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$\%$The same data is used for the activity. These are provided for you.

X $=[[\backslash$begin$\{$array$\}\{$llll$\}\{-2\}$&$\{-1\}$&$\{1\}$&$\{2\}\backslash$end$\{$array$\}].\text{'}$

Y$\}=[\backslash$begin$\{$array$\}\{$llll$\}\{3\}$&$\{1\}$&$\{0\}$&$\{1\}\backslash$end$\{$array$\}].$

$\%$Use the length$()$ command to determine the size of the column vector X$.$ Store this value in m$.$

$\%$Set up the appropriate matrix A to find the best$-$fit parabola of the form y$=$C$+$Dx$+$Ex$^2.$ The

$\%$first column of A will contain all $1\text{'}$s$,$ using the ones$()$ command. The second column of A

$\%$contains x values that are stored in X$.$ The third column of A contains the squared x values

$\%$that are stored in X$.$ Elementwise multiplication of X by itself, using $.*$ operator, will

$\%$produce the desired values for the third column.

$\%$Calculate the matrix products. These are provided for you.

A$\_$transposeA $=$ A$.\text{'}*$ A

A$\_$transposeY $=$ A$.\text{'}*$ Y

$\%$Use the backslash operation to solve the overdetermined system. Store this in Soln$2.$

$\%$Define the x values to use for plotting the best$-$fit parabola. This creates a vector x$.$

$\%$This is provided for you.

x$=-4$: $0\mathrm{.}1$ :$4$

$\%$Define the best$-$fit parabola, storing it in yquadratic. Elementwise multiplication of the

$\%$x values times themselves to square them is achieved by using $.*$ operator $($because x is a vector$).$

$\%$The following sequence of commands plots the data and the best$-$fit parabola. The command is

$\%$provided for you.

plot$($x$,$ yquadratic, X$,$ Y$,\text{'}$k$*\text{'})$;grid;shg

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