In wind tunnel tests for a new tall building in New York City the force, F, was measured exerted by the wind on a model of the new building at different known wind velocities, v. This data is tabulated on the right. Using the matrix formulation of Section 17.4.1, {Y}=[Z]{A}+{E}; {E}={Y}-[Z]{A}, conduct a polynomial regression of F on v as instructed below. F m (N) 10 25 • (a) Determine (but don't yet solve) the normal equations for a 2nd order polynomial (parabolic) regression of F on v. 20 70
In wind tunnel tests for a new tall building in New York City the force, F, was measured exerted by the wind on a model of the new building at different known wind velocities, v. This data is tabulated on the right. Using the matrix formulation of Section 17.4.1, {Y}=[Z]{A}+{E}; {E}={Y}-[Z]{A}, conduct a polynomial regression of F on v as instructed below. F m (N) 10 25 • (a) Determine (but don't yet solve) the normal equations for a 2nd order polynomial (parabolic) regression of F on v. 20 70
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![In wind tunnel tests for a new tall building in New York City the force, F, was measured exerted by
the wind on a model of the new building at different known wind velocities, v. This data is tabulated
on the right. Using the matrix formulation of Section 17.4.1, {Y}=[Z]{A}+{E}; {E}={Y}-[Z]{A},
conduct a polynomial regression of F on v as instructed below.
F
m
(N)
• (a) Determine (but don't yet solve) the normal eguations for a 2nd order polynomial
(parabolic) regression of F on v.
• (b) Solve the normal equations using Cholesky decomposition and Forward and Back
Substitution, since the coefficient matrix of the normal equations is symmetric.
• (c) Determine the equation of the regression curve in terms of v and F, the standard error of the
estimate, and the correlation coefficient.
• (d) Since the coefficient of the quadratic term seems small, investigate whether a straight
regression line might work: Modify the columns of the [Z] matrix and the elements of the {A}
vector such that the regression line becomes straight. Recompute the equation for the regression
line, the standard error of the estimate, and the correlation coefficient. Present your conclusions.
10
25
20
70
30
380
40
550
50
610
60
1220
70
830
80
1450](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd29303b-2f0e-4317-a180-294f2c1e25d4%2Fb3308f57-776d-4d95-94d0-0be3f0fb912b%2F28vnguk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In wind tunnel tests for a new tall building in New York City the force, F, was measured exerted by
the wind on a model of the new building at different known wind velocities, v. This data is tabulated
on the right. Using the matrix formulation of Section 17.4.1, {Y}=[Z]{A}+{E}; {E}={Y}-[Z]{A},
conduct a polynomial regression of F on v as instructed below.
F
m
(N)
• (a) Determine (but don't yet solve) the normal eguations for a 2nd order polynomial
(parabolic) regression of F on v.
• (b) Solve the normal equations using Cholesky decomposition and Forward and Back
Substitution, since the coefficient matrix of the normal equations is symmetric.
• (c) Determine the equation of the regression curve in terms of v and F, the standard error of the
estimate, and the correlation coefficient.
• (d) Since the coefficient of the quadratic term seems small, investigate whether a straight
regression line might work: Modify the columns of the [Z] matrix and the elements of the {A}
vector such that the regression line becomes straight. Recompute the equation for the regression
line, the standard error of the estimate, and the correlation coefficient. Present your conclusions.
10
25
20
70
30
380
40
550
50
610
60
1220
70
830
80
1450
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
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.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)