1. Introduction

This report aims to analyze the relationship between the Ruble-USD exchange rate and various financial indicators, such as the S&P 500 index and the price of gold. We will perform descriptive analytics on the Ruble-USD exchange rate over time, calculate basic descriptive statistics, visualize key trends, and examine the correlation between selected financial variables. Additionally, we will apply a simple linear regression model to predict the Ruble-USD exchange rate based on the S&P 500 index and gold prices.

2. Dataset Overview

The dataset contains daily data for the period from January 11, 2006, to March 12, 2020.
It includes the following variables:

t: Time period (daily)
Date: Actual date in mm/dd/yyyy format
Day: Day of the date
Month: Month of the date
Year: Year of the date
RubPerUSD: Exchange rate in rubles per US dollar
SP500: S&P 500 financial index value (USD)
Gold: Price of gold in USD per ounce
Silver: Price of silver in USD per ounce
Aluminum: Price of aluminum in USD per ton
Platinum: Price of platinum in USD per ounce
Brent: Price of Brent crude oil in USD per barrel
Cocoa: Price of cocoa beans in USD per metric ton

3. Data Loading and Overview

Load necessary libraries

library(readxl) 
library(ggplot2)

Load the dataset

file_path <- 'C:/Users/Valery/Desktop/domashka/1.xlsx' 
data <- read_excel(file_path)

View the first few rows of the data

head(data)

4. Table of Variables

Below is a table that classifies the variables in the dataset, indicating whether they are quantitative or qualitative, their measurement levels, and appropriate types of charts.

Create a table for variable classifications

variable_info <- data.frame( Variable = c("t", "Date", "Day", "Month", "Year", "RubPerUSD", "SP500", "Gold", "Silver", "Brent", "Cocoa"), Quantitative_or_Qualitative = c("Qualitative", "Qualitative", "Qualitative", "Qualitative", "Qualitative", "Quantitative", "Quantitative", "Quantitative", "Quantitative", "Quantitative", "Quantitative"), Measurement_Level = c("Counts", "Nominal", "Ordinal", "Ordinal", "Ordinal", "Ratio", "Ratio", "Ratio", "Ratio", "Ratio", "Ratio"), Appropriate_Charts = c("Bar plot", "Bar plot", "Bar plot", "Bar plot", "Bar plot", "Line chart, Boxplot", "Line chart, Boxplot", "Line chart, Boxplot", "Line chart, Boxplot", "Line chart, Boxplot", "Line chart, Boxplot") )

Display the table

variable_info

5. Descriptive Statistics and Visualizations

We will explore three key variables: RubPerUSD, SP500, and Gold. Below are the visualizations and descriptive statistics for these variables.

5.1. Line Chart of RubPerUSD (Ruble-USD Exchange Rate)

ggplot(data, aes(x = Date, y = RubPerUSD)) + geom_line(color = "blue") + labs(title = "Ruble-USD Exchange Rate", x = "Date", y = "Rub per USD") + theme_minimal()

5.2 Line Chart of SP500 (S&P 500 Index)

ggplot(data, aes(x = Date, y = SP500)) + geom_line(color = "green") + labs(title = "S&P 500 Index", x = "Date", y = "SP500 Value") + theme_minimal()

5.3. Line Chart of Gold (Price of Gold)

ggplot(data, aes(x = Date, y = Gold)) + geom_line(color = "gold") + labs(title = "Gold Price (USD per ounce)", x = "Date", y = "Gold Price (USD)") + theme_minimal()

5.4. Measures of Central Tendency

For the selected variables, we will calculate the mean, median, and standard deviation.

Calculating mean, median, and standard deviation for RubPerUSD

mean_rub <- mean(data$RubPerUSD, na.rm = TRUE)
median_rub <- median(data$RubPerUSD, na.rm = TRUE) 
sd_rub <- sd(data$RubPerUSD, na.rm = TRUE)

Calculating mean, median, and standard deviation for SP500

mean_sp500 <- mean(data$SP500, na.rm = TRUE)
median_sp500 <- median(data$SP500, na.rm = TRUE) 
sd_sp500 <- sd(data$SP500, na.rm = TRUE)

Calculating mean, median, and standard deviation for Gold

mean_gold <- mean(data$Gold, na.rm = TRUE)
median_gold <- median(data$Gold, na.rm = TRUE) 
sd_gold <- sd(data$Gold, na.rm = TRUE)

Displaying the results

mean_rub

## [1] 42.03178

median_rub

## [1] 32.36895

sd_rub

## [1] 16.46466

mean_sp500

## [1] 1773.56

median_sp500

## [1] 1539.59

sd_sp500

## [1] 626.9194

mean_gold

## [1] 1192.991

median_gold

## [1] 1241.675

sd_gold

## [1] 308.2245

5.5 Correlation Matrix

Now, lets calculate the correlation matrix for RubPerUSD, SP500, and Gold to understand the relationships between these variables.

Calculate the correlation matrix for the selected variables: RubPerUSD, SP500, and Gold

cor_matrix <- cor(data[c("RubPerUSD", "SP500", "Gold")], use = "complete.obs")

Display the correlation matrix

cor_matrix

##           RubPerUSD     SP500      Gold
## RubPerUSD 1.0000000 0.8479783 0.2827953
## SP500     0.8479783 1.0000000 0.3033126
## Gold      0.2827953 0.3033126 1.0000000

5.6. Complex Chart Combining Multiple Variables

We will create a combined line chart to compare RubPerUSD, SP500, Gold, and Brent over time.

Combined Line Chart for RubPerUSD, SP500, Gold, and Brent

ggplot(data) +
  geom_line(aes(x = Date, y = RubPerUSD, color = "RubPerUSD")) +
  geom_line(aes(x = Date, y = SP500, color = "SP500")) +
  geom_line(aes(x = Date, y = Gold, color = "Gold")) + 
  geom_line(aes(x = Date, y = Brent, color = "Brent")) + 
  labs(title = "Comparing Exchange Rate, S&P 500, Gold Price, and Brent Oil Price",
       x = "Date", y = "Value") +
  theme_minimal() +
  scale_color_manual(values = c("blue", "green", "gold", "brown"))

## Warning: Removed 14 rows containing missing values or values outside the scale range
## (`geom_line()`).

6. Linear Regression Model

In this section, we will perform linear regression with RubPerUSD as the dependent variable and SP500 and Gold as independent variables.

Linear Regression Model: RubPerUSD as dependent variable

model <- lm(RubPerUSD ~ SP500 + Gold, data = data)

Display the model summary

summary(model)

## 
## Call:
## lm(formula = RubPerUSD ~ SP500 + Gold, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.232  -6.649  -1.819   3.604  38.816 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.1274566  0.7248986   1.555  0.11998    
## SP500       0.0220244  0.0002786  79.068  < 2e-16 ***
## Gold        0.0015030  0.0005661   2.655  0.00798 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.71 on 2738 degrees of freedom
##   (51 пропущенное наблюдение удалено)
## Multiple R-squared:  0.7198, Adjusted R-squared:  0.7196 
## F-statistic:  3517 on 2 and 2738 DF,  p-value: < 2.2e-16

6.1. Plotting the Regression Results

Plotting the regression results

ggplot(data, aes(x = SP500, y = RubPerUSD)) +
  geom_point() +
  geom_smooth(method = "lm", aes(color = "SP500 vs RubPerUSD")) +
  labs(title = "Linear Regression: SP500 vs RubPerUSD", x = "SP500 Index", y = "RubPerUSD") +
  theme_minimal()

## `geom_smooth()` using formula = 'y ~ x'

## Warning: Removed 51 rows containing non-finite outside the scale range
## (`stat_smooth()`).

## Warning: Removed 51 rows containing missing values or values outside the scale range
## (`geom_point()`).

7. Conclusion

This report explored the relationship between the Ruble-USD exchange rate and financial indicators such as the S&P 500 index and gold prices.

Through descriptive analysis, correlation analysis, and linear regression modeling, we found that SP500 and Gold are significant predictors of the RubPerUSD exchange rate.

Visualizations helped to better understand the trends and dynamics between these variables.

Appendix: R Code for Calculations and Plots

Full code for data processing, statistical calculations, and plotting

Analysis of Ruble-USD Exchange Rates and Financial Indicators

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