The correlation is a measure of the co-variability of variables. It is used to measure the strength between two quantitative variables. It also tells the direction of a relationship between the variables. The positive value of the correlation coefficient indicates that there is a direct (supportive or positive) relationship between the variables while the negative value indicates there is a negative (opposite or indirect) relationship between the variables.
By definition, the correlation is the interdependence between two quantitative variables. The causation (known as) cause and effect, is when an observed event or action appears to have caused a second event or action. Therefore, It does not necessarily imply any functional relationship between the variables concerned. Correlation theory does not establish any causal relationship between the variables as it is interdependence between the variables. Knowledge of the value of the coefficient of correlation $r$ alone will not enable us to predict the value of $Y$ from $X$.
Sometimes there is a high Relationship between unrelated variables such as the number of births and the number of murders in a country. This is a spurious correlation.
For example, suppose there is a positive correlation between watching violent movies and violent behavior in adolescence. The cause of both these could be a third variable (extraneous variable) say, growing up in a violent environment which causes the adolescents to watch violence-related movies and to have violent behavior.
- The number of absences from class lectures decreases the grades.
- As the weather gets colder, air conditioning costs decrease.
- As the speed of the train (car, bus, or any other vehicle) is increased the length of time to get to the final point will also decrease.
- As the age of a chicken increases the number of eggs it produces also decreases.