• In this presentation, we analyze the relationship between trading volume and stock price using Simple Linear Regression.
• Goal: Predict stock closing price based on trading volume.
• Company Stock being analyzed: Apple.

\[ y = \beta_0 + \beta_1 x + \epsilon \]

where:

• \(y\) is Adjusted (Stock closing price)
• \(x\) is Volume (Trading volume)
• \(\beta_0\) is the intercept
• \(\beta_1\) is the slope
• \(\epsilon\) is the error component

Below is the code chunk used to produce the scatter plot on the previous slide:

ggplot(df, aes(x = Volume, y = Adjusted)) + geom_point(color = “blue”, alpha = 0.6) + geom_smooth(method = “lm”, color =“red”) + ggtitle(“Trading Volume vs. Adjusted Closing Price”)

Where df is:

df <- getSymbols(“AAPL”, src = “yahoo”, from = “2020-01-01”, to = “2024-01-01”, auto.assign = FALSE)

What this means

• The regression model suggests a statisically significant but weak negative relationship between trading volume and stock price.
• Intercept (178.26): Represents the estimated stock price when trading volume is zero.
• Slope (-0.0000004): Indicates that for every additional unit of trading volume, the adjusted closing price decreases slightly.
• The p-value confirms statistical significance, but the small coefficient suggests this effect is negligible in practical terms.
• Other factors likely play a stronger role in stock price movements.

Another method that could be used to analyze the relationship between trading volume and stock price is the Pearson Correlation Coefficient, which measures the strength of direction of the linear relationship between two variables:

\[ r = \frac{ \sum (x_i - \bar{x}) (y_i - \bar{y}) }{ \sqrt{ \sum (x_i - \bar{x})^2 } \sqrt{ \sum (y_i - \bar{y})^2 } } \]

where

• \(x\) represents trading volume
• \(y\) represents adjusted closing price
• \(\bar{x}\) and \(\bar{y}\) are the mean values of X and Y, respectively

This method provides insight into how strongly trading volume and price are correlated, rather than simply modeling price as a function of volume.

• Trading volume has a correlation with stock price, but the effect size is small.
• The model suggests that volume alone is not a strong indicator of stock price.
• Further improvements can be made using multiple regression.
• The Pearson Correlation Coefficient could be used as an alternative measure to analyze the relationship between trading volumn and stock price.

• Dataset Source: Yahoo Finance via ‘quantmod’