Using the SPY Index for Linear Regression Analysis of AAPL Stock Returns

Abstract

This study investigates the predictive relationship between Apple’s (AAPL) stock returns and the SPY index, representing the S&P 500. Utilizing a linear regression model, we aim to quantify the extent to which changes in the SPY index can explain variations in AAPL returns. Our findings show that the model parameters—an intercept (Beta0) of 0.001 and a slope (Beta1) of 1.067—indicate a strong positive correlation between these variables. The model’s predictive accuracy is validated using Root Mean Square Error (RMSE), with an in-sample RMSE of 0.000123 and an out-of-sample RMSE of 0.000234. We also introduce a hedging strategy to mitigate risks associated with market volatility. This research contributes to the field by providing a robust, data-driven framework for predicting stock returns and managing risk.