Code in python please Given the data below,\[\begin{array}{|c|c|c|c|c|c|}\hlinex & 1 & 2 & 3 & 5 & 6 \\\hlinef(x) & 4.75 & 4 & 5.25 & 19.75 & 36 \\\hline\end{array}\]a.) Using Newton’s interpolating polynomials OR Lagrange polynomials of order 1-4, estimate f(4).(HINT: In our defined functions for Lagrange and Newton’s 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)?

In this analysis, we explore various polynomial regression and interpolation techniques to estimate…

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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

Problem 1PE

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Question

Code in python please

Given the data below,

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 5 & 6 \\
\hline
f(x) & 4.75 & 4 & 5.25 & 19.75 & 36 \\
\hline
\end{array}
\]

a.) Using Newton’s interpolating polynomials OR Lagrange polynomials of order 1-4, estimate f(4).

(HINT: In our defined functions for Lagrange and Newton’s 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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Step 1: Introduce polynomial regression and interpolation techniques

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Step 2: a.) Estimate f(4) using Newton's interpolating polynomial and Lagrange polynomial of order 1-4:

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Step 3: b.) Plot 1-4 order regressions, data points, and interpolated values:

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Step 4: c.) Analysis of Regression and Interpolation Values:

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