See Part I for an overview of the linear models and the concept of “regression”.
Nomenclature
When we read and learn about regression (and econometrics), every term or concept goes by a variety of names.
Visit QuantInsti website to view the complete Nomenclature table Vivek Krishnamoorthy has created: https://blog.quantinsti.com/linear-regression/#nomenclature
Types of linear regression
1. Simple linear regression
Imagine that we hold the Coca-Cola (NYSE : KO) stock and are interested in its returns. Conventionally, we denote our variable of interest with the letter YY. We usually have multiple observations (taken to be nn) of it. So, the YY that we previously mentioned is an n-dimensional vector containing values YiYi.
Here and throughout this post, I use the scalar versions of the equations. You can refer to this section to view the matrix forms. You can also read a more detailed treatment of the analytical expressions and derivations in standard econometric textbooks like Baltagi (2011), Woolridge (2015) and Greene (2018).
We want to examine the relationship between our stock’s returns(Y) and the market returns(denoted as X). We believe the market returns i.e. the SPDR S&P 500 ETF (NYSEARCA : SPY) should tell us something about KO‘s returns. For each observation i,
Equation 1 is just a dolled-up version of y=mx+c that we’d seen earlier with an additional ϵi term. In it β0 and β1 are commonly referred to as the intercept and the slope respectively.
This is the simple linear regression model.
We call it simple, since there is only one explanatory variable here; and we call it linear, since the equation is that of a straight line. It’s easy for us to visualize it in our mind’s eye since they are like the X– and Y -coordinates on a Cartesian plane.
A linear regression is linear in its regression coefficients.
A natural extension to this model is the multiple linear regression model.
Stay tuned for the next installment in which Vivek will discuss multiple linear regression.
Visit QuantInsti for additional insight on this topic: https://blog.quantinsti.com/linear-regression/.
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