Question

Annual rainfall plays an important role in corn agriculture. The drought of 2011 literally affected corn prices for years. Given the following data, build a model and predict the harvest for 2016 given that the total rainfall was 6.45 inches. Critique your prediction.

YEAR	RAIN(INCHES)	REAPTONS)
2011	2.06	325
2012	5.11	408
2013	7.43	609
2014	6.12	512
2015	7.14	544

Answer 1

The following model can be formulated in Excel. The software can be used to predict the trend between the rainfall in a particular year and the reap in that year.

Excel was used to create a scatter plot between the rain in inches and the reap in tons for different years.

From the trendline options, we saw that the relationship between the rainfall and the reap is best explained by a polynomial equation which has an order 3 as it has the highest R- squared value.

The relationship is given by-

y = -3.1121x³ + 54.153x² - 231.78x + 599.6

This equation can be used to predict the harvest for 2016 which is the following year when the rainfall is 6.45 inches. x has to be replaced by 6.45 in the above equation.

y= -3.1121(6.45)³ + 54.153(6.45)² - 231.78 (6.45) + 599.6

y = 522.43 tons

The prediction of 522.43 tons of corn for the upcoming year seems to be in accordance with the pattern that we have seen in the previous years. The data is spread out over successive years as there is no linear increase in rainfall over the years as can be expected from the natural rainfall patterns. Hence the model is able to predict the reap (in tons) for the following year by using the polynomial relationship between the rainfall and reap that was obtained from the previous years.