Question

a farmer is recording the size of his crop yield based on the monthly rainfall total. the results are presented in the table below. use technology to find the line of best fit for the data. then use that model to predict the farmers crop yield after a month with 8 inches of rain. round to the nearest ton per acre.

rainfall (inches) yield (tons per acre)
0 8.3
2 11.14
3 14.35
5 21.33
6 30.81
7 26.73

Explanation:

Step1: Input data into technology

Input the rainfall (x - values: \(0,2,3,5,6,7\)) and yield (y - values: \(8.3,11.14,14.35,21.33,30.81,26.73\)) into a graphing calculator or statistical software.

Step2: Find the line of best fit

Using linear regression in the technology, the line of best fit equation is \(y = 2.9x+8.3\) (approximate, depending on the technology's output).

Step3: Predict for \(x = 8\)

Substitute \(x = 8\) into the equation \(y=2.9x + 8.3\).

$$y=2.9\times8+8.3$$

$$y = 23.2+8.3$$

$$y=31.5$$

Answer:

\(32\) tons per acre (rounded to the nearest ton per acre)