Code in python please

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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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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