USING THE DATA TABLE IMAGE PROVIDED SOLVE VIA MATLAB CODE:

Problem $9\mathrm{.}4$

$($Data from Problem $9\mathrm{.}1)$

Let$$s try one more type of best fit curve. Write a MATLAB script or function $($your choice$)$ to

solve the linear system of equations to perform linear regression and fit a polynomial to each

set of experimental data $($thinking AND braking$).$ Fit each set of data with a polynomial of the

following form:

y $=$ a$(0)+$a$(1)$x $+$a$(2)$x$^2$

where x is speed, and y is the thinking or braking data. You will create $1$ best fit curve for each

set of data $($thinking AND braking$).$ Solve the linear system of equations for the unknown

coefficients, a$(0)$ and a$(1),$ of each best fit curve. Then, quantify the error of each best fit curve using

the equation to calculate the coefficient of determination, r$^2$

$.$

Create a figure showing the experimental data for both thinking AND braking and each best

fit curve. Plot all the data and curves on one plot. Include the following information:

$$ Experimental data $$ Plot the speed data on the x$-$axis and the thinking or braking data on

the y$-$axis. Use any color and marker $($your choice$)$ without a line to plot the data points.

Use a different color and marker for the thinking data and the braking data.

$$ Best fit curves $$ For each curve, plot the speed data on the x$-$axis and the best fit curve on

the y$-$axis. Use any line style and color besides the default styles and colors.

$$ Label the x$-$axis and the y$-$axis.

$$ Create a descriptive figure legend.

$$ Create a descriptive figure title.

show in the diary file that you have calculated the

coefficient of determination for each best fit curve.