Statistics can help us answer some of life's most burning questions. How does the weather influence people's purchase habits? Does education affect long-term income? Can we predict a person's lifespan based on how much paddle-board yoga they do?
Regression Analysis deals with relationships between quantitative variables like the ones above i.e. the variables must be numerical. It lets us take a step beyond correlation and covariance to uncover more intricate patterns—provided that we have enough data and that the data was reliably collected.
Let's analyze some regression! An owner of a fancy restaurant wants to determine how sales of dishA, a time-consuming dish to prepare, are related to her profits on a given day. She recorded the number of dishA sales and her nightly profit for a month and graphed the data.
The x-axis is the number of dishA sold on a given evening. The y-axis is the restaurant's total profit that night. What does the data seem to be telling us about the relationship between the dishA sales and nightly profit at the restaurant.
As sales increase, profit increases up to a point, but then drops. Seems that eventually, additional dishA do not add to profits. They may take time away from more profitable items.
If the owner were to draw a curve that best represents the data, the curve will look like the below graph.