6. (20pts) Given the data below, and using MATLAB,Ꮖ4.04.24.54.75.15.55.96.36.87.1y 102.56 113.18 130.11 142.05 167.53 195.14 224.87 256.73 299.50 326.72(a) construct the least squares polynomial of degree 1 and compute the error;(b) construct the least squares polynomial of degree 3 and compute the error;(c) construct the least squares approximation of the form y = bear and compute theerror (hint: take logarithm on both sides).For each polynomial, provide its graph together with the data points from the table.Submit all your codes and results.

Step 1: Step 2: Step 3: Step 4:

Answered: 6. (20pts) Given the data below, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given the data X. 0.5 a. Construct the least squares polynomial of degree 1, and compute the error. b. Construct the least squares polynomial of degree 2, and compute the error. c. Construct the least squares approximation of the form be", and compute the error.(see text book page 504)
Consider the data points (2, 0), (3, 1), and (4, 5). Compute the least squares error for the given line. y = -4 + 2x Plot the points and the line. (Be sure to plot all points, even if they lie on the line.) No Solution 7 6 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Help Graph Layers Clear All Delete After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill WebAssign. Graphing Tool
Find the least squares regression line for temperature (x) and number of ice cream cones sold per hour (y). 65 70 75 80 85 90 95 100 105 y 8 10 11 13 12 16 19 22 23 Oŷ = 2.469x+48.240 ý = 0.383x-17.694 Oŷ = -125.376x+31.656 Oŷ = 0.4x-18
In order to study the relationship between age and length of time that a smoker has been smoking, the following data were collected. x= age of a smoker y= years since he or she started smoking. x = y= 26 8 32 9 27 7 24 6 34 10 20 4 Compute the coorelation and find the least squares line.
What geometric transformation of 3D space happens in this matrix-vector multiplication? 010 -1 0 0 0 01 9).( (3) Please note: All rotation directions to be understood as when looking along the rotation axis towards the origin. O Clockwise rotation by 90 degrees around the x3 axis Counter-clockwise rotation by 90 degrees around the x3 axis Clockwise rotation by 90 degrees around the x₂ axis Counter-clockwise rotation by 90 degrees around the x2 axis O Clockwise rotation by 90 degrees around the x₁ axis Counter-clockwise rotation by 90 degrees around the x₁ axis O Mirroring across the x₁-x2 plane Mirroring across the x₁-x3 plane Mirroring across the X₂-X3 plane
Use the method of least squares to fit the model to the data. Y hat= _+_x
To determine a functional relationship between the attenuation coefficient and the thickness of a sample of taconite, V. P. Singh [Si] fits a collection of data by using a linear least squares polynomial. The following collection of data is taken from a graph in that paper. Find the linear least squares polynomial fitting these data. Thickness (cm) Attenuation coefficient (dB/cm) 26.5 28.1 25.2 0.040 0,041 0.055 0.056 0,062 0.071 0.071 0.078 0.082 0,090 0.092 0.100 0.105 0.120 0.123 0.130 0,140 26.0 24.0 25.0 26.4 27.2 25.6 25,0 26.8 24.8 27.0 25.0 27.3 26.9 26.2
2. The Mach number of a moving object is the ratio of its speedto the speed of sound. The following table shows the speeds of a jet aircraft, in terms of Mach numbers, and the time tafter it starts to accelerate. Find the least- squares line of s as a function of t. t(min) 0.00 s(Mach Number) 0.88 0.60 0.97 1.20 1.03 1.80 1.11 2.40 1.19 3.00 1.25
The following table gives the gold medal times for every other Summer Olympics for the women's 100 meter freestyle (swimming). Year Time (seconds) 1912 82.2 1924 72.4 1932 66.8 1952 66.8 1960 61.2 1968 60.0 1976 55.65 1984 55.92 1992 54.64 2000 53.8 2008 53.1 Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.) Find the correlation coefficient r. (Round your answer to four decimal places.)r = Find the estimated gold medal time for 1924. (Use your equation from part (d). Round your answer to two decimal places.) Find the estimated gold medal time for 1992. (Use your equation from part (d). Round your answer to two decimal places.) Use the least squares line to estimate the gold medal time for the 2012 Summer Olympics. (Use your equation from part (d). Round your answer to two decimal places.) ch12#1
When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is log(Area) = 0.490 + 2.004 log(Time). WWhat is the predicted area of the circle, in cm2, 4 seconds after the stone is dropped? O 49.72 cm2 O 199.43 cm2 O 311.89 cm? O 1854.10 cm2
Data for motor vehicle production in a country for the years 1997 to 2004 are given in the table. Year 1997 1998 1999 2000 2001 2002 2003 2004 Thousands 1,578 1,671 1,805 2,009 2,391 3,219 4,415 5,092 (A) Find the least squares line for the data, using x = 0 for 1990. y = (Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to the nearest tenth as needed.)

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