** Forecasting graph **

Project objective

#investigate the most recent values in the forecast data value
Weeks<- 1:6
Values<- c(17,13,15,11,17,14)

Part A Have forecasts written out

forecasts_a <- Values[-length(Values)]
actual_a <- Values[-1] 
mse_a<- mean((actual_a- forecasts_a)^2)
mse_a

## [1] 16.2

forecast_week_6_a <- tail(Values,1)
forecast_week_6_a

## [1] 14

Part B Average all of the data as forecast

cumulative_averages<- cumsum(Values[-length(Values)]) / (1:(length(Values) -1))
cumulative_averages

## [1] 17.0 15.0 15.0 14.0 14.6

forecasts_b <-cumulative_averages
actual_b<- Values[-1]
mse_b <- mean((actual_b - forecasts_b)^2)
mse_b

## [1] 8.272

forecast_month_8_b <- mean(Values)
forecast_month_8_b

## [1] 14.5

Part C which method is better

better_method<- ifelse(mse_a< mse_b, "Most recent value", "average of all data")
list(
MSE_most_recent_value = mse_a,
forecast_month_8_most_recent = forecast_week_6_a,
MSE_average_of_all_data = mse_b,
forecast_month_8_average = forecast_month_8_b,
better_method = better_method)

## $MSE_most_recent_value
## [1] 16.2
## 
## $forecast_month_8_most_recent
## [1] 14
## 
## $MSE_average_of_all_data
## [1] 8.272
## 
## $forecast_month_8_average
## [1] 14.5
## 
## $better_method
## [1] "average of all data"

Example 2

Step 1: install packages for functions

options(repos = c(CRAN = "https://cloud.r-project.org/"))
install.packages("dplyr")

## 
## The downloaded binary packages are in
##  /var/folders/gd/twcyysvs7_qf79bsx18dh2xm0000gn/T//Rtmp935IzX/downloaded_packages

install.packages("zoo")

## 
## The downloaded binary packages are in
##  /var/folders/gd/twcyysvs7_qf79bsx18dh2xm0000gn/T//Rtmp935IzX/downloaded_packages

library(dplyr)

## 
## 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)

## 
## Attaching package: 'zoo'

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

##step 2: create a data frame

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))
plot(df$month, df$data, type = "o", col = "blue", xlab = "Month", ylab = "Contracts",
     main = "Alabama Building Contracts")

## Step 3:MSE

df$avg_contract <- c(NA, NA, NA,
                     (df$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 <- df %>%
mutate(
  squared_error = ifelse(is.na(avg_contract), NA, (data - avg_contract)^2)
  )
mse <- mean(df$squared_error, na.rm = TRUE)
mse

## [1] 1354.296

Step 4: Alpha and MSE

alpha = 0.2
exp_smooth <- rep(NA, length(df$data))
exp_smooth[1] <- df$data[1]
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)

Step 5: better method use

better_method <- ifelse(mse_exp_smooth, "Three Month Contract Avgerage",
"Expontential Smoothing")
list(
  MSE_moving_average = mse,
  MSE_exponential_smoothing = mse_exp_smooth,
  better_method = better_method
)

## $MSE_moving_average
## [1] 1354.296
## 
## $MSE_exponential_smoothing
## [1] 2593.762
## 
## $better_method
## [1] "Three Month Contract Avgerage"

Example 3:

## Step 1: GG Plot
library(ggplot2)
library(readxl)
df1 <- read_excel("Mortgage.xlsx")
ggplot(df1, aes( x = Year, y = Interest_Rate)) +
  geom_line() +
  geom_point() +
  xlab("Year") +
  ylab("Interest_Rate") + 
  ggtitle("Morgages")

Step 2 forecast

model <- lm(Interest_Rate ~ Period, data = df1)
summary(model)

## 
## Call:
## lm(formula = Interest_Rate ~ Period, data = df1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3622 -0.7212 -0.2823  0.5015  3.1847 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.69541    0.43776  15.295 3.32e-13 ***
## Period      -0.12890    0.03064  -4.207 0.000364 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.039 on 22 degrees of freedom
## Multiple R-squared:  0.4459, Adjusted R-squared:  0.4207 
## F-statistic:  17.7 on 1 and 22 DF,  p-value: 0.0003637

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

##        1 
## 3.472942