**Predicting Average Interest Rate for a 30-Year Fixed-Rate Mortgage Over a 20-Year Period

Project Objective

To investigate the relationship between period and interest rate and forecast the interest rate for period 25

Question 1: Construct a time series plot

Step 1: Install and load libraries

#install.packages("ggplot2")

library(readxl)
library(ggplot2)

Step 2: Import the data

df <- read_excel("Mortgage.xlsx")

Step 3: Summarize the data

summary(df) 

##       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 interest rate is 5.08

Step 4: Construct a time series plot

 ggplot(df, aes(x = Period, y = Interest_Rate)) +
  geom_line() +
  geom_point() +
  xlab("Period") + 
  ylab("Interest_Rate") + 
  ggtitle("Time Series Plot of Mortgage Interest Rate")

Interpreation: We observe there is a downward trend in interest rate from period 1 to period 22 and then there is upward from period 23 to 24.

Question 2: Develop the linear trend equation for this time series.

# Develop a linear trend equation
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

Interpretation: 
- Result - estimated linear trend equation: Interest_Rate = 6.70 - 0.13*Period OR
- T_hat = 6.70 - 0.13*t
- The R-squared is 0.45 (The model explains 45% of the variability in the dependent variable)
- The overall model is significant as p-value < 0.05

Question 3: Using the linear trend equation from question 3B, forecast the average interest rate for period 25 (i.e., 2024).

# Forecast the average interest rate for period 25
forecast_period_25 <- predict(model, newdata = data.frame(Period = 25))
forecast_period_25

##        1 
## 3.472942

Interpretation: We can see that the average interest rate for period 25 is 3.47.