Regarding a linear regression analysis of this relationship, we find that the slope of the line is close to 0.5, and the relationship is a direct linear relationship between the amount of tar in a cigarette and the amount of nicotine.
Nonlinear trends in statistical data can be the most challenging to work with. When non-linear relationships exist, there may be a mathematical relationship which is based on a logarithm, or other multi-factor influence. However, true non-linear relationship, such as the height and weight of a specific person who shops in a given department store may leave the statistician without any relationship whatsoever. Non-linear data can also be the result of data which is being acted on by an artificial, outside force. In this case, the statistician is able to verify the existence of an outside force, and then approach the process of identifying the force.
An example of this situation is the expected relationship between supply and demand, and company profit based on the sales of a given product in the market place. In the early 1980's, the Coleco company produces a product called "Cabbage Patch dolls." The typical lifecycle of a new toy product is one to two years, but Coleco was able to extend the life of their product for four to five Christmas seasons by artificially affecting the relationship between supply and demand. The company had the production capacity to produce 4-5 times the amount of dolls which it shipped to the market during the first three years of the dolls life cycle. This would have produced a typical bell shaped curve, plotting a rising demand, and increasing profits which gave way to a declining demand and declining profits in a short period. However the company did not produce product equal to their capacity, nor equal to the demand. As a result, the company was able to continue a high level of demand, and an inflated retail based on the high demand for an extended period. The result was that the doll stayed popular for almost a decade, and the company was able to reap ongoing higher levels of profits. The longer bell curve, identified by an irregular and nonlinear relation between time and supply and demand was created by the unique marketing strategy for the company.