Question

Given the data set with t values in the first column and y values in the second column, write a script file that:

-Curve fits the given data set with an appropriate polynomial function

-Outputs the R² value of the appropriate fit along with the values of the polynomial order higher and lower (ex. If you choose a 2^nd order fit, display the R² value for first, second, and third order fits.)

- Estimate the value of the data at t = 15.5 using a 3 point interpolation.

Copy and paste the below values in excel and use that to pull data into your Matlab script file.

If you need any additional information then comment, thanks!

0	3
0.5	1.68569428820791
1	-3.95784854932628
1.5	-2.70275004645052
2	-8.20804222177874
2.5	-9.7888937947024
3	-10.8794243196858
3.5	-16.6350020109363
4	-15.3341094985447
4.5	-20.575599024921
5	-22.2647035001955
5.5	-22.9502699366898
6	-28.6160632481857
6.5	-27.0985091529083
7	-31.8763653389923
7.5	-33.4893475992729
8	-33.5897736790413
8.5	-38.9634230062392
9	-37.0581929509318
9.5	-41.1733606982684
10	-42.5247497074079
10.5	-41.8608395460318
11	-46.7395103467172
11.5	-44.2753705569831
12	-47.5296212422044
12.5	-48.4328411108291
13	-46.8263426410198
13.5	-51.0067929600693
14	-47.8122186368842
14.5	-50.0081973545762
15	-50.2755632708189
15.5	-47.5491275196853
16	-50.8277773078467
16.5	-46.7308822816937
17	-47.6721512398972
17.5	-47.1148702832052
18	-43.0920066727989
18.5	-45.2650085942502
19	-40.0934765705277
19.5	-39.5845544477838

Answer 1

clear
clc
A=xlsread('Exam2_Data.xlsx');
t=A(:,1);
y=A(:,2);
SST=sum((y-mean(y)).^2);
for i=1:3
fprintf('For %d order fit\n\n',i);
disp('Polynomial coefficients are');
C=polyfit(t,y,i)
SSR=sum((y-polyval(C,t)).^2);
R2=1-SSR/SST;
fprintf('R^2 is %f\n\n',R2);
end
for i=2:length(t)-1
T=[t(i-1) t(i) t(i+1)];
Y=[y(i-1) y(i) y(i+1)];
  
if(t(i)<15.5&t(i+1)>15.5)
C=polyfit(T,Y,2);
disp('Value at 15.5 is ');
polyval(C,15.5)
return
end
end

Kindly revert for any queries

Thanks.