#** Project Objective

To analyse the average interest rate (%) for a 30-year fixed-rate mortgage over a 20-year period (FreddieMac website) and predict future rate.

Question 3A : Develop the Model & Assess Predictor Significance

Step 1 : Install and load required

library(readxl)  # For reading Excel files

## Warning: 套件 'readxl' 是用 R 版本 4.4.2 來建造的

library(ggplot2) # For creating plots

Step 2 : # Load data from Excel file

df <- read_excel(file.choose())  # Choose file using a file dialog

summary(df)

##       Year                         Period       InterestRate  
##  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

Step 3 : # Visualize the Data

ggplot(df, aes(x = Period, y = InterestRate)) +
  geom_line() +               # Add line for time series
  geom_point() +              # Add points for data visualization
  xlab("Period") +            # Label for x-axis
  ylab("Interest Rate") +     # Label for y-axis
  ggtitle("30-year fixed-rate mortgage over a 20-year period")  # Title of the plot

## Question 3B : Fit a linear model (InterestRate ~ period)

model <- lm(InterestRate ~ Period, data = df)
summary(model)

## 
## Call:
## lm(formula = InterestRate ~ 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

Question 3C : Create a new data frame with the predictor ‘Period’ for the forecast

new_data1 <- data.frame(Period = 25)

# Predict the interest rate for period 25
prob1 <- predict(model, newdata = new_data1, type = "response")

# Print the forecasted interest rate
cat("Forecasted average interest rate for period 25 (2024):", prob1, "\n")

## Forecasted average interest rate for period 25 (2024): 3.472942