Cause and Effect Relationship

In a relationship in which one variable is independent and the other is dependent, some people use the terms ‘cause’ and ‘effect’. In the production of rice for a given dosage of fertilizer, the amount of fertilizer is the ‘cause’ and ‘production of rice’ is the effect. Thus in this regression relationship, we can say that there is a ‘cause’ and ‘effect’ relationship between the variables. A special food may be tested on poultry. The amount of food is the ‘cause’ and the weight of the birds is an ‘effect’.

The ‘effect’ variable is also called the response variable. But there may be a regression relationship between two variables $X$ and $Y$ in which there is no cause and effect (casual) relationship between them. In some cases a change in $X$ does cause a change in $Y$, but it does not happen always. Sometimes the change in $Y$ is not caused by change in $X$. The dependence of $Y$ on $X$ should not be interpreted as a cause and effect relationship between $X$ and $Y$.

In regression analysis, the word dependence means that there is a distribution of $Y$ values for given single value of $X$. For a given height of 60 inches for men, there may be very large number of people with different weights. The distribution of these weights depends upon the fixed value of $X$. It is in this sense that the word dependence is used. Thus dependence does not mean response (effect) due to some cause. Some examples are discussed here to elaborate upon the idea.

1. The sun rises and the shining sun increases the temperature. Let temperature be noted by $X$. With an increase in $X$, the ice on the mountains melts and the average thickness of ice ${Y_i}$ decreases. It is possible that the thickness of ice decreases due to an increase in temperature. But it is also possible that the thickness of the ice is decreasing due to the weight and hardening of the ice. We may be regressing the thickness $Y$ against the temperature $X$ only while another important factor is being ignored. In this type of problem, more than one regression equation is developed and then the equations are solved simultaneously to estimate the unknown parameters.
2. We may think that an increase in the number of workers $X$ increases the production of fans $Y$ in a factory. The increase in $Y$ may be due to a change in the administration and some changes about the leave rules and other benefits.

In a regression relationship there may or may not be a casual relationship between $X$ and $Y$. The cause and effect relationship between two variables is also called causation. It is important to note that the statistical method of regression analysis does not discuss the cause and effect relationship between the variables. Sometimes it is not possible to identify which variable is the ‘cause’ and which one is the ‘effect’. In fact, the answer is to be found not in regression analysis but in another area of the relationship between the variables.