The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. When three polynomial trend equations are compared, which of them provides the best fit?
A) Linear
B) Exponential
C) Quadratic
D) Cubic

Question

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011.   The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated.  When three polynomial trend equations are compared, which of them provides the best fit?
A) Linear 
B) Exponential 
C) Quadratic 
D) Cubic

Quizplus · Accepted Answer

The cubic model provides the best fit because it has the highest R-squared value of 0.9858, indicating a strong correlation between time and revenue. The quadratic model has an R-squared value of 0.9657, the exponential model has an R-squared value of 0.9529, and the linear model has the lowest R-squared value of 0.9404. Therefore, the cubic model is the best choice for modeling the trend in annual revenues over time.

The Following Table Shows the Annual Revenues (In Millions of Dollars)