Understanding least squares

In some instances, we might want to prove that there is a functional relationship between two variables and, hence, just use one of them in our model – since the other can be easily approximated by an expression. In this case, it is useful to rely on the least squares method. Given a set of points (x_i,y_i) and a function such as y'_i = f(x_i), this method minimizes the square of the differences between y'_i and y_i. The general expression for the minimization that we are calculating is as follows:

We will use two columns from our data table, namely weight and mpg:

1. Create a new table in a new sheet.
2. Copy the values of the weight and mpg columns.

3. Order the rows by the value of weight; the resulting table is as follows:

4. Insert a line chart to see what the functional relationship looks like, as follows:

Let's say that we assume...