Fitting a curve to your data in MATLAB can show trends and estimate values not included in the data set. In this problem, you will use MATLAB$$s built$-$in polynomial curve fitting functions to determine the best equation for the data given in the Excel file $$swingData$.$xlsx$.$

a$)$ Read the Excel file $$swingData$.$xlsx$$ into the Workspace and call it swingData $($this must be done using a function in your m$-$file$).$

i$)$ The first column of swingData is the time in seconds incremented from $0$ to $4.$ Save this column as a separate variable called Time.

ii$)$ The second column of swingData is the swing height at different time increments. Save this column as a separate variable called yPosition.

b$)$ Using the polyfit$()$ function in MATLAB, find the best$-$fit coefficients for the given data in swingData. Call the output of the polyfit function coeffs. Test different order polynomials in the polyfit function to find the best$-$fit curve for the data.

c$)$ Create an equation using the coefficients in coeffs $($this should be done by referencing the values from coeffs$).$ Call this equation yEqn.

d$)$ Calculate how well your equation fits the given data points using the sum of squared errors method. Call the output SSE$\_$yEqn. Refer to your lecture slides if you don$$t remember.

i$)$ Is the value high or low? What does that value tell you about your equation? Write your answer as a comment inside your m$-$file.

e$)$ Using the polyval$()$ function in MATLAB, find the swing height at $5\mathrm{.}4$ seconds if the swing$$s motion were to follow your equation. Assign the output to Height.