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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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)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2F9764f85d-bdeb-47b9-a0ac-88a0b40b4872%2Fmqu0ffk_processed.png&w=3840&q=75)
Transcribed Image Text: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)?
Expert Solution
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Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Introduce polynomial regression and interpolation techniques
VIEWStep 2: a.) Estimate f(4) using Newton's interpolating polynomial and Lagrange polynomial of order 1-4:
VIEWStep 3: b.) Plot 1-4 order regressions, data points, and interpolated values:
VIEWStep 4: c.) Analysis of Regression and Interpolation Values:
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