Course Name: Financial Time Series Analysis for Trading, Section No: 7, Unit No: 4, Unit type: Quiz
Hi,
What is SSE? What does it mean by SSE lesser than 1? And how do you calculate MSE and finding out that it’s a better fit?
Hi SZE,
Imagine you just built a regression model, and now you want to check how well it performs. The best way to do this is to compare the actual values with the predicted values and see how much they differ. Let’s walk through it together.
First, let’s take a simple dataset where you have actual values and predicted values from your model. You subtract each predicted value from the actual value to find the error:
| Actual | Predicted | Error (Actual - Predicted) |
|---|---|---|
| 10 | 8 | 2 |
| 11 | 13 | -2 |
| 15 | 14 | 1 |
Now, if you just sum up these errors, you get:
That looks pretty small, right? But here’s the problem: errors can cancel each other out. If you have big positive and negative errors, they might add up to a small total, even though your model is performing poorly. So summing errors isn’t very useful.
To avoid this, we square the errors. This does two things: it makes all errors positive, and it penalizes larger errors more. Let’s apply this to our dataset:
| Actual | Predicted | Error (Actual - Predicted) | Squared Error |
|---|---|---|---|
| 10 | 8 | 2 | 4 |
| 11 | 13 | -2 | 4 |
| 15 | 14 | 1 | 1 |
Now, instead of just summing the raw errors, we sum the squared errors:
SSE (Sum of Squared Errors) = 4 + 4 + 1 = 9
This gives us a better idea of the total error without cancellation. But we don’t just want the sum—we want an average measure that tells us how large our errors typically are. That’s where the Mean Squared Error (MSE) comes in.
MSE is simply the SSE divided by the number of data points:
So what does this number tell us? A lower MSE means your model’s predictions are closer to the actual values. The squaring operation also ensures that large errors have a bigger impact, so the model learns to minimize those more effectively. That’s why MSE is widely used in optimization, especially in gradient-based learning methods.
So in summary, MSE is a way of measuring how far off our predictions are, while also making sure that big mistakes get penalized more than small ones. It’s a key metric in regression models, helping you understand and improve your predictions!
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