Linear Trend Regression Approach
Step 1: Install and load required libraries
library(readxl)
library(ggplot2)
Step 2: Import the data
mortgage_rates <- read_excel("Mortgage.xlsx")
Data Description: A description of the features are presented in the table below.
Variable | Definition
------------- | -------------
1. Period | Year # of data
2. Interest_Rates | Mortgage Rate
Step 3: Summarize the data
summary(mortgage_rates)
## 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
Interpretation: On average the mortgage rate was around 5.084% over the past 24 years.
Step 4: Construct a time Series Plot
ggplot(mortgage_rates, aes(x=Period, y=Interest_Rate)) +
geom_line() +
geom_point() +
xlab("Period") +
ylab("Rates") +
ggtitle("Time series plot of Mortgage Rates")
Interpretation: We can notice a decreasing pattern with a main increase in the rate towards 2023.
Step 5: Devolop a linear Trend Equation
model <- lm(Interest_Rate ~ Period, data = mortgage_rates )
summary(model)
##
## Call:
## lm(formula = Interest_Rate ~ Period, data = mortgage_rates)
##
## 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
Result - estimated linear trend equation: rates= 6.70 - 0.13*period
The R- square is 0.45 (Fits the data Moderatly)
The overall model is significant as the p-value < 0.05
Step 6: Calculate the fitted values from the model
mortgage_rates$predicted_rates <- predict(model)
Interpretation: This is able to show predictions of what the interest rate should look like each year
Calculate the residuals
mortgage_rates$residuals <- mortgage_rates$Interest_Rate - mortgage_rates$predicted_rates
Interpretation: Looking at the difference between the actual rate and the estimated rate
Forecast the mortgage rates in 2024 (i.e., Period 25)
Forecast_Period_25 <- predict(model, newdata = data.frame(Period = 25))
Forecast_Period_25
## 1
## 3.472942
Interpretation: The interest rate would be around 3.47 in the year 2024.