# Cause and Effect Relation

In a relation, 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 relation, we can say that there is ‘cause’ and ‘effect’ relation between the variables. Some special food may be tested on poultry birds. The amount of food is ‘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 relation 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 cause and effect relation 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 the idea.

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

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