# Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Newton’s interpolating polynomial

This screenshot is topic for part 1 and 2 for Writing Goal, research , Curve Fitting and Literature Proposal.

Part 3 Complete the following problems from the textbook. Show all your work. If you write code, include screenshots of your code and any test runs that you perform. Remember that all work should be your own original work and assistance received from any source and any references used must be authorized and properly documented.

17.23) 17.23 Develop, debug, and test a program in either a high-level language or macro language of your choice to implement linear regression. Among other things: (a) include statements to document the code, and (b) determine the standard error and the coeffi cient of determination.

18.17) Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Newton’s interpolating polynomial based on Fig. 18.7

18.18) Test the program you developed in Prob. 18.17 by duplicating the computation from

18.21) 18.21 Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Lagrange interpolation. Base it on the pseudocode from Fig. 18.11. Test it by duplicating Example 18.7.

18.23 Develop, debug, and test a program in either a high-level language or macro language of your choice to implement cubic spline interpolation based on Fig. 18.18. Test the program by duplicating Example 18.10 Use Newton’s interpolating polynomial to determine y at x 5 8 to the best possible accuracy. Compute the fi nite divided ifferences as in Fig. 18.5 and order your points to attain optimal accuracy and convergence.

19.10) Develop a user-friendly program for the DFT based on the algorithm from Fig. 19.12. Test it by duplicating Fig. 19.13.

19.12 Develop a user-friendly program for the FFT based on the algorithm from Fig. 19.18. Test it by duplicating Fig. 19.13.

20.23 Use multiple linear regression to derive a predictive equation for dissolved oxygen concentration as a function of temperature and chloride based on the data from Table P20.21. Use the equation to estimate the concentration of dissolved oxygen for a chloride concentration of 5 g/L at T 5 178C.

20.25 In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water fl ow in the river that is being impounded. For some rivers, long-term historical records of such fl ow data are diffi cult to obtain. In contrast, meteorological data on precipitation is often available for many years past. Therefore, it is often useful to determine a relationship between fl ow and precipitation. This relationship can then be used to estimate fl ows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed: