Introduction to linear regression

In this video lecture we explain the main characteristics of linear regression and how to perform it on large data sets using RHadoop. Let us continue first with songs complexity example. Recall we have a data set of songs and for each song we know its complexity measured by UNIGRAM and BIGRAM entropy. Based on the scatter plot we can conclude there must be a relatively strong linear relation between these two variables. Therefore we look for two parameters, beta zero and beta one, that define a line which fits well (best) the dots in the plot.

The criteria to find best line is actually a sum-of-square of vertical residuals. These are vertical distances between the data points and the vertical projections of these points to the line along the y axis. Note that we can also consider non-linear regression. For example, the goal of quadratic regression is to find parabola that fits best the data points. Criteria might be again the sum of squares of vertical residuals. Likewise we can define the exponential regression.