#Class Exercise 16

#Question 1

#Enter Data

weeks<- 1:6
values<- c(17,13,15, 11,17,14)

#Most recent values as forecast

forecast_a <- values[-length(values)]#exclude the last value
actual_a <- values[-1]#exclude the first value
mse_a<- mean((actual_a - forecast_a)^2)
mse_a #result = 16.2

## [1] 16.2

APE <- abs((actual_a - forecast_a) / actual_a) * 100
APE #30.77%

## [1] 30.76923 13.33333 36.36364 35.29412 21.42857

absolute_errors<- abs(forecast_a - actual_a)
mae <- mean(absolute_errors)
mae##3.8

## [1] 3.8

forecast_week_7_a<- tail(values, 1)
forecast_week_7_a #result = 14 

## [1] 14

#Average all the data

cumulative_averages<- cumsum(values[-length(values)]) / (1:(length(values) - 1))
forcast_b<- cumulative_averages
actual_b<- values[-1]#exclude the first
mse_b <- mean((actual_b - forcast_b)^2)
mse_b #result = 8.27

## [1] 8.272

forecast_week_7_b<- mean(values)
forecast_week_7_b #result = 14.5

## [1] 14.5

#Which method is better

better_method<- ifelse(mse_a < mse_b, "Most Recent Values", "Average of All Data")
list(
  MSE_most_recent_value = mse_a,
  forcast_week_7_most_recent = forecast_week_7_a,
  MSE_average_of_all_data = mse_b,
  forcast_week_7_average = forecast_week_7_b,
  Better_Method = better_method
)

## $MSE_most_recent_value
## [1] 16.2
## 
## $forcast_week_7_most_recent
## [1] 14
## 
## $MSE_average_of_all_data
## [1] 8.272
## 
## $forcast_week_7_average
## [1] 14.5
## 
## $Better_Method
## [1] "Average of All Data"

#Question 2

#Insert Data

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 Received",
     main = "The values of Alabama building contracts")

#Interpretation- the time series plot represents a horizontal pattern

#Three month moving average

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 squared errors 
#df <- df %>%
  #mutate(
  #  squared_error = ifelse(is.na(avg_shipment), NA,(data - avg_shipment)^2)
#  )

#Compute MSE
mse<- mean(df$squared_error, na.rm = TRUE)

## Warning in mean.default(df$squared_error, na.rm = TRUE): argument is not
## numeric or logical: returning NA

mse# results: 2040.44

## [1] NA

#Exponential Smoothing 
alpha= 0.2
exp_smooth <- rep(NA, length(df$data)) 
exp_smooth [1] <- df$data[1] #starting point
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 Moving Average", "Exponential Smoothing 
")
list(
  MSE_moving_average = mse,
  MSE_exponential_smoothing = mse_exp_smooth,
  Better_Method = better_method
)#Result-Better Method- Three Month Moving Average

## $MSE_moving_average
## [1] NA
## 
## $MSE_exponential_smoothing
## [1] 2593.762
## 
## $Better_Method
## [1] NA

#Question 3 #install.packages(“readxl”)

library(readxl) library(ggplot2)

#load data

#df1<- read_excel(file.choose())

#Time series plot

#ggplot(df1, aes(x= Year, y= Interest_Rate)) + 
#  geom_line() + 
#  geom_point() + 
#  xlab("Year") +
#  ylab ("Interest Rate") +
#  ggtitle("Time Series Plot of Mortgage")
#Interpretation- we observe a decreasing trend in the graph

#Develop Linear Equation

#model <- lm(Interest_Rate ~ Period, data = df1)
#summary(model)
#Result- Linear Trend Equation: Interest Rate = 6.7 - 0.13t

#Interest Rate for period 25

#forecast_period_25<- predict(model, newdata = data.frame(Period = 25))
#forecast_period_25#3.47