A fast way to compute Least Squares Teo Zhi Shen Anderson - - PowerPoint PPT Presentation

A fast way to compute Least Squares

Teo Zhi Shen Anderson Serangoon Junior College

Least squares and Linear regression

Used in the study of relationships between variables X and Y to :

• 1. Determine how strong the relationship is between the 2 variables X and Y
• 2. Predict effects on Y caused by changes in X
• 3. Predict a trend between X and Y

Method of Least Squares

Minimises the squares of the differences between the data points and modelled equation.

Scatter plot

Rise of Big Data

More information generated Increasingly large data sets Longer computation times + Reduced efficiency

Applications of Least Square

Used in :

The Two point method

The new two point method aims to form the line of best fit based on 2 points. 1.Geometric Centre of the scatter plot 2.” Centre of Mass”

• f the scatter plot

Improvements

2 Point Method Current Method

• Simpler

computational steps

• Contains complex
• perations like partial

derivatives

• Lesser operations
• More operations

Aims and Objectives

To determine whether the Two Point Method is indeed faster and more efficient than the current method for computing least square.

Computation Time

Through the use of Python, the computation time for both methods can be compared with one another to confirm that the 2 point method is indeed faster.

Comparing Computing Times

Trends

For smaller sets of data, the current method is faster. However for larger sets, the 2 point method is faster.

Conclusion

The new Two point method is indeed faster in calculating large data sets. However, both methods are still vulnerable to outlier values. Additionally , the new Two Point method can only be used to improve the efficiency of linear regression but not non-linear data sets.