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Code in python please

Code in python please

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter12: Review Of Calculus And Probability
Section: Chapter Questions
Problem 2RP
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Code in python please

Given the data below, X f(x) 1 4.75 2 4 3 5.25 5 19.75 6 36 a.) Using Newton's interpolating polynomials OR Lagrange polynomials of order 1-4, estimate f(4). (HINT: In our defined functions for Lagrange and Newtons polynomials 'order' is assumed based on the number of provided datapoints (i.e. first order has two datapoints, second order has three data points, etc.). Removing datapoints reduces the assumed order. Start by removing the datapoint furthest from the point of interest). b.) Use 'polyfit' and 'polyval' to plot 1-4 order regressions using the data, plot the datapoints provided in the table, and plot the interpolated values from part 'a' on the same plot (use pylab.scatter to plot the individual interpolation points). The plot should have a legend labeling each interpolation and each regression. c.) Look at the various order regressions and the interpolated values for f(4). Do the regression values and the interpolated values agree at each order? Why or why not? Which do you think is the best estimate for the value of f(4)?
Transcribed Image Text:Given the data below, X f(x) 1 4.75 2 4 3 5.25 5 19.75 6 36 a.) Using Newton's interpolating polynomials OR Lagrange polynomials of order 1-4, estimate f(4). (HINT: In our defined functions for Lagrange and Newtons polynomials 'order' is assumed based on the number of provided datapoints (i.e. first order has two datapoints, second order has three data points, etc.). Removing datapoints reduces the assumed order. Start by removing the datapoint furthest from the point of interest). b.) Use 'polyfit' and 'polyval' to plot 1-4 order regressions using the data, plot the datapoints provided in the table, and plot the interpolated values from part 'a' on the same plot (use pylab.scatter to plot the individual interpolation points). The plot should have a legend labeling each interpolation and each regression. c.) Look at the various order regressions and the interpolated values for f(4). Do the regression values and the interpolated values agree at each order? Why or why not? Which do you think is the best estimate for the value of f(4)?
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