- 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:
Y
_{i}= b_{0}+ b_{1}X_{i }+ e_{i}- b
_{0}= the y-intercept. Y_{i}= b_{0}, when observation X_{i}= 0 (zero) - b
_{1}= the slope coefficient – the change in Y per unit change in X. - X
_{i}= the observation for the independent variable. Ex: the value of a stock index. - Y
_{i}= the observed dependent variable for X_{i}. - e
_{i}= 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.

- b

- 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.

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