Estimating the line of best fit
In this section, we’ll dive deeper into the least squares method, the gold standard for estimating the line of best fit. We’ll explore the intuition behind this technique and walk through various examples to illustrate its power in uncovering patterns in data.
To better understand the least squares method, let’s walk through a couple of examples:
- Example 1: A school principal wants to understand the relationship between students’ study hours and their test scores. The principal plots the data on a graph, with study hours on the horizontal axis and test scores on the vertical axis. Each data point represents a student’s study hours and the corresponding test score.
Applying the least squares method, the principal aims to find the line that minimizes the sum of the squared residuals – the squared vertical distances between the actual test scores and the predicted scores generated by the line. Once the...
