9.1 Linear regression, part 2

Assume we have the following (limited) number of points where we wish to fit a function of the form $y=bx$.

x	y
1	3
2	5
4	4
4	10

For this example we are forcing the intercept term $a$ to equal zero - for most cases you will just fit the linear equation (see Exercise 9.7 where you will consider the intercept $a$). Figure 9.1 displays a quick scatterplot of these data:

Figure 9.1: A scatterplot of a small dataset.

The goal here is to work to determine the value of $b$ that is most likely (in other words, consistent) with the data. However, before we tackle this further we need to understand how to quantify more likely in a mathematical sense. In order to do this, we need to take a quick excursion into probability distributions. Let’s go!