Menyesuaikan Fungsi ke Data

NAMA MAHASISWA : MUHAMMAD FAQIH

NIM : 220605110069

MATA KULIAH : KALKULUS

DOSEN PENGAMPU : Prof. Dr. Suhartono, M.Kom

JURUSAN : TEKNIK INFORMATIKA

UNIVERSITAS : UIN MAULANA MALIK IBRAHIM MALANG

BAB 6 : MENYESUAIKAN FUNGSI KE DATA

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

Utils <- read.csv("http://www.mosaic-web.org/go/datasets/utilities.csv")
gf_point(ccf ~ temp, data = Utils) %>%
  gf_labs(y = "Natural gas usage (ccf/month)", 
          x = "Average outdoor temperature (F)")

Salah satu cara untuk merepresentasikan sebuah data yang sangat simple yaitu Fungsi Garis lurus

f(x) = ax + b

Didalam fungsi f(x), variabel x digunakan untuk input, a dan b adalah parameter.

f <- fitModel(ccf ~ A * temp + B, data = Utils)

Output dari fitmodel () adalah fungsi dengan bentuk matematika

gf_point(ccf ~ temp, data = Utils) %>%
  slice_plot(f(temp) ~ temp)

f2 <- fitModel(
  ccf ~ A * temp + B + C *sqrt(temp),
  data = Utils)
gf_point(
  ccf ~ temp, data = Utils) %>%
  slice_plot(f2(temp) ~ temp)

Hondas <- read.csv("http://www.mosaic-web.org/go/datasets/used-hondas.csv")
head(Hondas)

##   Price Year Mileage Location Color Age
## 1 20746 2006   18394  St.Paul  Grey   1
## 2 19787 2007       8  St.Paul Black   0
## 3 17987 2005   39998  St.Paul  Grey   2
## 4 17588 2004   35882  St.Paul Black   3
## 5 16987 2004   25306  St.Paul  Grey   3
## 6 16987 2005   33399  St.Paul Black   2

carPrice1 <- fitModel(
  Price ~ A + B * Age + C * Mileage, data = Hondas
)

Kita bisa memplot fungsi yang sudah disesuaikan seperti dibawah ini.

library(mosaicCalc)
contour_plot(
  carPrice1(Age = age, Mileage = miles) ~ age + miles,
  domain(age=2:8, miles=range(0, 60000)))

carPrice3 <- fitModel(
  Price ~ A + B * Age + C * Mileage + D * Age * Mileage +
    E * Age^2 + F * Mileage^2 + G * Age^2 * Mileage + 
    H * Age * Mileage^2,
  data = Hondas)
gf_point(Mileage ~ Age, data = Hondas, fill = NA) %>%
contour_plot(
  carPrice3(Age=Age, Mileage=Mileage) ~ Age + Mileage)

library(mosaicCalc)
car_price2 <- makeFun(22137 - 7.495e2*age - 9.414e-2*miles +
                         3.450e-3*age*miles ~ age & miles)
contour_plot(
  car_price2(Kualitas, Kuantitas ) ~ Kualitas + Kuantitas,  
  domain(Kualitas = range(0, 10), Kuantitas = range(0, 100000))) %>%
  gf_labs(title = "Harga barang (IDR)")

Pemasangan Polinomial

polinomial sangat sering digunakan dalam pemodelan.

Utilities = read.csv("http://www.mosaic-web.org/go/datasets/utilities.csv")
project(ccf ~ 1 + temp + I(temp^2), data = Utilities)

##  (Intercept)         temp    I(temp^2) 
## 317.58743630  -6.85301947   0.03609138

I( ) digunakan untuk memberi tahu perangkat lunak untuk mengambil eksponen dalam matematika.

Koefisien memberi tahu kita bahwa model kuadrat ccf versus temp yang paling pas adalah:

ccfQuad <- makeFun(317.587 - 6.853*T + 0.0361*T^2 ~ T)
gf_point(ccf ~ temp, data = Utilities) %>%
  slice_plot(ccfQuad(temp) ~ temp) 

REFERENCES https://dtkaplan.github.io/RforCalculus/fitting-functions-to-data.html#curves-and-linear-models