$1.$ Plot the given data above as points. Label the axes and create a title.

$2.$ Perform a regression analysis on the data using a linear approximation. Plot the approximation in

a new figure, along with the original data. How well does this fit match the data?

$3.$ Perform a regression analysis on the data using a quadratic approximation. Plot the

approximation in a new figure, along with the original data. Label the axes and create a title.

$4.$ Perform a regression analysis on the data using a cubic approximation. Plot the approximation in

a new figure, along with the original data. Label the axes and create a title.

$5.$ Perform a regression analysis on the data using a $4$

th

$-$order approximation. Plot the approximation

in a new figure, along with the original data. Label the axes and create a title.

$6.$ In a new figure, plot all four of the approximations, along with the original data. Label the axes,

create a title, and create a legend.

$7.$ Which of the four approximations appears to be the best fit?

$8.$ Determine the estimated discharge for a gauge depth of $10$ ft for each of the four approximations.

Are these estimated values reasonable? Why or why not?

$9.$ Determine the estimated discharge for a gauge depth of $2$ ft for each of the four approximations.

Are these estimated values reasonable? Why or why not? What does this tell you about

extrapolating curve fittings to areas where you do not have data?