Correlation and regression

By the end of the study, the reader will be able to;

1.Define correlation

2.Define regression

3.Define and understand the correlation equation.

4.Compute a

5.Compute b

6.Find correlation coefficient r

7.Understand intrapolation

8.Understand extrapolation

Table of contents

1.Introduction

-Define correlation

-Define regression

-History of correlation and regression

2.Main body

-The correlation equation

-Computation of a

-Computation of b

-Computation of correlation  coefficient  r

-Intrapolation

-Extrapolation

3.Practice questions on correlation and regression.

4.Summary of correlation and regression

5.Referrences.

1.Introduction

What is correlation? Correlation can be defined as any statistical relationship between between bivariate data often in a linear relationship.

What is regression? Regression is that property of bivariate statistical data to be independent of one another.

What is the history of correlation and regression? The history of correlation and regression dates to the nineteenth century.Two statisticians are credited to the formulation of correlation and regression;Karl Pearson and Sir Francis Galton invented correlation and regression.

Karl Pearson, one of the statisticians credited on formulation of regression and correlation.

Image source:https://en.m.wikipedia.org/wiki/Karl_Pearson

Sir Francis Galton one of the inventors of correlation and regression

Image source: https://en.m.wikipedia.org/wiki/Francis_Galton

2.The main body

Let us consider the following example;

The number of reading hours and examination results of ten students in school A were recorded and tabulated respectively as X and Y respectively as shown in the table below;

Let us now add more columns to our table,we will add the columns of X²,Y² and XY

What is the linear correlation equation?

This is an equation showing the linear relationship between variable y and x and it goes;

y = ax + b

How then do we compute a;

a = (Σx)(Σy) - nΣxy / (Σx)² - nΣx²

And so we can then easily compute a from the data in our table;

a = (55)(43) - 10(266) / (55)² - 10(385)

= -295/ -825 = 0.3576

To calculate b we use the formulae;

b = (Σx)(Σxy) - (Σy)(Σx²) / (Σx)² - nΣx²

Therefore to find our b;

(55)(266) - (43)(385) / (55)² - 10(385)

= -1925 / -825 = 2.3333

With the following a and b we have found our linear correlation equation which is;

y = 0.3576x + 2.3333

Sx =

After doing that let us now proceed to find the correlation coefficient r and to do that we first find the standard deviation of x and y;