Table of Contents
- What Is Regression?
- Key Takeaways
- How Regression Works
- Regression and Econometrics
- Calculating Regression
- Example of Regression Analysis in Finance
- Explain Like I’m 5 Years Old
- Why Is This Method Called Regression?
- What Is the Purpose of Regression?
- How Do I Interpret a Regression Model?
- What Are the Assumptions That Must Hold for Regression Models?
- The Bottom Line
What Is Regression?
Let me explain regression to you directly: it's a statistical method that looks at how a dependent variable relates to one or more independent variables. You use it to predict or understand how shifts in those independent variables connect to changes in the dependent one.
The most straightforward type is linear regression, which maps out a straight-line relationship between variables—often called simple regression or ordinary least squares (OLS). Picture it as a line of best fit on a graph, where the slope shows how one variable affects the other, and the y-intercept tells you the dependent variable's value when the independent one is zero. There are nonlinear versions too, but they're more complicated.
Key Takeaways
Regression ties a dependent variable to independents and reveals if changes in the latter associate with the former. It fits a line to data to check dispersion around it. You'll see it in economics and finance for things like valuing assets or forecasting. Remember, certain assumptions about your data must hold for the results to make sense. It's great for spotting associations in data, but don't count on it for causation. Also, this isn't the same as regression to the mean in statistics.
How Regression Works
Regression quantifies correlations in your dataset and checks if they're statistically significant. You have simple linear regression for one independent variable predicting the dependent Y, or multiple for two or more. Stepwise regression lets you test each variable individually.
In finance, you might use it to forecast sales based on weather, past data, GDP, or other factors. The CAPM, a common regression model, prices assets and calculates capital costs.
Regression and Econometrics
Econometrics applies statistical tools to finance and economics data, like studying how income affects spending. If data shows a link, regression measures its strength and significance. Add variables like GDP or inflation for multiple linear regression, the go-to in econometrics. But watch out—critics say it over-relies on outputs without tying back to theory or causation.
Calculating Regression
Linear models often use least squares to find the best-fit line by minimizing squared distances from data points to the line. Software handles this, but the formulas are: for simple, Y = a + bX + u; for multiple, Y = a + b1X1 + b2X2 + ... + btXt + u. Here, Y is what you're predicting, X are your independents, a is the intercept, b the slopes, and u the error.
Example of Regression Analysis in Finance
Take how factors like commodity prices or interest rates move asset prices—regression sorts that out. In CAPM, you regress stock returns against a market index like the S&P 500 to get beta, the slope showing risk relative to the market. Add Fama-French factors like market cap or ratios for better estimates.
Explain Like I’m 5 Years Old
Regression checks if two things connect, like how doing one activity links to another. It uses past patterns to guess what happens next.
Why Is This Method Called Regression?
It likely comes from Francis Galton in the 19th century, describing how data like heights regress to an average—most cluster around the mean, with few extremes.
What Is the Purpose of Regression?
You use it to find and measure associations in data, testing their significance for predictions based on history.
How Do I Interpret a Regression Model?
For Y = 1.0 + 3.2X1 - 2.0X2 + 0.21, it means Y rises 3.2 per unit of X1 (holding X2 constant), drops 2 per unit of X2 (holding X1), starts at 1 when both are zero, with a 0.21 error.
What Are the Assumptions That Must Hold for Regression Models?
Your data needs linearity, constant variance (homoskedasticity), independent variables, and normal distribution for proper results.
The Bottom Line
Regression determines relationship strength between a dependent variable and others, useful in finance and beyond, but it shows associations, not causes.
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