Project Objective
To investigate mortgage rates, identify trends, and forecast future rates using time series and linear modeling
Question 1 & 2: Develop the Model & Asses Predictor
Significance
Step 1: Install and load requried libraries
#install.packages("readxl")
#install.packages("ggplot2")
library(readxl) #allows us to import excel files
library(ggplot2) #allows us to make time series plot
Step 2: Import & clean the data
file_path <- "/Users/ericheredia/Downloads/Mortgage.xlsx"
mortgage_data <- read_excel(file_path)
head(mortgage_data)
## # A tibble: 6 × 3
## Year Period Interest_Rate
## <dttm> <dbl> <dbl>
## 1 2000-01-01 00:00:00 1 8.05
## 2 2001-01-01 00:00:00 2 6.97
## 3 2002-01-01 00:00:00 3 6.54
## 4 2003-01-01 00:00:00 4 5.83
## 5 2004-01-01 00:00:00 5 5.84
## 6 2005-01-01 00:00:00 6 5.87
Step 3: Summarize the data
head(mortgage_data)
## # A tibble: 6 × 3
## Year Period Interest_Rate
## <dttm> <dbl> <dbl>
## 1 2000-01-01 00:00:00 1 8.05
## 2 2001-01-01 00:00:00 2 6.97
## 3 2002-01-01 00:00:00 3 6.54
## 4 2003-01-01 00:00:00 4 5.83
## 5 2004-01-01 00:00:00 5 5.84
## 6 2005-01-01 00:00:00 6 5.87
summary(mortgage_data)
## Year Period Interest_Rate
## Min. :2000-01-01 00:00:00 Min. : 1.00 Min. :2.958
## 1st Qu.:2005-10-01 18:00:00 1st Qu.: 6.75 1st Qu.:3.966
## Median :2011-07-02 12:00:00 Median :12.50 Median :4.863
## Mean :2011-07-02 18:00:00 Mean :12.50 Mean :5.084
## 3rd Qu.:2017-04-02 06:00:00 3rd Qu.:18.25 3rd Qu.:6.105
## Max. :2023-01-01 00:00:00 Max. :24.00 Max. :8.053
Data Description: A description of some of the features are presented in the table below.
Variable | Definition
------------|--------------
1. Period | A numeric identifier
2. Interest Rate | The avg. interest rate for the corresponding year
summary(mortgage_data)
Interpretation : The median interest rate is 4.86 for the 30 year fixed rate.
Step 4: Build time series plot
library(ggplot2)
ggplot(mortgage_data, aes(x = Period, y = Interest_Rate)) +
geom_line() +
geom_point() +
labs(title = "30-Year Fixed-Rate Mortgage Interest Rates (Time Series)",
x = "Period (Years Since 2000)",
y = "Interest Rate (%)") +
theme_minimal()
Interpretation: There is a general decline over the past two decades, with significant recent upward movement.
Step 5: Build the linear regression model
model <- lm(Interest_Rate ~ Period, data = mortgage_data)
intercept <- coef(model)[1]
slope <- coef(model)[2]
cat("Trend Equation: Interest Rate = ", round(intercept, 2), " + ", round(slope, 2), " * Period\n")
## Trend Equation: Interest Rate = 6.7 + -0.13 * Period
Interpretation: There is a general declining trend in mortgage interest rates over the observed time period.
Question 3: Forecast the AVG interest rate for period 25
period_25 <- 25
forecast <- intercept + slope * period_25
cat("Forecasted Interest Rate for Period 25 (2024): ", round(forecast, 2), "%\n")
## Forecasted Interest Rate for Period 25 (2024): 3.47 %
Interpretation:The linear trend equation predicts that the average interest rate for a 30-year fixed mortgage will be approximately 3.47% in 2024.