Problem 2: Curve Fitting: The data points (xi, Yi) were observed (-3,3), (-1, –1), (1,3) and (3, 15). -3 Thus, the x-values and y-values are: = 1 and ỹ = 1 The plot shows these data points and both the best-fit line 3 15. 16 and the best-fit parabola. 14 a. Record the design matrix D you would use to find the best-fit line. 12 10 y = Bo + B1 x D = 4 Given for free: The product D™D is DTD = -2 -3 -2 -1 1 2 3 X-axis b. Find the inverse of the product D" D -唱9 (D"D)-1 and record it in the box. c. Solve the normal equation ( D"D)B = D"ỷ to find the vector B = with the best-fit parameters for the line. Hint: D"ÿ = Parameter vector ß. d. It can be shown that the best-fit line gives the estimates Ўest Find the error vector: y- ỹest · Then give the root mean square error. RMSE = Error vector = Parabolic design matrix D: e. Let's start over and try a parabolic fit. Record the design matrix D you would use to find the best-fit parabola y = Bo + B1 x + B2 x2 D f. Nice! The parabola fits perfectly, and you would find B = 2 Using this parabola, estimate y(2) = DDDD N O O DODD DDDD DDDD DDDD

Problem 2: Curve Fitting: The data points (xi, Yi) were observed (-3,3), (-1, –1), (1,3) and (3, 15). -3 Thus, the x-values and y-values are: = 1 and ỹ = 1 The plot shows these data points and both the best-fit line 3 15. 16 and the best-fit parabola. 14 a. Record the design matrix D you would use to find the best-fit line. 12 10 y = Bo + B1 x D = 4 Given for free: The product D™D is DTD = -2 -3 -2 -1 1 2 3 X-axis b. Find the inverse of the product D" D -唱9 (D"D)-1 and record it in the box. c. Solve the normal equation ( D"D)B = D"ỷ to find the vector B = with the best-fit parameters for the line. Hint: D"ÿ = Parameter vector ß. d. It can be shown that the best-fit line gives the estimates Ўest Find the error vector: y- ỹest · Then give the root mean square error. RMSE = Error vector = Parabolic design matrix D: e. Let's start over and try a parabolic fit. Record the design matrix D you would use to find the best-fit parabola y = Bo + B1 x + B2 x2 D f. Nice! The parabola fits perfectly, and you would find B = 2 Using this parabola, estimate y(2) = DDDD N O O DODD DDDD DDDD DDDD

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: QUESTION 9 earch Make a scatter plot of the data and determine which type of model best fits the…

Q: Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph. H has…

Q: Which graph matches the equation 2y-15 =-y-x? A y C y 8 Center: (0, -1) Radius: 4 4 Center: (-1, 0)…

A: The equation of circle is given as 2y-15=-y2-x2 The equation of circle whose center (h, k) and…

Q: Main Street. To remove an item, you can press on the box and the trash can icon to the right of the…

Q: Study the given data and graph and then identify the best label for each axis

A: A scatterplot is given and the objective is to study the given data and graph and then identify the…

Q: 10 8 10 6 + 2 10 -8 -6-4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 Write an equation for the graph in…

A: Step 1:Step 2: Hope this helps!

Q: 5. A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one…

A: given equation :(x+1.5)2+(y-1)2=16 ....(1)we have to find the graph that represent the position and…

Q: 9. What is the axis of symmetry for the graph? a. y = -4 b. x = - 6 %3D yA 12 C. y = 6 d. x = -4 10…

A: We will find out the required values.

Q: Given the centre of the cirele (-5,2) and it meets the line y= 1 at one point, find the equation of…

Q: Circle A is given by the equation: (x - 5)² + (y + 7)² = 81. Where is the center of circle A? (-7,5)…

A: (1) The equation of the circle is given byThe general equation of the circle centered at and having…

Q: 2. -2 -2. 4 Select the general form equation of the circle whose graph is shown above. Select one:…

Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Problem 2: Curve Fitting: The data points (xi, y;) were observed (-3,3), (-1,–1), (1,3) and (3, 15).
-3"
31
Thus, the x-values and y-values are: X =
and ý =
The plot shows these data points and both the best-fit line
3.
15
16
and the best-fit parabola.
14
a. Record the design matrix D you would use to find the best-fit line.
12
****
10
8
y = Bo + B1 x
D =
4
2
[4
Given for free: The product D"D is D"D =
-2
-3
-2
-1
1
3
х-ахis
b. Find the inverse of the product DT D
(D"D)-1 :
-E到
and record it in the box.
c. Solve the normal equation ( D"D)B = D"ỷ to find the vector B =
with the best-fit parameters for the line.
Hint: D'ÿ = 40l
Parameter vector B.
d. It can be shown that the best-fit line gives the estimates
ỹest =
Find the error vector: ý - ỹest ·
7
Then give the root mean square error.
RMSE =
Error vector =
Parabolic design matrix D:
e. Let's start over and try a parabolic fit. Record the design matrix D
you would use to find the best-fit parabola y = Bo + B1 x + B2 x2
D =
f. Nice! The parabola fits perfectly, and you would find B
= 2. Using this parabola, estimate y(2) =
DDDD
ODDO
DD DD
DDDD
DDDI

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

mail.google.com/mail/u/2/#search/berryk%40elms.edu?projector=1 nnect Search List Screening Appoint... Opportunity Queue RC RRL G Google Google Docs m Elms College 6) Graph the following equation; (x-2)2+(y - 3)² = 4 Also, identify the center and the radius of the circle. Genetics
Hello part A. Plot each point and label each with its coordinates. Part B. Useing the x-axis as the line of reflection plot the image of each point. Parts C. Label the image of each point with its coordinates. Part D. Include a label Useing a letter. For example the image of point A should be label A. Here is a list of points A=(0.5,4) B=(-4,5) C =(7,-2) D=(6,0) E=(0,-3
4. y=x²-2x+3 X -2 -1 0 1 2 y (a = 1, b = -2, c = 3) 1st differences 2nd differences Concave up or down? Location of vertex (_____________). Answer Check each graph on desmos. 2. concave upward, vertex (0,-4) 3. concave upward, vertex (-1,2) 4. concave upward, vertex (1,2)
Match the graphs to their equations. (x – 3)2 (y – 2)? 1 - 1 - 3)? (y + 2)? 1 (y + 2)² 1 0 (x + 3)² а. 2 3 4 5 1 -2 (x + 3)? (у — 2) -3 = 1 -4 -5 7t b. -7 -6 -5 -4 -3 -2 -2 -3 -4 -5 || 2. > >
Match the equation with its graph. (x - 5)2 + (y + 6)² = 1 16 4 y y 12 12 1아 10 8 8 6F 4 4 2 2 4 6 8 10 12 -2 -12-10-8 -6 -4 -2 12-10-8-6 -4 -2 2 2 4 6 8 10 12 -4 -4 -6 -6 -8 -8 - 10 - 10 -12 -12 y y 12 12 10 10 8 6F 6F 4 4 2 2 4 6 8 10 12 2 4 6 8 10 12 -2 -12-10-8 -6 -4 -2 2 -12-10-8 -6 -4 -2 -4 -4 -6 -아 -8 -8 - 10 - 10 -12 -12 21