# Re-calculating the errors/residuals in regression using another variable range (Stock price and volatility) [closed]

We are working on using regression to do analysis of stock returns (i.e. predicting the stock price). We have some fundamental metrics like PE ratio and EBITDA (which are the independent variables), and the dependent variable is the price. We want to test the hypothesis (through regression only at this time) that some of the fundamental metrics are a good indicator of long-term price movement.

We are wondering if we can be a bit creative (or may be it makes no sense statistically? ....) and see if we can actually adjust the error terms something like the below by using another variable volatility to apply against the Y (price) and use it to adjust the "actual" error calculated. The hope is that the line of fit will better take into consideration the point estimate and the price volatility. We are relatively new to this and so would appreciate if there are better ways to do it or if you think the below is a good way. How can we do it in R?

You don't have to adjust residual error by volatility, since you can remove cluster volatility in the log price returns using a GARCH model before running any kind of regression. Below is a plot of volatility over time, $$\sigma(t)$$, as well as the SP500 log price returns with cluster volatility removed (red line). Be sure to always use the log price return, i.e., $$\log(\frac{P_{t-1}}{P_t})= \log(P_t)-\log(P_{t-1})$$ as the outcome, as it is more normally distributed than price.