Question

In Matlab:

A list of average monthly high temperatures for the city of Monroe Louisiana is given below:

Month Temperature (in◦F)

January 56

February 60

March 69

April 77

May 84

June 90

July 94

August 94

September 88

October 79

November 68

December 58

For convenience, label January as 1, February as 2, and so forth. Then fit a quadratic and fourth-degree polynomials through these data on the same figure window. Include the label and a legend. Based on your fourth order polynomial fit, estimate the temperature on August 10.

Answer 1

MATLAB Code:

close all
clear
clc

m = 1:12;
t = [56 60 69 77 84 90 94 94 88 79 68 58];

p2 = polyfit(m, t, 2);
p4 = polyfit(m, t, 4);

mm = linspace(1,12,365); % 365 days
plot(m, t, 'o', mm, polyval(p2, mm), mm, polyval(p4, mm))
xlabel('Month'), ylabel('Temperature')
legend('Data Points', 'Polynomial (Degree 2)', 'Polynomial (Degree 4)', 'Location', 'northwest')

p4val = linspace(polyval(p4, 8), polyval(p4, 9), 31); % For the month of August (31 days)
fprintf('Estimated temperature using 4th degree polynomial on August 10: %f\n', p4val(10)); % Aug. 10

Output:

Estimated temperature using 4th degree polynomial on August 10: 91.123767

Plot: