Linear regression is one of the most widely used statistical methods available today. It is used by data analysts and students in almost every discipline. However, for the standard ordinary least squares method, there are several strong assumptions made about data that is often not true in real world data sets. This can cause numerous problems in the least squares model. One of the most common issues is a model overfitting the data. Ridge Regression and LASSO are two methods used to create a better and more accurate model. I will discuss how overfitting arises in least squares models and the reasoning for using Ridge Regression and LASSO include analysis of real world example data and compare these methods with OLS and each other to further infer the benefits and drawbacks of each method.

In mathematics, a rational number is any number that can be expressed as the quotient
or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q
may be equal to 1, every integer is a rational number. The set of all rational numbers,
often referred to as ”the rationals”, is usually denoted by a boldface Q (or blackboard
bold , Unicode ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian
for ”quotient”. The decimal expansion of a rational number always either terminates
after a finite number of digits or begins to repeat the same finite sequence of digits over
and over. Moreover, any repeating or terminating decimal represents a rational number.
These statements hold true not just for base 10, but also for any other integer base (e.g.
binary, hexadecimal). A real number that is not rational is called irrational. Irrational
numbers include √2, , e, and . The decimal expansion of an irrational number continues
without repeating. Since the set of rational numbers is countable, and the set of real
numbers is uncountable, almost allreal numbers are irrational.

Through the modification of the kernel on a Ubuntu system, we managed to solve the n-Queens problem after changing the default time-slice, swappiness, latency and wakeup-granularity to different values and testing the problem.