Class Exercise 16 Homework
##Question 1 Code
###All the code in question one
week <- 1:6 #This is the independent variable - time
sales <- c(17,13,15,11,17,14) #This is the dependent variable
forecast_a <- sales[-length(sales)] #Excludes the last value
actual_a <- sales[-1] #Excludes the first sale
mse_a <- mean((actual_a - forecast_a)^2)
mse_a #Mean Sqaured Error is 16.2## [1] 16.2forecast_week7_a <- tail(sales, 1)
forecast_week7_a## [1] 14cumulative_averages <- cumsum(sales[-length(sales)]) / (1:(length(sales) - 1))
cumulative_averages## [1] 17.0 15.0 15.0 14.0 14.6forecast_b <- cumulative_averages
actual_b <- sales[-1] #Exclude the first value
mse_b <- mean((actual_b - forecast_b)^2)
mse_b #Mean square error is 8.272## [1] 8.272forecast_week7_b <- mean(sales)
forecast_week7_b## [1] 14.5better_method <- ifelse(mse_a < mse_b, "Most Recent Value", "Average of All Data" )
list(
MSE_Most_Recent_Value = mse_a,
Forecast_Week7_Most_Recent = forecast_week7_a,
MSE_average = mse_b,
Forecast_Week7_Average = forecast_week7_b,
Better_method = better_method
)## $MSE_Most_Recent_Value
## [1] 16.2
##
## $Forecast_Week7_Most_Recent
## [1] 14
##
## $MSE_average
## [1] 8.272
##
## $Forecast_Week7_Average
## [1] 14.5
##
## $Better_method
## [1] "Average of All Data"Question 2 Code
All the code & Interp for Q2
#install.packages("dplyr")
#install.packages("zoo")
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(zoo)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric#Time Series Data
df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
data=c(240,352,230,260,280,322,220,310,240,310,240,230))
summary(df)## month data
## Min. : 1.00 Min. :220.0
## 1st Qu.: 3.75 1st Qu.:237.5
## Median : 6.50 Median :250.0
## Mean : 6.50 Mean :269.5
## 3rd Qu.: 9.25 3rd Qu.:310.0
## Max. :12.00 Max. :352.0plot(df$month, df$data, type = "o", col = "blue", xlab = "Month", ylab = "Building Contracts(in millions)", main = "Alabama building contracts" )
df$avg_data3 <- c(NA, NA, NA,
(df$data[1] + df$data[2] + df$data[3]) / 3,
(df$data[2] + df$data[3] + df$data[4]) / 3,
(df$data[3] + df$data[4] + df$data[5]) / 3,
(df$data[4] + df$data[5] + df$data[6]) / 3,
(df$data[5] + df$data[6] + df$data[7]) / 3,
(df$data[6] + df$data[7] + df$data[8]) / 3,
(df$data[7] + df$data[8] + df$data[9]) / 3,
(df$data[8] + df$data[9] + df$data[10]) / 3,
(df$data[9] + df$data[10] + df$data[11]) / 3
)
df <- df %>%
mutate(
squared_error = ifelse(is.na(avg_data3), NA, (data - avg_data3)^2)
)
mse <- mean(df$squared_error, na.rm = TRUE)
mse #Output the MSE- 2040.444## [1] 2040.444alpha <- 0.2
exp_smooth <- rep(NA, length(df$data))
exp_smooth[1] <- df$data[1] #Starting point
for(i in 2: length(df$data)){
exp_smooth[i] <- alpha * df$data[i-1] + (1 - alpha) * exp_smooth[i-1]
}
mse_exp_smooth <- mean((df$data[2:12] - exp_smooth[2-12])^2)
mse_exp_smooth #Output the MSE - 2281.898## [1] 2281.898#Comparison
better_method <- ifelse(mse_exp_smooth, "Three- Month Building Contracts", "Exponential Smoothing")
#Results
list(
MSE_Moving_Average = mse,
MSE_Exponential_Smoothing = mse_exp_smooth,
Better_method = better_method
)## $MSE_Moving_Average
## [1] 2040.444
##
## $MSE_Exponential_Smoothing
## [1] 2281.898
##
## $Better_method
## [1] "Three- Month Building Contracts"Question 3,4,5 code
All the code for these questions with interps too kinda
#install.packages("ggplot2")
#install.packages("readxl")
library(ggplot2)
library(readxl)
df <- read_excel("Mortgage.xlsx")
summary(df)## Year Period Interest_Rate
## Min. :2000-01-01 00:00:00 Min. : 1.00 Min. :2.958
## 1st Qu.:2005-10-01 18:00:00 1st Qu.: 6.75 1st Qu.:3.966
## Median :2011-07-02 12:00:00 Median :12.50 Median :4.863
## Mean :2011-07-02 18:00:00 Mean :12.50 Mean :5.084
## 3rd Qu.:2017-04-02 06:00:00 3rd Qu.:18.25 3rd Qu.:6.105
## Max. :2023-01-01 00:00:00 Max. :24.00 Max. :8.053ggplot(df, aes(x = Period, y = Interest_Rate)) +
geom_line() +
geom_point() +
xlab("Period") +
ylab("Interest_Rate") +
ggtitle("Time Series Plot of Mortage Rates")
model <- lm(Interest_Rate ~ Period, data =df)
summary (model)##
## Call:
## lm(formula = Interest_Rate ~ Period, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3622 -0.7212 -0.2823 0.5015 3.1847
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.69541 0.43776 15.295 3.32e-13 ***
## Period -0.12890 0.03064 -4.207 0.000364 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.039 on 22 degrees of freedom
## Multiple R-squared: 0.4459, Adjusted R-squared: 0.4207
## F-statistic: 17.7 on 1 and 22 DF, p-value: 0.0003637df$predicted_rates <- predict(model)
df$residuals <- df$Interest_Rate - df$predicted_rates
mse <- mean(df$residuals^2)
cat("Mean Squared Error(MSE)", mse, "\n")## Mean Squared Error(MSE) 0.989475df$percentage_error <- abs(df$residuals / df$Interest_Rate) * 100
mape <- mean(df$percentage_error)
cat("Mean Absolute Percentage Error (MAPE):", mape, "%\n")## Mean Absolute Percentage Error (MAPE): 15.79088 %forecast_period_25 <- predict(model, newdata = data.frame(Period = 25))
forecast_period_25## 1
## 3.472942