Lab 8 Assignment Due on 04/02 at the beginning of lab. Submit your m-file, diary

Question

Lab 8 Assignment

Due on 04/02 at the beginning of lab.

Submit your m-file, diary showing a successful run, and figure.

1) Download

Lab 8 data2.mat

to your current directory from our shared folder.

Note:

The variable loaded from here is called

data

. Load the file in your workspace

from the command window to confirm. After loading

Lab 8 data2

in your code,

you must call on the variable in your code by

data

.

2) Write an m-file to load data from

Lab 8 data2.mat

and compute the least squares

approximation for the data. This should be the best fit

parabola

. The function

will have no input and no output.

Your function should work for any

.mat

file containing an

m×2 matrix,

where m is a positive integer.

•

The function should plot the data points and the approximating parabola

in one figure with a legend.

•

The function should print the equation of the parabola of best fit.

•

See the in-class exercise answer for plot and print formatting.

Note:

The equation of a parabola is

y = Ct^2 + Dt + E

Pseudo-code:

function lsaparabola

% Load data. The data has the to be in the same directory or sub-directory

% as this function. It’s file name should go in ’filename.mat’.

% Retrieve the size of the data.

% The data is ordered pairs (t,y) with the first column being the t values,

% and the second column being the y values.

% Form coefficient matrix A and the right hand side b in Ax = b.

% We are fitting the parabola y = Ct^2 + Dt + E. Given data points (t,y),

% we want to find the C, D, E that form the parabola that best fits this

% data.

Form A

Form b

% Find the least squares solution x. This found from the projection of b

% onto the column space of A.

% Retrieve the parameters C, D, E.

C = x(1); D = x(2); E = x(3); % actual MATLAB code

% Form the parabola y = Ct^2 + Dt + E to plot.

Form t as a linearly spaced vector between the

minimum and maximum t data values.

Form y, the parabola.

% Plot the data and the parabola of best fit on the same axes with

% appropriate formatting.

% Print the result.

% ’%f’, as opposed to ’%d’, prints the result as a floating point with

% out the scientific notation.

end

Explanation / Answer

%provide data to debug this code

load data2.mat
xs=data(:,1);
y=data(:,2);
A=[xs(1)^2 xs(1) 1;
xs(2)^2 xs(2) 1;
xs(3)^2 xs(3) 1];
b=[y(1);y(2);y(3)];
x=A;

C = x(1); D = x(2); E = x(3); % actual MATLAB code
points=min(xs):.1:ma(xs);
y_points=polyval(x,points);
plot(xs,y,'*',points,y_points)
legend('Data points','Parabola of best fit')
fprintf('The parabola of best fit is: (%f)t^2 + (%f)t + E ',x);

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