szZt2/fa6+9ptVq33jjjV9eTdYFYOLmy7r3DQZDVFSUnZ1dRkbGgQMHpkyZIoQ4dOjQL68m6wIwcfMlXgBGeXl5bdu2jYqKeuCsZe19Cv7/FBQUrFq1KiAgQAjxkHoLDAwcOXKk8XJVVVWXLl0WLlxorozPlom/gVdffTU4ONicwczg559/bt++fXx8fP3I3LlzbWxs9Hp9o2tKuQBM33wp977BYLhz545Go/noo4+MP96/f79Hjx7R0dG/vKaUC8D0zZd1ARjV1tb6+voKIZoqeMva+xyi/z8//PDDtm3b7t+/36ZNm6auc/v27cOHD48bN874o42NzahRo7Zt22aujM+WKb8BIcSlS5c8PT3Nlso8CgsL7969GxoaWj/i5+dXXV197dq1hleTdQGYuPlC0r0vhLh169ZLL73k7+9v/FGj0Tg7O1dVVTW6mqwLwMTNF/IuAKM33njDysrK2PG/ZHF7n4L/P7/97W+PHj169OhRd3f3pq5TVFQkhOjZs2f9SM+ePa9cuVJbW2uOiM+YKb8BIcSlS5euXr3q6+tra2vbr1+/devWmS3hs+Pm5pafn288emF07NgxGxsbV1fXhleTdQGYuPlC0r0vhPDy8jp8+LCxugwGw8GDB0+dOjV69OhGV5N1AZi4+ULeBSCE+Prrr1etWrVlyxZra+sHXsHi9j4F/3hu3rwphLC3t68fcXBwMBgMd+/eVS6UWd2/f//KlSu5ubmvvPLK1q1bBw4cGBsbm5aWpnSup6XT6Tw9PXU6nfHHrVu3ZmVlzZ49u9HBDFkXgImbL+vebygzM7Nt27YhISGxsbFRUVGNZmVdAPUevvkSL4A7d+5Mnjx5xYoV3bt3b+o6Frf3tUoHsDAGg0EIodFoGo1YWVkplsm89Hr9Rx99NHDgQA8PDyHEmDFjamtrly5d+oc//KFVKxmeL5aUlMydO3fLli3R0dEpKSmNZqVfAA/ffOn3vhBi9OjRXbt2/dvf/vanP/3J3d197ty5DWelXwAP33yJF8DMmTN9fHxmzpz5kOtY3N637F1ifs7OzkKIO3fu1I/cuXNHp9M1fE4nt9atW//Hf/yH8c/baOzYsXfv3r18+bKCqZrLgQMHevfu/c0332RnZ2/cuFGrbfwMWO4F8MjNl3vvG3Xr1m3s2LHvvPPO7NmzV69e3WhW7gUgHrX5si6A7du3f/nllxs2bHj41Sxu71Pwj8fNzU2j0Zw/f75+5MKFCw9/x1oyt27d+u///m/j81YjYw3Y2toqF6p5HDhwICwsLCIi4scffxwzZswDryPxAjBl8yXe+7t27Ro1alTDTfPx8bl48WKjD5rJugBM3HxZF8CJEydKS0tdXV2N3+z/9ttvP/74Y41G8/nnnze8msXtfQr+8Tg4OAQGBmZnZxt/1Ov1+/fvj4iIUDaVOZ05c2bAgAENPzi6f//+rl27Gp/bWi69Xj9jxoyJEyeuWrXqIV8ikHUBmLj5su59IUS7du0OHDiQm5tbP3L8+HF3d/e2bds2vJqsC8DEzZd1AcyaNevLBnr27BkcHPzll1/Wf63AyPL2vpm/lmcRfv3rXzf6FvjatWsnTJhQU1NjMBgOHDhgZWW1ZMmSb775ZuLEifb29pcuXVIo6bPykN+AXq8fPHiwk5PTsmXL9u/fHx8f36pVq507dyoVtbnk5OQIIebPn7/p/6uurja0gAVg4ubLuvcNBkNtba2/v7+Hh8emTZv+67/+KykpqVWrVmvWrDHOSr8ATNx8iRdAQy+++GLD78Fb7t6n4B/gl/U2ffp0IcS9e/eMP+7cuXPQoEEdOnQIDg4+ffq0EhmfrYf/BqqqqhITE729ve3s7Pz9/Q8ePKhQzOa0Zs2aBz4DvnnzpqEFLADTN1/KvW909+7d6dOn9+jRw3iu1q1bt9ZPSb8ADCZvvsQLoF6jgrfcva8xNHg3BQAAyIH34AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEqLgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFD7QIL7zwgkajWb16daPxsrIya2trjUZz9uzZx7rDtWvXOjo6PvJqjo6Oq1ateqx7BtAsKHigBdm5c2ejkT179uj1ekXCAHimKHigpejbt++RI0du3brVcHD37t19+/ZVKhKAZ4eCB1qKwYMHd+7c+dNPP60fqaioOHToUERERP3I/fv333rrLR8fn/bt27/44ov79u2rn6qsrJw5c2aXLl26dOny6quv1tTUNLzzzZs3DxgwoF27dr179964caMZNgfAw1HwQEvRqlWr8PDwhkfp9+3b1759+2HDhtWPxMfHJycnT5o0adu2bb169Ro9evSePXuMU6NHj962bducOXMyMjJ+/PHHRYsW1d8qKytrxowZo0aN2rVr14gRI6ZNm/bLN/sBmJsBQAvQr1+/mTNnHjt2zMrK6tatW8bB8PDwmJiYb775Rgjx97//vaCgQKvVZmZm1t9q1KhRL7zwgsFg+Otf/yqE2LNnj3G8pqbGzc2tU6dOBoPh3r17HTt2XLZsWf2tZsyY4eTkZLzcqVOn9957zzzbCKAhXsEDLYifn5+Li8tnn30mhKiurj548GB4eHj97OnTp/V6/fjx4+tHxo8f//3339fW1p48edLe3n706NHGcZ1ON27cOOPls2fPlpaWBgcHl/5LQEDArVu3CgoKzLhlABqj4IEWRKPR1B+lP3jwoE6nCwwMrJ8tKipq1aqVk5NT/Ujnzp3v379/8+bNmzdvurm5Nbyrrl27Gi9cuXJFCOHv79/pXyZNmiSEuHPnzrPfIABN0iodAIBZjRs37t/+7d9++umn3bt3jxkzxtraun7KWOclJSX1HV9cXKzRaJycnNzc3IqKihreT2lpqfGC8dvwt27dMuVr8QDMhlfwQMvi7+/v5OS0ffv2ffv2Nfz8vBCiX79+Wq224afw/vznP/fp06dNmzaDBg0qKyvbv3+/cbyurm737t3Gy71799bpdHv37q2/1eLFi4cPH/7sNwXAw/AKHmhZjJ+lf/PNN4UQjWq4S5cuMTEx8+bNq6mp6d279+7du/fs2ZOdnS2ECAgICAwMjIyMTE5O7tq165o1ayorK423cnR0TExMnDVr1o0bN/r373/48OGVK1f+6U9/Mv+mAWiIggdanHHjxr333nsTJ07U6XSNpjIzM11cXD788MOCgoJevXrt2bOn/oN1e/bsmTt37jvvvKPX60ePHv373/8+OjraOJWamuro6Lhp06aUlJTnn39+9erVsbGx5twiAL+kMRgMSmcAAADNjPfgAQCQEAUPAICEKHgAACREwQMAICEKHgAACVHwAABIiIIHAEBCFDwAABKi4AEAkBAFDwCAhCh4AAAkRMEDACAhCh4AAAlR8AAASIiCBwBAQhQ8AAASouABAJAQBQ8AgIQoeAAAJETBAwAgIQoeAAAJUfAAAEiIggcAQEIUPAAAEvpf7LMrAP55VuEAAAAASUVORK5CYII=)
# Method1: Hand calculation
ni <- c(2, 3, 3, 2)
means <- tapply(y, xx, mean)
vars <- tapply(y, xx, var)
round(rbind(means, vars), 2)
## 1 2 3 4
## means 24 27 29.67 23.5
## vars 8 7 4.33 0.5
sum(y^2) # gives 7115
## [1] 7115
totalSS <- sum(y^2) - 10 * (mean(y))^2 # gives 92.5
RSSf <- sum(vars*(ni-1)) # gives 31.17
groupSS <- totalSS - RSSf # gives 61.3331.17/6
meangroupSS <- groupSS/3 # gives 20.44
meanErrorSS <- RSSf/6 # gives 5.194
Fvalue <- meangroupSS/meanErrorSS # gives 3.936
pvalue <- 1-pf(Fvalue, df1=3, df2=6)
#### Method 2: Illustrate using dummy variables
#################################
#Create the design matrix X for the full regression model
g <- 4
n1 <- 2
n2 <- 3
n3 <- 3
n4 <- 2
n <- n1+n2+n3+n4
X <- matrix(0, ncol=g, nrow=n) #Set X as a zero matrix initially
X[1:n1,1] <- 1 #Determine the first column of X
X[(n1+1):(n1+n2),2] <- 1 #the 2nd column
X[(n1+n2+1):(n1+n2+n3),3] <- 1 #the 3rd
X[(n1+n2+n3+1):(n1+n2+n3+n4),4] <- 1 #the 4th
#################################
####Fitting the full model####
#################################
#Estimation
XtXinv <- solve(t(X)%*%X)
betahat <- XtXinv %*%t(X)%*%y #Estimation of the coefficients
Yhat <- X%*%betahat #Fitted Y values
Resids <- y - Yhat #Residuals
SSE <- sum(Resids^2) #Error sum of squares
S2hat <- SSE/(n-g) #Estimation of sigma-square; mean square for error
Sigmahat <- sqrt(S2hat)
##############################################################
####Fitting the reduced model -- the 4 means are equal #####
##############################################################
Xr <- matrix(1, ncol=1, nrow=n)
kr <- dim(Xr)[2]
#Estimation
Varr <- solve(t(Xr)%*%Xr)
hbetar <- solve(t(Xr)%*%Xr)%*%t(Xr)%*% y #Estimation of the coefficients
hYr = Xr%*%hbetar #Fitted Y values
Resir <- y - hYr #Residuals
SSEr <- sum(Resir^2) #Total sum of squares
###################################################################
####F-test for comparing the reduced model with the full model ####
###################################################################
FStat <- ((SSEr-SSE)/(g-kr))/(SSE/(n-g)) #The test statistic of the F-test
alpha <- 0.05
Critical_value_F <- qf(1-alpha, g-kr,n-g) #The critical constant of F-test
pvalue_F <- 1-pf(FStat,g-kr, n-g) #p-value of F-test
modelA <- c(22, 26)
modelB <- c(28, 24, 29)
modelC <- c(29, 32, 28)
modelD <- c(23, 24)
SSerror = sum( (modelA-mean(modelA))^2 ) + sum( (modelB-mean(modelB))^2 )
+ sum( (modelC-mean(modelC))^2 ) + sum( (modelD-mean(modelD))^2 )
## [1] 9.166667
SStotal <- sum( (y-mean(y))^2 )
SSgroup <- SStotal-SSerror
####
#### Method 3: Use the built-in function lm directly
#####################################
aa <- "modelA"
bb <- "modelB"
cc <- "modelC"
dd <- "modelD"
Expl <- c(aa,aa,bb,bb,bb,cc,cc,cc,dd,dd)
is.factor(Expl)
## [1] FALSE
Expl <- factor(Expl)
model1 <- lm(y~Expl)
summary(model1)
##
## Call:
## lm(formula = y ~ Expl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.000 -1.417 0.000 1.750 2.333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.000 1.612 14.892 5.77e-06 ***
## ExplmodelB 3.000 2.081 1.442 0.1994
## ExplmodelC 5.667 2.081 2.724 0.0345 *
## ExplmodelD -0.500 2.279 -0.219 0.8336
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.279 on 6 degrees of freedom
## Multiple R-squared: 0.6631, Adjusted R-squared: 0.4946
## F-statistic: 3.936 on 3 and 6 DF, p-value: 0.07227
anova(model1)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## Expl 3 61.333 20.4444 3.9358 0.07227 .
## Residuals 6 31.167 5.1944
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
###Alternatively ###
xxf <- factor(xx)
is.factor(xxf)
## [1] TRUE
model2 <- lm(y~xxf)
summary(model2)
##
## Call:
## lm(formula = y ~ xxf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.000 -1.417 0.000 1.750 2.333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.000 1.612 14.892 5.77e-06 ***
## xxf2 3.000 2.081 1.442 0.1994
## xxf3 5.667 2.081 2.724 0.0345 *
## xxf4 -0.500 2.279 -0.219 0.8336
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.279 on 6 degrees of freedom
## Multiple R-squared: 0.6631, Adjusted R-squared: 0.4946
## F-statistic: 3.936 on 3 and 6 DF, p-value: 0.07227
anova(model2)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## xxf 3 61.333 20.4444 3.9358 0.07227 .
## Residuals 6 31.167 5.1944
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1