Latihan

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summary(cars)

##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

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summary(cars)

##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Regresi Linear

Pada analisis ini digunakan data cars dengan dist sebagai variabel respon dan speed sebagai variabel prediktor.

Membuat Model Regresi

model <- lm(dist ~ speed, data = cars)
summary(model)

## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## speed         3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12

Model Akhir

coef(model)

## (Intercept)       speed 
##  -17.579095    3.932409

Model regresi yang diperoleh adalah:

\(begin:math:display\) \widehat{dist} = -17.579 + 3.932\(speed\) \(end:math:display\)

Interpretasi

Koefisien speed sebesar 3.932 menunjukkan bahwa setiap kenaikan speed sebesar 1 satuan akan meningkatkan dist rata-rata sebesar 3.932 satuan.

Intercept sebesar -17.579 menunjukkan nilai prediksi dist ketika speed bernilai 0.

Plot Regresi

plot(cars$speed, cars$dist,
     main = "Hubungan Speed dan Dist",
     xlab = "Speed",
     ylab = "Dist")

abline(model)