Data Preparation

##The data for this analysis includes monthly contract values.

# Create the data frame
month <- 1:12
contract <- c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230)

df <- data.frame(month, contract)

3-Month Moving Average

Calculate the 3-month moving average.

knitr::opts_chunk$set(echo = TRUE)
df$avg_sale3 <- c(
  NA, NA, NA,
  (df$contract[1] + df$contract[2] + df$contract[3]) / 3,
  (df$contract[2] + df$contract[3] + df$contract[4]) / 3,
  (df$contract[3] + df$contract[4] + df$contract[5]) / 3,
  (df$contract[4] + df$contract[5] + df$contract[6]) / 3,
  (df$contract[5] + df$contract[6] + df$contract[7]) / 3,
  (df$contract[6] + df$contract[7] + df$contract[8]) / 3,
  (df$contract[7] + df$contract[8] + df$contract[9]) / 3,
  (df$contract[8] + df$contract[9] + df$contract[10]) / 3,
  (df$contract[9] + df$contract[10] + df$contract[11]) / 3
)

Mean Squared Error (MSE) for 3-Month Moving Average

knitr::opts_chunk$set(echo = TRUE)
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
df <- df %>%
  mutate(
    square_error = ifelse(is.na(avg_sale3), NA, (contract - avg_sale3)^2)
  )

mse <- mean(df$square_error, na.rm = TRUE)
mse
## [1] 2040.444

#Exponential Smoothing ##Calculate the exponential smoothing values and MSE.

knitr::opts_chunk$set(echo = TRUE)
alpha <- 0.2
exp_smooth <- rep(NA, length(df$contract))
exp_smooth[1] <- df$contract[1]
for (i in 2:length(df$contract)) {
  exp_smooth[i] <- alpha * df$contract[i-1] + (1 - alpha) * exp_smooth[i-1]
}

mse_exp_smooth <- mean((df$contract[2:12] - exp_smooth[2:12])^2)
mse_exp_smooth
## [1] 2593.762

Linear Trend Equation

Use the mortgage data to calculate a linear trend equation.

knitr::opts_chunk$set(echo = TRUE)
library(readxl)
## Warning: package 'readxl' was built under R version 4.2.3
# Load the mortgage data
df <- read_excel("C:\\Users\\dotua\\Downloads\\Mortgage.xlsx")


# Fit a linear regression model
model <- lm(Interest_Rate ~ Period, data = df)
summary(model)
## 
## Call:
## lm(formula = Interest_Rate ~ Period, data = df)
## 
## 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