A pairs trade relies on the fact that - if the correlation between two stocks is atleast 95% they follow a similar trend. But due to temporary market conditions like the announcement of results in a company or due to mishaps in another company, the stock direction of that company may deviate from the mean value.
Given the striking similarities between the two banks used for this capstone, a change in the business environment of one bank, affects the paired bank in a similar manner. However because of a high correlation, the deviated stock tries to return to the mean path. Pairs trading is a market neutral strategy wherein when one stock is bought, another is sold short.
We exercise this opportunity when the stock deviates from its expected trend and should enter the trade if the standard deviation exceeds 95%.

Linear regression is a statistical operation wherein the input is an array of two sets of numbers and the output contains different parameters, including the intercept and constant needed for constructing the straight line equation.
Linear regression analyzes two separate variables in order to define a single relationship. In price-action analysis, this refers to the variables of price and time. Quantitative traders who use charts recognize the ups and downs of price printed horizontally from day-to-day, minute-to-minute, or week-to-week, depending on the evaluated time frame. The different time frame approaches are what make linear regression analysis so attractive.

Logic behind Pairs Trading: https://zerodha.com/varsity/chapter/pair-trading-basics/
Density curves in equity: https://mintpaisa.com/procedure-of-executing-pair-trade/
Error Ratio computation: https://zerodha.com/varsity/chapter/the-error-ratio/
Correlation and Cointegration: https://blog.quantinsti.com/pairs-trading/#cointegration
Z-Score relevance: https://medium.com/auquan/pairs-trading-data-science-7dbedafcfe5a