code 13.1
## code 12.1의 자료를 사용함
## code 12.1visit<-c(350,460,350,430,350,380,430,470,450,490,340,300,440,450,300)
fee<-c(5.5,7.5,8,8,6.8,7.5,4.5,6.4,7,5,7.2,7.9,5.9,5,7)
ad<-c(3.3,3.3,3,4.5,3,4,3,3.7,3.5,4,3.5,3.2,4,3.5,2.7)
region<-c("A","A","A","A","A","B","B","B","B","B","C","C","C","C","C")
interaction<-fee*ad
da<-c(1,1,1,1,1,0,0,0,0,0,0,0,0,0,0)
db<-c(0,0,0,0,0,1,1,1,1,1,0,0,0,0,0)
sale<-data.frame(visit, fee, ad, interaction, region, da, db)
result.13.1<-lm(visit ~ da + db + fee, data=sale)
summary(result.13.1)##
## Call:
## lm(formula = visit ~ da + db + fee, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.98 -42.70 -14.44 42.67 78.55
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 493.14 94.60 5.213 0.000289 ***
## da 32.79 36.14 0.907 0.383735
## db 67.98 36.03 1.887 0.085813 .
## fee -19.26 13.83 -1.393 0.191021
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 55.82 on 11 degrees of freedom
## Multiple R-squared: 0.3934, Adjusted R-squared: 0.2279
## F-statistic: 2.378 on 3 and 11 DF, p-value: 0.1256result.13.2<-lm(visit ~ region + fee, data=sale)
summary(result.13.2)##
## Call:
## lm(formula = visit ~ region + fee, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.98 -42.70 -14.44 42.67 78.55
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 525.93 102.09 5.152 0.000317 ***
## regionB 35.20 38.33 0.918 0.378198
## regionC -32.79 36.14 -0.907 0.383735
## fee -19.26 13.83 -1.393 0.191021
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 55.82 on 11 degrees of freedom
## Multiple R-squared: 0.3934, Adjusted R-squared: 0.2279
## F-statistic: 2.378 on 3 and 11 DF, p-value: 0.1256code 13.2
library(ggplot2)
sale$predict<-predict(result.13.1)
ggplot(sale, aes(x=fee, y=predict, linetype=region)) + geom_line() 
dot1<-data.frame(sale$fee, sale$predict, sale$region)
names(dot1)<-c("fee", "predict", "region")
ggplot(sale, aes(x=fee, y=predict, linetype=region)) + geom_line() +
geom_point(data=dot1, shape=region)
code 13.3
x<-c(97,95,92,90,89,87,86,85,85,84,83,82,81,80,79,78,76,74,71,67,84)
y<-c(93,91,87,87,84,82,83,82,88,80,84,86,78,78,75,77,75,73,81,60,83.9903)
trt<-c(1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0)
rd<-data.frame(x, y, trt)
rd #저장된 데이터 출력## x y trt
## 1 97 93.0000 1
## 2 95 91.0000 1
## 3 92 87.0000 1
## 4 90 87.0000 1
## 5 89 84.0000 1
## 6 87 82.0000 1
## 7 86 83.0000 1
## 8 85 82.0000 1
## 9 85 88.0000 1
## 10 84 80.0000 1
## 11 83 84.0000 0
## 12 82 86.0000 0
## 13 81 78.0000 0
## 14 80 78.0000 0
## 15 79 75.0000 0
## 16 78 77.0000 0
## 17 76 75.0000 0
## 18 74 73.0000 0
## 19 71 81.0000 0
## 20 67 60.0000 0
## 21 84 83.9903 0code 13.4
rd$x2<-x-84
result.13.3<-lm(y ~ x + trt + x2*trt, data=rd)
summary(result.13.3)##
## Call:
## lm(formula = y ~ x + trt + x2 * trt, data = rd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.0287 -1.7000 -0.4778 0.4944 10.7450
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.7611 17.4455 -0.273 0.788208
## x 1.0566 0.2240 4.717 0.000199 ***
## trt -2.3181 2.5708 -0.902 0.379823
## x2 NA NA NA NA
## trt:x2 -0.2510 0.3581 -0.701 0.492841
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.749 on 17 degrees of freedom
## Multiple R-squared: 0.7686, Adjusted R-squared: 0.7278
## F-statistic: 18.82 on 3 and 17 DF, p-value: 1.208e-05rd$predict<-predict(result.13.3)
rd$trt.factor<-as.factor(rd$trt)
ggplot(rd, aes(x=x, y=y, color=trt.factor, linetype=trt.factor)) +
geom_point() + stat_smooth(method=lm, se=FALSE) +
geom_vline(xintercept=84, color="red") +
annotate("text", x=87, y=90, label="구분점=84")
code 13.5
install.packages(“rgl”)
result.13.4<-lm(visit ~ fee + ad, data=sale)
result.13.4$coef## (Intercept) fee ad
## 306.52619 -24.97509 74.13096result.13.4$coef[1]## (Intercept)
## 306.5262result.13.4$coef[2]## fee
## -24.97509result.13.4$coef[3]## ad
## 74.13096height<-matrix(,15,15)
x.fee<-sort(sale$fee) #좌표를 정렬함. 예쁘게 그리기 위해선 이 편이 좋음
x.ad<-sort(sale$ad)
x.fee ## [1] 4.5 5.0 5.0 5.5 5.9 6.4 6.8 7.0 7.0 7.2 7.5 7.5 7.9 8.0 8.0x.ad## [1] 2.7 3.0 3.0 3.0 3.2 3.3 3.3 3.5 3.5 3.5 3.7 4.0 4.0 4.0 4.5for (i in 1:nrow(sale)) #x.fee - x.ad 좌표에 따른 높이를 계산함
{
for (j in 1:nrow(sale))
{
height[i,j]<-(result.13.4$coef[1] +
result.13.4$coef[2]*x.fee[i] +
result.13.4$coef[3]*x.ad[j])/100
}
}
library(rgl) #없다면 install.packages("")문으로 설치함
surface3d(x=x.fee, y=x.ad, z=height,
alpha=0.7, back="lines", color="blue")
rgl.bbox(color="grey60", emission="grey40", xlen=0,ylen=0,zlen=0)
axes3d(edges=c("x--", "y+-", "z--"))
mtext3d("fee(thousand)",edge="x--",line=2, color="black")
mtext3d("ad(thousand)",edge="y+-",line=3, color="black")
mtext3d("visit(hundred)",edge="z--",line=3, color="black")code 13.6, code 13.7
result.13.6<-lm(visit ~ fee + ad + fee*ad)
summary(result.13.6)##
## Call:
## lm(formula = visit ~ fee + ad + fee * ad)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.573 -32.774 -1.152 20.189 95.205
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 88.838 585.071 0.152 0.882
## fee 6.203 82.823 0.075 0.942
## ad 136.779 167.071 0.819 0.430
## fee:ad -8.967 23.600 -0.380 0.711
##
## Residual standard error: 49.25 on 11 degrees of freedom
## Multiple R-squared: 0.5277, Adjusted R-squared: 0.3989
## F-statistic: 4.096 on 3 and 11 DF, p-value: 0.03528result.13.6$coef## (Intercept) fee ad fee:ad
## 88.838451 6.202687 136.779279 -8.967063result.13.6$coef[1]## (Intercept)
## 88.83845result.13.6$coef[2]## fee
## 6.202687result.13.6$coef[3]## ad
## 136.7793result.13.6$coef[4]## fee:ad
## -8.967063height<-matrix(,15,15)
x.fee<-sort(sale$fee)
x.ad<-sort(sale$ad)
x.fee## [1] 4.5 5.0 5.0 5.5 5.9 6.4 6.8 7.0 7.0 7.2 7.5 7.5 7.9 8.0 8.0x.ad## [1] 2.7 3.0 3.0 3.0 3.2 3.3 3.3 3.5 3.5 3.5 3.7 4.0 4.0 4.0 4.5## 원래 그림
for (i in 1:nrow(sale))
{
for (j in 1:nrow(sale))
{
height[i,j]<-(result.13.6$coef[1] +
result.13.6$coef[2]*x.fee[i] +
result.13.6$coef[3]*x.ad[j] +
result.13.6$coef[4]*x.fee[i]*x.ad[j])/100
}
}
surface3d(x=x.fee, y=x.ad, z=height,
alpha=0.7, back="lines", color="blue")
rgl.bbox(color="grey60", emission="grey40", xlen=0,ylen=0,zlen=0)
axes3d(edges=c("x--", "y+-", "z--"))
mtext3d("fee(thousand)",edge="x--",line=2, color="black")
mtext3d("ad(thousand)",edge="y+-",line=3, color="black")
mtext3d("visit(hundred)",edge="z--",line=3, color="black")
## 확 뒤틀고 싶을 때
for (i in 1:nrow(sale))
{
for (j in 1:nrow(sale))
{
height[i,j]<-(result.13.6$coef[1] +
result.13.6$coef[2]*x.fee[i] +
result.13.6$coef[3]*x.ad[j] +
result.13.6$coef[4]*x.fee[i]*x.ad[j]*i*j)/15000
}
}code 13.8
x<-seq(1, 4, by=0.1)
y<-exp(x)
ln.x<-log(x)
ln.y<-log(y)
sim1<-data.frame(x, y)
sim2<-data.frame(x, ln.y)
head(sim1)## x y
## 1 1.0 2.718282
## 2 1.1 3.004166
## 3 1.2 3.320117
## 4 1.3 3.669297
## 5 1.4 4.055200
## 6 1.5 4.481689ggplot(sim1, aes(x=x, y=y)) + geom_line() +
geom_line(data=sim2, aes(x=x, y=ln.y), linetype=2) +
annotate("text", x=3.5, y=40, label="y=x") +
annotate("text", x=3.5, y=5, label="ln(y)=x")
code 13.9
#code 12.1의 자료 sale을 사용
#만약, 연속해서 앞의 자료를 사용하기 위해서는 다음의 subset문을 사용하여 원상태로 자료를 돌림
sale<-subset(sale, select=c("visit", "fee", "ad", "interaction", "region", "da", "db"))
sale$visit.center <- with(sale, visit - mean(visit))
sale$fee.center <- with(sale, fee - mean(fee))
sale$ad.center <- with(sale, ad - mean(ad))
sale$interaction.center <- with(sale, interaction - mean(interaction))
result.13.9.1<-lm(visit ~ ad.center + fee.center, data=sale)
summary(result.13.9.1)##
## Call:
## lm(formula = visit ~ ad.center + fee.center, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -63.795 -33.796 -9.088 17.175 96.155
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 399.33 12.26 32.585 4.42e-13 ***
## ad.center 74.13 25.97 2.855 0.0145 *
## fee.center -24.98 10.83 -2.306 0.0398 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.46 on 12 degrees of freedom
## Multiple R-squared: 0.5215, Adjusted R-squared: 0.4417
## F-statistic: 6.539 on 2 and 12 DF, p-value: 0.01201result.13.9.2<-lm(visit ~ ad + fee, data=sale)
summary(result.13.9.2)##
## Call:
## lm(formula = visit ~ ad + fee, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -63.795 -33.796 -9.088 17.175 96.155
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 306.53 114.25 2.683 0.0199 *
## ad 74.13 25.97 2.855 0.0145 *
## fee -24.98 10.83 -2.306 0.0398 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.46 on 12 degrees of freedom
## Multiple R-squared: 0.5215, Adjusted R-squared: 0.4417
## F-statistic: 6.539 on 2 and 12 DF, p-value: 0.01201sale## visit fee ad interaction region da db visit.center fee.center
## 1 350 5.5 3.3 18.15 A 1 0 -49.33333 -1.1133333
## 2 460 7.5 3.3 24.75 A 1 0 60.66667 0.8866667
## 3 350 8.0 3.0 24.00 A 1 0 -49.33333 1.3866667
## 4 430 8.0 4.5 36.00 A 1 0 30.66667 1.3866667
## 5 350 6.8 3.0 20.40 A 1 0 -49.33333 0.1866667
## 6 380 7.5 4.0 30.00 B 0 1 -19.33333 0.8866667
## 7 430 4.5 3.0 13.50 B 0 1 30.66667 -2.1133333
## 8 470 6.4 3.7 23.68 B 0 1 70.66667 -0.2133333
## 9 450 7.0 3.5 24.50 B 0 1 50.66667 0.3866667
## 10 490 5.0 4.0 20.00 B 0 1 90.66667 -1.6133333
## 11 340 7.2 3.5 25.20 C 0 0 -59.33333 0.5866667
## 12 300 7.9 3.2 25.28 C 0 0 -99.33333 1.2866667
## 13 440 5.9 4.0 23.60 C 0 0 40.66667 -0.7133333
## 14 450 5.0 3.5 17.50 C 0 0 50.66667 -1.6133333
## 15 300 7.0 2.7 18.90 C 0 0 -99.33333 0.3866667
## ad.center interaction.center
## 1 -0.18 -4.8806667
## 2 -0.18 1.7193333
## 3 -0.48 0.9693333
## 4 1.02 12.9693333
## 5 -0.48 -2.6306667
## 6 0.52 6.9693333
## 7 -0.48 -9.5306667
## 8 0.22 0.6493333
## 9 0.02 1.4693333
## 10 0.52 -3.0306667
## 11 0.02 2.1693333
## 12 -0.28 2.2493333
## 13 0.52 0.5693333
## 14 0.02 -5.5306667
## 15 -0.78 -4.1306667cor(sale[,1:4])## visit fee ad interaction
## visit 1.000000000 -0.44327318 0.55631986 0.009207291
## fee -0.443273183 1.00000000 0.03043758 0.770308920
## ad 0.556319857 0.03043758 1.00000000 0.652477416
## interaction 0.009207291 0.77030892 0.65247742 1.000000000cor(sale[,8:11])## visit.center fee.center ad.center interaction.center
## visit.center 1.000000000 -0.44327318 0.55631986 0.009207291
## fee.center -0.443273183 1.00000000 0.03043758 0.770308920
## ad.center 0.556319857 0.03043758 1.00000000 0.652477416
## interaction.center 0.009207291 0.77030892 0.65247742 1.000000000code.13.10
# code 13.9의 자료를 사용
head(sale)## visit fee ad interaction region da db visit.center fee.center ad.center
## 1 350 5.5 3.3 18.15 A 1 0 -49.33333 -1.1133333 -0.18
## 2 460 7.5 3.3 24.75 A 1 0 60.66667 0.8866667 -0.18
## 3 350 8.0 3.0 24.00 A 1 0 -49.33333 1.3866667 -0.48
## 4 430 8.0 4.5 36.00 A 1 0 30.66667 1.3866667 1.02
## 5 350 6.8 3.0 20.40 A 1 0 -49.33333 0.1866667 -0.48
## 6 380 7.5 4.0 30.00 B 0 1 -19.33333 0.8866667 0.52
## interaction.center
## 1 -4.8806667
## 2 1.7193333
## 3 0.9693333
## 4 12.9693333
## 5 -2.6306667
## 6 6.9693333sale$std.visit<-with(sale, visit.center/sd(visit))
sale$std.fee<-with(sale, fee.center/sd(fee))
sale$std.ad<-with(sale, ad.center/sd(ad))
sale$std.interaction<-with(sale, std.fee*std.ad)
result.13.10.1<-lm(std.visit ~ std.ad + std.fee, data=sale)
summary(result.13.10.1)##
## Call:
## lm(formula = std.visit ~ std.ad + std.fee, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0043 -0.5320 -0.1431 0.2704 1.5137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.905e-16 1.929e-01 0.000 1.0000
## std.ad 5.703e-01 1.998e-01 2.855 0.0145 *
## std.fee -4.606e-01 1.998e-01 -2.306 0.0398 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7472 on 12 degrees of freedom
## Multiple R-squared: 0.5215, Adjusted R-squared: 0.4417
## F-statistic: 6.539 on 2 and 12 DF, p-value: 0.01201result.13.10.2<-lm(visit ~ ad + fee, data=sale)
summary(result.13.10.2)##
## Call:
## lm(formula = visit ~ ad + fee, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -63.795 -33.796 -9.088 17.175 96.155
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 306.53 114.25 2.683 0.0199 *
## ad 74.13 25.97 2.855 0.0145 *
## fee -24.98 10.83 -2.306 0.0398 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.46 on 12 degrees of freedom
## Multiple R-squared: 0.5215, Adjusted R-squared: 0.4417
## F-statistic: 6.539 on 2 and 12 DF, p-value: 0.01201code 13.11
result.13.11.1<-lm(std.visit ~ std.ad + std.fee + std.interaction, data=sale)
summary(result.13.11.1)##
## Call:
## lm(formula = std.visit ~ std.ad + std.fee + std.interaction,
## data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.96929 -0.51593 -0.01814 0.31782 1.49873
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.002296 0.200281 0.011 0.9911
## std.ad 0.596085 0.218104 2.733 0.0195 *
## std.fee -0.461142 0.207316 -2.224 0.0480 *
## std.interaction -0.080829 0.212734 -0.380 0.7112
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7753 on 11 degrees of freedom
## Multiple R-squared: 0.5277, Adjusted R-squared: 0.3989
## F-statistic: 4.096 on 3 and 11 DF, p-value: 0.03528result.13.11.2<-lm(visit ~ ad + fee + interaction, data=sale)
summary(result.13.11.2)##
## Call:
## lm(formula = visit ~ ad + fee + interaction, data = sale)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.573 -32.774 -1.152 20.189 95.205
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 88.838 585.071 0.152 0.882
## ad 136.779 167.071 0.819 0.430
## fee 6.203 82.823 0.075 0.942
## interaction -8.967 23.600 -0.380 0.711
##
## Residual standard error: 49.25 on 11 degrees of freedom
## Multiple R-squared: 0.5277, Adjusted R-squared: 0.3989
## F-statistic: 4.096 on 3 and 11 DF, p-value: 0.03528code 13.12
## 1, 2, 3종 제곱합
result.13.12.1<-lm(visit ~ ad + fee, data=sale)
result.13.12.2<-lm(visit ~ fee + ad, data=sale)
result.13.12.3<-lm(visit ~ ad + fee + interaction, data=sale)
result.13.12.4<-lm(visit ~ fee + ad + interaction, data=sale)
#1종 제곱합
anova(result.13.12.1)## Analysis of Variance Table
##
## Response: visit
## Df Sum Sq Mean Sq F value Pr(>F)
## ad 1 17484 17484.2 7.7612 0.01647 *
## fee 1 11976 11975.8 5.3160 0.03979 *
## Residuals 12 27033 2252.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(result.13.12.2)## Analysis of Variance Table
##
## Response: visit
## Df Sum Sq Mean Sq F value Pr(>F)
## fee 1 11100 11100.4 4.9274 0.04646 *
## ad 1 18360 18359.6 8.1498 0.01449 *
## Residuals 12 27033 2252.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#2종 제곱합
library(car)
Anova(result.13.12.1, type=2)## Anova Table (Type II tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## ad 18360 1 8.1498 0.01449 *
## fee 11976 1 5.3160 0.03979 *
## Residuals 27033 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Anova(result.13.12.2, type=2)## Anova Table (Type II tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## fee 11976 1 5.3160 0.03979 *
## ad 18360 1 8.1498 0.01449 *
## Residuals 27033 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#3종 제곱합.
Anova(result.13.12.1, type=3)## Anova Table (Type III tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## (Intercept) 16215 1 7.1977 0.01993 *
## ad 18360 1 8.1498 0.01449 *
## fee 11976 1 5.3160 0.03979 *
## Residuals 27033 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Anova(result.13.12.2, type=3)## Anova Table (Type III tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## (Intercept) 16215 1 7.1977 0.01993 *
## fee 11976 1 5.3160 0.03979 *
## ad 18360 1 8.1498 0.01449 *
## Residuals 27033 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#2종 제곱합. 교호작용이 있는 경우
Anova(result.13.12.3, type=2) ## Anova Table (Type II tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## ad 1625.8 1 0.6702 0.4303
## fee 13.6 1 0.0056 0.9416
## interaction 350.2 1 0.1444 0.7112
## Residuals 26683.1 11Anova(result.13.12.4, type=2)## Anova Table (Type II tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## fee 13.6 1 0.0056 0.9416
## ad 1625.8 1 0.6702 0.4303
## interaction 350.2 1 0.1444 0.7112
## Residuals 26683.1 11#2종 제곱합. 교호작용이 있는 경우
Anova(result.13.12.3, type=3) ## Anova Table (Type III tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## (Intercept) 55.9 1 0.0231 0.8821
## ad 1625.8 1 0.6702 0.4303
## fee 13.6 1 0.0056 0.9416
## interaction 350.2 1 0.1444 0.7112
## Residuals 26683.1 11Anova(result.13.12.4, type=3)## Anova Table (Type III tests)
##
## Response: visit
## Sum Sq Df F value Pr(>F)
## (Intercept) 55.9 1 0.0231 0.8821
## fee 13.6 1 0.0056 0.9416
## ad 1625.8 1 0.6702 0.4303
## interaction 350.2 1 0.1444 0.7112
## Residuals 26683.1 11code 13.13
install.packages(“leaps”)
null<-lm(visit ~ 1, data=sale)
full<-lm(visit ~. , data=sale)
step(null, scope=list(lower=null, upper=full), direction="forward")## Start: AIC=125.51
## visit ~ 1
##
## Df Sum of Sq RSS AIC
## + visit.center 1 56493 0 -928.96
## + std.visit 1 56493 0 -928.40
## + ad 1 17484 39009 121.95
## + ad.center 1 17484 39009 121.95
## + std.ad 1 17484 39009 121.95
## + db 1 14963 41530 122.89
## + fee 1 11100 45393 124.23
## + fee.center 1 11100 45393 124.23
## + std.fee 1 11100 45393 124.23
## + region 2 16173 40320 124.45
## <none> 56493 125.51
## + da 1 963 55530 127.25
## + std.interaction 1 574 55919 127.35
## + interaction 1 5 56489 127.51
## + interaction.center 1 5 56489 127.51
##
## Step: AIC=-928.96
## visit ~ visit.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## + da 1 2.7882e-27 1.1803e-26 -930.14
## <none> 1.4591e-26 -928.96
## + fee 1 1.7264e-27 1.2864e-26 -928.85
## + fee.center 1 1.7264e-27 1.2864e-26 -928.85
## + std.fee 1 1.7264e-27 1.2864e-26 -928.85
## + region 2 3.0206e-27 1.1570e-26 -928.44
## + interaction 1 8.0819e-28 1.3783e-26 -927.82
## + interaction.center 1 8.0819e-28 1.3783e-26 -927.82
## + db 1 1.8949e-28 1.4401e-26 -927.16
## + std.interaction 1 5.1960e-29 1.4539e-26 -927.02
## + ad 1 5.8900e-30 1.4585e-26 -926.97
## + ad.center 1 5.8900e-30 1.4585e-26 -926.97
## + std.ad 1 5.8900e-30 1.4585e-26 -926.97
##
## Step: AIC=-930.14
## visit ~ visit.center + da## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## + fee 1 3.7977e-27 8.0049e-27 -933.97
## + fee.center 1 3.7977e-27 8.0049e-27 -933.97
## + std.fee 1 3.7977e-27 8.0049e-27 -933.97
## + interaction 1 1.7011e-27 1.0101e-26 -930.48
## + interaction.center 1 1.7011e-27 1.0101e-26 -930.48
## <none> 1.1803e-26 -930.14
## + region 1 2.3230e-28 1.1570e-26 -928.44
## + db 1 2.3230e-28 1.1570e-26 -928.44
## + std.interaction 1 3.2000e-30 1.1799e-26 -928.15
## + ad 1 1.8000e-30 1.1801e-26 -928.15
## + ad.center 1 1.8000e-30 1.1801e-26 -928.15
## + std.ad 1 1.8000e-30 1.1801e-26 -928.15
##
## Step: AIC=-933.97
## visit ~ visit.center + da + fee## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## <none> 8.0049e-27 -933.97
## + ad 1 6.4599e-28 7.3589e-27 -933.23
## + ad.center 1 6.4599e-28 7.3589e-27 -933.23
## + std.ad 1 6.4599e-28 7.3589e-27 -933.23
## + interaction 1 5.1376e-28 7.4911e-27 -932.96
## + interaction.center 1 5.1376e-28 7.4911e-27 -932.96
## + region 1 2.9585e-28 7.7090e-27 -932.53
## + db 1 2.9585e-28 7.7090e-27 -932.53
## + std.interaction 1 3.2700e-30 8.0016e-27 -931.97##
## Call:
## lm(formula = visit ~ visit.center + da + fee, data = sale)
##
## Coefficients:
## (Intercept) visit.center da fee
## 3.993e+02 1.000e+00 -4.064e-14 1.655e-14step(full, direction="backward")## Start: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center + ad.center + interaction.center + std.visit +
## std.fee + std.ad + std.interaction## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center + ad.center + interaction.center + std.visit +
## std.fee + std.ad## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center + ad.center + interaction.center + std.visit +
## std.fee## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center + ad.center + interaction.center + std.visit## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center + ad.center + interaction.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center + ad.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center +
## fee.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + db + visit.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + da + visit.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense##
## Step: AIC=-931.76
## visit ~ fee + ad + interaction + region + visit.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## - interaction 1 0 0 -934.95
## <none> 0 -931.76
## - region 2 0 0 -928.05
## - ad 1 0 0 -926.00
## - fee 1 0 0 -925.82
## - visit.center 1 19822 19822 119.80
##
## Step: AIC=-934.95
## visit ~ fee + ad + region + visit.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## <none> 0 -934.95
## - region 2 0 0 -930.24
## - fee 1 0 0 -927.41
## - ad 1 0 0 -919.80
## - visit.center 1 21140 21140 118.76##
## Call:
## lm(formula = visit ~ fee + ad + region + visit.center, data = sale)
##
## Coefficients:
## (Intercept) fee ad regionB regionC
## 3.993e+02 2.773e-14 -2.946e-14 3.199e-14 6.441e-14
## visit.center
## 1.000e+00step(null, scope = list(upper=full), direction="both")## Start: AIC=125.51
## visit ~ 1
##
## Df Sum of Sq RSS AIC
## + visit.center 1 56493 0 -928.96
## + std.visit 1 56493 0 -928.40
## + ad 1 17484 39009 121.95
## + ad.center 1 17484 39009 121.95
## + std.ad 1 17484 39009 121.95
## + db 1 14963 41530 122.89
## + fee 1 11100 45393 124.23
## + fee.center 1 11100 45393 124.23
## + std.fee 1 11100 45393 124.23
## + region 2 16173 40320 124.45
## <none> 56493 125.51
## + da 1 963 55530 127.25
## + std.interaction 1 574 55919 127.35
## + interaction 1 5 56489 127.51
## + interaction.center 1 5 56489 127.51
##
## Step: AIC=-928.96
## visit ~ visit.center## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## + da 1 0 0 -930.14
## <none> 0 -928.96
## + fee 1 0 0 -928.85
## + fee.center 1 0 0 -928.85
## + std.fee 1 0 0 -928.85
## + region 2 0 0 -928.44
## + interaction 1 0 0 -927.82
## + interaction.center 1 0 0 -927.82
## + db 1 0 0 -927.16
## + std.interaction 1 0 0 -927.02
## + ad 1 0 0 -926.97
## + ad.center 1 0 0 -926.97
## + std.ad 1 0 0 -926.97
## - visit.center 1 56493 56493 125.51
##
## Step: AIC=-930.14
## visit ~ visit.center + da## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## + fee 1 0 0 -933.97
## + fee.center 1 0 0 -933.97
## + std.fee 1 0 0 -933.97
## + interaction 1 0 0 -930.48
## + interaction.center 1 0 0 -930.48
## <none> 0 -930.14
## - da 1 0 0 -928.96
## + region 1 0 0 -928.44
## + db 1 0 0 -928.44
## + std.interaction 1 0 0 -928.15
## + ad 1 0 0 -928.15
## + ad.center 1 0 0 -928.15
## + std.ad 1 0 0 -928.15
## - visit.center 1 55530 55530 127.25
##
## Step: AIC=-933.97
## visit ~ visit.center + da + fee## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Warning: attempting model selection on an essentially perfect fit is
## nonsense## Df Sum of Sq RSS AIC
## <none> 0 -933.97
## + ad 1 0 0 -933.23
## + ad.center 1 0 0 -933.23
## + std.ad 1 0 0 -933.23
## + interaction 1 0 0 -932.96
## + interaction.center 1 0 0 -932.96
## + region 1 0 0 -932.53
## + db 1 0 0 -932.53
## + std.interaction 1 0 0 -931.97
## - fee 1 0 0 -930.14
## - da 1 0 0 -928.85
## - visit.center 1 45365 45365 126.22##
## Call:
## lm(formula = visit ~ visit.center + da + fee, data = sale)
##
## Coefficients:
## (Intercept) visit.center da fee
## 3.993e+02 1.000e+00 -4.064e-14 1.655e-14library(leaps)
test<-regsubsets(visit ~ fee + ad + interaction, data=sale)
summary(test)## Subset selection object
## Call: regsubsets.formula(visit ~ fee + ad + interaction, data = sale)
## 3 Variables (and intercept)
## Forced in Forced out
## fee FALSE FALSE
## ad FALSE FALSE
## interaction FALSE FALSE
## 1 subsets of each size up to 3
## Selection Algorithm: exhaustive
## fee ad interaction
## 1 ( 1 ) " " "*" " "
## 2 ( 1 ) " " "*" "*"
## 3 ( 1 ) "*" "*" "*"plot(test, scale="bic")
plot(test, scale="adjr2")
plot(test, scale="r2")