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Describe the error in the conclusion. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. As the number of cigarettes increases the pulse rate increases. Conclusion: Cigarettes cause the pulse rate to increase.

By definition it can be seen that linear correlation analysis is a statistical techniques use in the measurement of causation, direction, degree and significance of co-variation between two or more variables.

The conclusion cigarettes cause the pulse rate to increase is not valid because linear correlation tells us the strength of the relationship. Correlation does not imply a casual relation. Where a causal relation says that if one variable increases it causes to increase the other variable as an effect.

It means we cannot say which variable is the cause if there is a significant linear correlation exists between two variables. Linear correlation always depicts the strength of the relationship between two variables but it never depicts the casual relationship between two variables. Suppose if there is a positive linear relationship between height and weight we cannot say that height causes weight to increase or decrease and similarly weight causes height to increase or decrease.

The conclusion from a linear correlation between two variables is that they are related to each other, but not that one causes the other. In given case as it conveys there is a casual relationship exists is not accepted because of the fact of casual relationship between cigarettes smoking and pulse rate. Contrary to casual relation, the linear relationship between two variables describes the power/strength of relation between cigarette smoked and pulse rate. In other words, correlation does not imply causation.

To prove a causal relationship, further analysis is required. For valid linear correlation between two variable required the mutual influence of each variable on other so that there can be arise a relationship between two variables of cause and effect. Like there is a correlation between demand and supply (Pagano, 1981).

Where demand can cause to increase or decrease the supply as an effect. So, for check valid correlation relation between cigarette smoking and increasing pulse rate, it should be determined that there exists a relation and if it exists then establish the cause and effect relation if any. But as we conclude that there does not occur such cause and effect relation so it is not valid.

Reference:

Pagano, R. R. (1981). Understanding statistics in the behavioral sciences. St. Paul: West Pub. Co