Analisis Regresi
Muayyad
March 4, 2021
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regresi linier sederhana
#memanggil package
library(readxl)
#input data
datprom=read_excel("E:\\Praktikum 3.xlsx", sheet="Sheet1")
datprom## # A tibble: 15 x 2
## `Promosi (kali/bulan) (X)` `Penjualan (unit/hari) (Y)`
## <dbl> <dbl>
## 1 25 100
## 2 27 105
## 3 29 108
## 4 30 122
## 5 35 120
## 6 50 145
## 7 55 143
## 8 60 150
## 9 63 148
## 10 65 157
## 11 70 161
## 12 71 175
## 13 73 174
## 14 75 176
## 15 80 185str(datprom)## tibble [15 x 2] (S3: tbl_df/tbl/data.frame)
## $ Promosi (kali/bulan) (X) : num [1:15] 25 27 29 30 35 50 55 60 63 65 ...
## $ Penjualan (unit/hari) (Y): num [1:15] 100 105 108 122 120 145 143 150 148 157 ...#mengganti nama kolom
colnames(datprom)[1]="X"
colnames(datprom)[2]="Y"
#membangun model regresi
regresi=lm(Y~X,data=datprom) #menggunkan fungsi lm (linier model)
regresi##
## Call:
## lm(formula = Y ~ X, data = datprom)
##
## Coefficients:
## (Intercept) X
## 69.609 1.392summary(regresi)##
## Call:
## lm(formula = Y ~ X, data = datprom)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.315 -3.158 -1.982 3.391 10.626
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 69.60912 4.31285 16.14 5.57e-10 ***
## X 1.39216 0.07551 18.44 1.06e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.554 on 13 degrees of freedom
## Multiple R-squared: 0.9632, Adjusted R-squared: 0.9603
## F-statistic: 339.9 on 1 and 13 DF, p-value: 1.058e-10#plot regresi
plot(datprom$X,datprom$Y,main="Plot data Promosi (X) dan Penjualan (Y)",
xlab="Promosi (X)",ylab="Penjualan (Y)")
abline(regresi,col="red")
#selang kepercayaan bagi parameter
confint(regresi)## 2.5 % 97.5 %
## (Intercept) 60.291787 78.926462
## X 1.229028 1.555287confint(regresi, level = 0.80)## 10 % 90 %
## (Intercept) 63.786043 75.432205
## X 1.290206 1.494109#derajat bebas
n=nrow(datprom);n## [1] 15db_r=1
db_s=n-2;db_s## [1] 13y_dugaan=regresi$fitted.values;y_dugaan## 1 2 3 4 5 6 7 8
## 104.4131 107.1974 109.9817 111.3738 118.3346 139.2170 146.1778 153.1386
## 9 10 11 12 13 14 15
## 157.3150 160.0994 167.0601 168.4523 171.2366 174.0209 180.9817rataan_Y=mean(datprom$Y);rataan_Y## [1] 144.6# Manual ANOVA
JKR=sum((y_dugaan-rataan_Y)^2)
JKR## [1] 10484.62JKS=sum((datprom$Y-y_dugaan)^2)
JKS## [1] 400.9846JKT=JKR+JKS
JKT## [1] 10885.6KTR=JKR
KTR## [1] 10484.62KTS=JKS/db_s
KTS## [1] 30.84497tabel_anova=data.frame(SK=c("Regresi","Sisaan","Total"),
db=c(db_r,db_s,db_r+db_s),
JK=c(JKR,JKS,JKT),
KT=c(KTR,KTS,""))
tabel_anova## SK db JK KT
## 1 Regresi 1 10484.6154 10484.6154043329
## 2 Sisaan 13 400.9846 30.8449688974669
## 3 Total 14 10885.6000#melihat anova/ tabel sidik ragam
anova(regresi)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X 1 10485 10484.6 339.91 1.058e-10 ***
## Residuals 13 401 30.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Koefisien detterminasi atau R^2
R2<-JKR/JKT
R2## [1] 0.9631638#prediksi jika X*=45
prediksi<- regresi$coefficients[[1]]+regresi$coefficients[[2]]*45
prediksi## [1] 132.2562regresi melalui titik origin
#input data
tanah=read_excel("E:\\Praktikum 4.xlsx", sheet="Sheet4")
tanah## # A tibble: 15 x 2
## X Y
## <dbl> <dbl>
## 1 29 27.8
## 2 6 5.7
## 3 8 9.3
## 4 17 15.8
## 5 2 3.1
## 6 23 24.8
## 7 11 11.5
## 8 30 34.7
## 9 17 18
## 10 14 16.5
## 11 19 19.3
## 12 4 5.6
## 13 24 23.5
## 14 1 1.5
## 15 12 12.8plot(tanah)
#regresi dengan intersep
reg1=lm(Y~X,data=tanah)
summary(reg1)##
## Call:
## lm(formula = Y ~ X, data = tanah)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3264 -0.8277 -0.0201 0.6771 3.6185
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.63924 0.75684 0.845 0.414
## X 1.01508 0.04436 22.885 6.9e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.554 on 13 degrees of freedom
## Multiple R-squared: 0.9758, Adjusted R-squared: 0.9739
## F-statistic: 523.7 on 1 and 13 DF, p-value: 6.896e-12anova(reg1)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X 1 1265.0 1265.03 523.7 6.896e-12 ***
## Residuals 13 31.4 2.42
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#plot regresi model dengan intersep
plot(tanah$X,tanah$Y,main="Plot data Luas Tanah (X) dan Harga (Y)",
xlab="Luas Tanah (X)",ylab="Harga (Y)")
abline(reg1,col="red")
#regresi tanpa instersep
reg2=lm(Y~X-1,data=tanah)
summary(reg2)##
## Call:
## lm(formula = Y ~ X - 1, data = tanah)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6084 -0.5855 0.2379 0.9658 3.3048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## X 1.04684 0.02328 44.97 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.538 on 14 degrees of freedom
## Multiple R-squared: 0.9931, Adjusted R-squared: 0.9926
## F-statistic: 2023 on 1 and 14 DF, p-value: < 2.2e-16anova(reg2)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X 1 4785.7 4785.7 2022.6 < 2.2e-16 ***
## Residuals 14 33.1 2.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(reg2)## 2.5 % 97.5 %
## X 0.9969159 1.096764#plot regresi model tanpa intersep
abline(reg2,col="blue")
regresi Linier Berganda
#input data
data=read_excel("E:\\Praktikum-5.xlsx",sheet="Sheet1")
data## # A tibble: 25 x 4
## NO y x1 x2
## <dbl> <dbl> <dbl> <dbl>
## 1 1 16.7 7 560
## 2 2 11.5 3 220
## 3 3 12.0 3 340
## 4 4 14.9 4 80
## 5 5 13.8 6 150
## 6 6 18.1 7 330
## 7 7 8 2 110
## 8 8 17.8 7 210
## 9 9 79.2 30 1460
## 10 10 21.5 5 605
## # ... with 15 more rowsplot(data) 
#melihat plot
#x1 vs y
plot(data$x1,data$y,main="Jumlah Minuman (X1) dan Lama Pengantaran (Y)",
xlab="Jumlah Minuman (X1)",ylab="Lama Pengantaran (Y)")
#x2 vs y
plot(data$x2,data$y,main="Jarak Tempuh (X2) dan Lama Pengantaran (Y)",
xlab="Jarak Tempuh (X2)",ylab="Lama Pengantaran (Y)")
#membuat model regresi
reg_ganda=lm(y~x1+x2,data=data)
summary(reg_ganda)##
## Call:
## lm(formula = y ~ x1 + x2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7880 -0.6629 0.4364 1.1566 7.4197
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.341231 1.096730 2.135 0.044170 *
## x1 1.615907 0.170735 9.464 3.25e-09 ***
## x2 0.014385 0.003613 3.981 0.000631 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.259 on 22 degrees of freedom
## Multiple R-squared: 0.9596, Adjusted R-squared: 0.9559
## F-statistic: 261.2 on 2 and 22 DF, p-value: 4.687e-16You can also embed plots, for example:
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