Example #1
Step 1: Basic Data
weeks <- 1 - 6
values <- c(17, 13, 15, 11, 17, 14)
forecasts_a <- values [-length(values)]
actual_a <- values [-1]
mse_a <- mean((actual_a - forecasts_a)^2)
mse_a
## [1] 16.2
forecast_week_7_a <- tail(values, 1)
forecast_week_7_a
## [1] 14
Step 2: Avergaes
cumlative_avergaes <- cumsum(values[-length(values)]) / (1:(length(values) - 1))
cumlative_avergaes
## [1] 17.0 15.0 15.0 14.0 14.6
forecasts_b <- cumlative_avergaes
actual_b <- values [-1]
mse_b <- mean((actual_b - forecasts_b)^2)
mse_b
## [1] 8.272
forecast_week_7_b <- mean(values)
forecast_week_7_b
## [1] 14.5
Step 3: Better Method
better_method <- ifelse(mse_a < mse_b, "Most Recent Value", "Average of All Data")
list(
MSE_most_recent_value = mse_a,
forecast_week_7_most_recent = forecast_week_7_a,
MSE_average_of_all_data = mse_b,
forecaset_week_7_avergae = forecast_week_7_b,
better_method = better_method
)
## $MSE_most_recent_value
## [1] 16.2
##
## $forecast_week_7_most_recent
## [1] 14
##
## $MSE_average_of_all_data
## [1] 8.272
##
## $forecaset_week_7_avergae
## [1] 14.5
##
## $better_method
## [1] "Average of All Data"
Example 2
Step 1: Installing and Adding Packagaes
options(repos = c(CRAN = "https://cloud.r-project.org/"))
install.packages("dplyr")
##
## The downloaded binary packages are in
## /var/folders/xb/_nbl119s1sv5w0hp78k9qgb00000gn/T//RtmpV5lXhJ/downloaded_packages
install.packages("zoo")
##
## The downloaded binary packages are in
## /var/folders/xb/_nbl119s1sv5w0hp78k9qgb00000gn/T//RtmpV5lXhJ/downloaded_packages
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(zoo)
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
Step 2: Creating Data Frame
df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
data=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230))
plot(df$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$data[5]) / 3,
(df$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$data[11]) / 3)
df <- df %>%
mutate(
squared_error = ifelse(is.na(avg_contract), NA, (data - avg_contract)^2)
)
mse <- mean(df$squared_error, na.rm = TRUE)
mse
## [1] 2040.444
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)
mse_exp_smooth
## [1] 2593.762
Step 5: Better Method
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] 2040.444
##
## $MSE_exponential_smoothing
## [1] 2593.762
##
## $better_method
## [1] "Three Month Contract Avgerage"
Example 3:
Step 1: Install and Download
library(readxl)
library(ggplot2)
df1 <- read_excel("Mortgage.xlsx")
Step 2: GGPlots
ggplot(df1, aes( x = Year, y = Interest_Rate)) +
geom_line() +
geom_point() +
xlab("Year") +
ylab("Interest_Rate") +
ggtitle("Morgages")
Step 3: Forecasting
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