- This is the “least squares” method.
- Situational Example:
- “If a country’s broad stock index (X) appreciates 5%, by how much will the value of that index’s largest air transportation stock change?”
- You will apply this type of modeling in the equity section, when looking at the CAPM approach to asset valuation.
- Simple Regression can be expressed as follows:
Yi = b0 + b1Xi + ei
- b0 = the y-intercept. Yi = b0, when observation Xi = 0 (zero)
- b1 = the slope coefficient – the change in Y per unit change in X.
- Xi = the observation for the independent variable. Ex: the value of a stock index.
- Yi = the observed dependent variable for Xi.
- ei = the error term or the part of the dependent value not explained by the independent variable; the expected value of the error term is zero and this is one of the standard assumptions for simple regression.
- Note: the y-intercept and slope coefficient are the known as the model’s parameters.
- A hat “^” is typically used when referring to predicted values and the subscript “i” typically refers to actual observations.
Six Assumptions of Simple Linear Regression
- Y and X must have a liner relationship.
- X is not random.
- The expected value of e is 0 (zero).
- The e term does not exhibit heteroskedasticity, meaning that the error term’s variance is the same for all observations.
- The error term is uncorrelated across all observations (or no serial correlation).
- The error term has a normal distribution.
A violation of one or more of these assumptions threatens the validity of your model’s conclusions.