Statistical Measures: Covariance, Correlation, and Regression Analysis

Covariance

Covariance measures the directional relationship between the returns on two assets. A positive covariance means that asset returns move together, while a negative covariance means they move inversely.

Scatter Diagram

A scatter diagram is used to examine the relationship between both the axes (X and Y) with one variable. In the graph, if the variables are correlated, then the points drop along a curve or line. A scatter diagram or scatter plot gives an idea of the nature of the relationship. These relationships can include:

• Perfect positive correlation
• Perfect negative correlation
• High degree of positive correlation
• High degree of negative correlation
• Low degree of positive correlation
• Low degree of negative correlation
• No correlation

Karl Pearson Coefficient of Correlation and Its Properties and Method of Calculation

A coefficient of correlation is generally applied in statistics to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. There are various types of correlation coefficients. However, Pearson’s correlation (also known as Pearson’s R) is the correlation coefficient that is frequently used in linear regression.

Correlation Coefficient Properties

1. The correlation coefficient remains in the same measurement as in which the two variables are measured.
2. The sign of the correlation coefficient will always be the same as the variance.
3. The numerical value of the correlation coefficient will be between -1 to +1. It is known as a real number value.
4. A negative value of the coefficient suggests that the correlation is strong and negative. If 'r' approaches -1, it means that the relationship is moving towards the negative side.

Concept of Spearman's Rank Correlation

Spearman’s rank correlation measures the strength and direction of association between two ranked variables. It basically gives a measure of the monotonicity of the relation between two variables, i.e., how well the relationship between two variables could be represented using a monotonic function.

The Concept of Regression

Regression is a statistical method used in finance, investing, and other disciplines that attempts to determine the strength and character of the relationship between one dependent variable (usually denoted by Y) and a series of other variables (known as independent variables).

Regression Lines and Their Estimation in a Bivariate Series

Bivariate Regression Analysis is a type of statistical analysis that can be used during the analysis and reporting stage of quantitative market research. It is often considered the simplest form of regression analysis, and is also known as Ordinary Least-Squares regression or linear regression.

In order to determine the relationship, Bivariate Regression Analysis uses a linear regression line (because the relationship between the variables is assumed to be linear) in order to help measure how the two variables change together, simultaneously.

Least Square Method

The least square method is the process of finding the best-fitting curve or line of best fit for a set of data points by reducing the sum of the squares of the offsets (residual part) of the points from the curve. During the process of finding the relation between two variables, the trend of outcomes are estimated quantitatively. This process is termed as regression analysis. The method of curve fitting is an approach to regression analysis. This method of fitting equations approximates the curves to given raw data using the least squares principle.