Computing regression parameters

Once we've determined that two variables have some kind of relationship, the next step is to determine a way to estimate the dependent variable from the value of the independent variable. With most real-world data, there are a number of small factors that will lead to random variation around a central trend. We'll be estimating a relationship that minimizes these errors.

In the simplest cases, the relationship between variables is linear. When we plot the data points, they will tend to cluster around a line. In other cases, we can adjust one of the variables by computing a logarithm or raising it to a power to create a linear model. In more extreme cases, a polynomial is required.

How can we compute the linear regression parameters between two variables?

Getting ready

The equation for an estimated line is this:

Given the independent variable, x, the estimated or predicted value of the dependent variable, , is computed from the α and β parameters.

The goal is to...