Question

Regression Analysis is a statistical technique to which we correlate (or attempt to correlate) a relationship between 2 variables that are predicated on an interval level of measurement. In essence, we are using Regression to Predict the strength of a relationship between 2 variables that may or may not be related.

The Regression is measured by a Correlation Coefficient. What is a Correlation Coefficient?

Answer 1

Solution

Correlation Coefficient is a number lying between – 1 and + 1, indicating the strength of linear relationship between two variables.

A coefficient of – 1 and + 1 implies that the two variables are perfectly linearly related; i.e., the the relationship can be represented by a straight line.

- 1 would mean that as one variable changes (increase or decreases), the other variable changes in the opposite direction (decreases or increases).    

1 would mean that as one variable changes (increase or decreases), the other variable changes in the same direction (increase or decreases).

A coefficient of zero implies that there is no linear relationship between the two variables. [it does not mean there no relationship]

The square of correlation coefficient further quantifies the strength of linear relationship. It represents the proportion of variation in one variable, called response or dependent variable that can be explained by the other variable, called predictor or independent variable.

Once, correlation is fouind to be high, the exact linear relationship is established by regression analysis.

As a rule of thumb,

Value of r	Strength of relationship
-1.0 to -0.5 or 1.0 to 0.5	Strong
-0.5 to -0.3 or 0.3 to 0.5	Moderate
-0.3 to -0.1 or 0.1 to 0.3	Weak
-0.1 to 0.1	None or very weak

Answer

DONE