Question 2-Class exercise 16

# Q2
library(dplyr)

## Warning: package 'dplyr' was built under R version 4.3.3

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(zoo)

## Warning: package 'zoo' was built under R version 4.3.3

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
                 data=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230))
# time series plot
plot(df$month, df$data, type = "o", col= "blue", xlab = "Month", ylab = "Contracts",
     main= "Monthly Contracts")

# horizontal pattern can be observed from this graph
#three month 
df$avg_shipment <- c(NA,NA,NA,
                     (df$data[1] + df$data[2]+ df$data[3])/3,
                     (df$data[2]+ df$data[3]+ df$data[4])/3,
                     (df$data[3] + df$data[4]+ df$data[5])/3,
                     (df$data[4] + df$data[5]+ df$data[6])/3,
                     (df$data[5] + df$data[6]+ df$data[7])/3,
                     (df$data[6] + df$data[7]+ df$data[8])/3,
                     (df$data[7] + df$data[8]+ df$data[9])/3,
                     (df$data[8] + df$data[9]+ df$data[10])/3,
                     (df$data[9] + df$data[10]+ df$data[11])/3)
# calculate the square errors
df<- df %>%
  mutate(
    squared_error= ifelse(is.na(avg_shipment), NA, (data- avg_shipment)^2)
  )
# computer mse
mse <- mean(df$squared_error, na.rm = TRUE)
mse # 2040.44

## [1] 2040.444

# exponential smoothing
alpha = 0.2
exp_smooth <- rep(NA, length(df$data))
exp_smooth[1] <- df$data[1] # starting p
for(i in 2 : length(df$data)){
  exp_smooth[i] <- alpha * df$data[i-1]+(1- alpha)* exp_smooth[i-1]
}
mse_exp_smooth <- mean((df$data[2:12]-exp_smooth[2:12])^2)
mse_exp_smooth# 2593.762

## [1] 2593.762

# compare 
better_method <- ifelse(mse < mse_exp_smooth, "Three Month average", "Exponential smoothing")
list(
  MSE_moving_average= mse,
  MSE_exponential_smoothing= mse_exp_smooth,
  Bette_method= better_method
)

## $MSE_moving_average
## [1] 2040.444
## 
## $MSE_exponential_smoothing
## [1] 2593.762
## 
## $Bette_method
## [1] "Three Month average"

#three month average is the better method since it has a lower mean

Question 2-Class exercise 16

2024-05-01