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 12 inches of rain. round to the nearest ton per acre.

rainfall (inches) yield (tons per acre)
0 10.32
2 16.01
4 26.27
6 27.6
7 24.41
8 22.43

Explanation:

Step1: Input data into technology

Input the rainfall (x - values: \(0,2,4,6,7,8\)) and yield (y - values: \(10.32,16.01,26.27,27.6,24.41,22.43\)) into a graphing calculator or statistical software.

Step2: Find the line of best fit

Using linear regression (since we are looking for a line of best fit), the equation of the line of best fit is \(y = 1.9x+10.3\) (approximate value from technology - based linear regression).

Step3: Predict for \(x = 12\)

Substitute \(x = 12\) into the equation \(y=1.9x + 10.3\).

$$y=1.9\times12+10.3$$

$$y = 22.8+10.3$$

$$y=33.1$$

Answer:

\(33\) tons per acre