Exercise $1.($Component Skill $5\mathrm{.}3)$ USE MATLAB AND SHOW THE CODE PLEASE

The file salmon$\_$data.mat contains the annual count of Chinook salmon taken at Bonneville on

the Columbia river from the years $1938$ to $2020.$ In this problem, we will fit these data with various

polynomial curves to predict the salmon population in $2021.$

a$.$ Download the file salmon$\_$data.mat from the Homework $5$ page on Canvas. Make sure this

file is in the same folder as your hw$5.$m script. In the Exercise $1$ section of your hw$5.$m script,

type

load$(\text{'}$salmon$\_$data.mat'$)$;

This will automatically create two variables. The first variable is called salmon. This is

an $831$ column vector of the annual salmon count taken at Bonneville. The second variable

is called year. This is an $831$ column vector of the corresponding years for which the salmon

count was recorded.

Treating salmon as the $y-$variable and year as the $x-$variable, use the MATLAB built$-$in func$-$

tion polyfit to find the coefficients of the first$-$degree polynomial that best fits the salmon

data in the least$-$squares sense. Assign the row vector of coefficients of this first$-$degree poly$-$

nomial to the variable A$1.$ You may get MATLAB warnings about the polynomial

being badly conditioned. Normally, we'd heed these warnings, but let's ignore them for

the purposes of this exercise.

Answer:

b$.$ Use the MATLAB built$-$in function polyfit to find the coefficients of the third$-$degree poly$-$

nomial that best fits the salmon data in the least$-$squares sense. Assign the row vector of

coefficients of this third$-$degree polynomial to the variable A$2.$ c$.$ Use the MATLAB built$-$in function polyfit to find the coefficients of the fifth$-$degree polynomial that best fits the salmon data in the least$-$squares sense. Assign the row vector of

coefficients of this fifth$-$degree polynomial to the variable A$3.$ PLEASE USE MATLAB TO SOLVE ALL OF THESE QUESTIONS