Question

O 26 points 1 Previous Arcwors STreCalcT 3Fou 00 The more corn a farmer plants per acre, the greater is the yield the farmer can expect, but only up to a point. Too many plants per acre can cause overcrowding and des data give crop yields per acre for various densities of corn plantings, as found by researchers at a university test farm. Density (plants/acre) Crop yield (bushels/acre) 15,000 20,000 25,000 40,000 5,000 50,000 30,000 35,000 42 97 139 141 121 92 (a) Find the quadratic polymomial that best fits the data. (Let y be the crop yield in bushels/acre and x the density in thousands of plants/acre. Round all numeric decimal places.) (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. 150 150 100 100 50 50 1020 0 40 50 6 0on

Answer 1

MATLAB Code:

close all
clear
clc

x = 15:5:50;
y = [42 97 117 139 141 121 92 66];

p = polyfit(x,y,2); % degree 2 (quadratic) polynomial fit
fprintf('Quadratic Polynomial: p(x) = (%f)*x^2 + (%f)*x + (%f)\n', p)

xx = linspace(min(x) - 5, max(x) + 5, 100); % 100 samples between min - 5 and max + 5 of x
yy = polyval(p, xx); % evaluating the quadratic polynomial at the above 100 samples

plot(x,y,'o',xx,yy), xlabel('Density (x1000)'), ylabel('Crop Yield')
legend('Data Points', 'Quadratic Fit')
title('Quadratic Fit of Crop Yield vs. Density')

Output:

Quadratic Polynomial: p(x) = (-0.278333)*x^2 + (18.465476)*x + (-167.732143)

Plot:

Quadratic Fit of Crop Yield vs. Density 160 140 120 100 Ф 80 O Data Points Quadratic Fit 60 40 20 -20 10 15 20 25 30 35 40 45 5055 Density (x1000)