Question $2(25$ points$)$

Estimate the parameters of the given ellipse in general form that best fits these points where $h$ and $k$ are

the coordinates of the center of the ellipse, and $$ and $$ are the semi$-$major and semi$-$minor axes respectively.

You will read the data from 'data.txt$\text{'}$ file, where left column is for $x$ and right column is for $y.$

$\frac{(x-h{)}^2}{{}^2}+\frac{(y-k{)}^2}{{}^2}=1$

Model the problem using nonlinear least squares regression. Estimate $h,k,,.$ Notice that the first

half of the data and the last half of the data have the same $x$ values.

this is the data from 'data.txt$\text{'}$:

$5\mathrm{.}2618\mathrm{.}639$

$5\mathrm{.}0948\mathrm{.}374$

$5\mathrm{.}2918\mathrm{.}118$

$4\mathrm{.}8258\mathrm{.}258$

$5\mathrm{.}1758\mathrm{.}533$

$5\mathrm{.}1638\mathrm{.}491$

$4\mathrm{.}8078\mathrm{.}751$

$5\mathrm{.}2788\mathrm{.}223$

$5\mathrm{.}1679\mathrm{.}064$

$4\mathrm{.}8518\mathrm{.}996$

$4\mathrm{.}7188\mathrm{.}299$

$4\mathrm{.}7718\mathrm{.}151$

$5\mathrm{.}1018\mathrm{.}981$

$5\mathrm{.}2748\mathrm{.}584$

$4\mathrm{.}9078\mathrm{.}860$

$4\mathrm{.}8928\mathrm{.}574$

$5\mathrm{.}2498\mathrm{.}425$

$4\mathrm{.}8768\mathrm{.}573$

$5\mathrm{.}0718\mathrm{.}780$

$5\mathrm{.}2878\mathrm{.}204$

$5\mathrm{.}1818\mathrm{.}564$

$5\mathrm{.}0799\mathrm{.}123$

$5\mathrm{.}0608\mathrm{.}756$

$4\mathrm{.}7478\mathrm{.}197$

$4\mathrm{.}8728\mathrm{.}500$

$4\mathrm{.}9548\mathrm{.}737$

$4\mathrm{.}9958\mathrm{.}917$

$5\mathrm{.}1178\mathrm{.}610$

$4\mathrm{.}9608\mathrm{.}738$

$4\mathrm{.}7338\mathrm{.}087$

$4\mathrm{.}8968\mathrm{.}497$

$4\mathrm{.}7497\mathrm{.}933$

$4\mathrm{.}9439\mathrm{.}170$

$4\mathrm{.}7267\mathrm{.}869$

$5\mathrm{.}2598\mathrm{.}433$

$4\mathrm{.}9638\mathrm{.}817$

$4\mathrm{.}9698\mathrm{.}950$

$4\mathrm{.}8728\mathrm{.}356$

$5\mathrm{.}0049\mathrm{.}151$

$4\mathrm{.}8708\mathrm{.}811$

$4\mathrm{.}9258\mathrm{.}679$

$4\mathrm{.}9208\mathrm{.}301$

$5\mathrm{.}2348\mathrm{.}258$

$5\mathrm{.}0428\mathrm{.}545$

$5\mathrm{.}2628\mathrm{.}581$

$5\mathrm{.}2038\mathrm{.}430$

$5\mathrm{.}1878\mathrm{.}133$

$5\mathrm{.}2718\mathrm{.}190$

$5\mathrm{.}1418\mathrm{.}580$

$4\mathrm{.}8258\mathrm{.}911$

$5\mathrm{.}2928\mathrm{.}299$

$4\mathrm{.}7188\mathrm{.}332$

$5\mathrm{.}1228\mathrm{.}701$

$4\mathrm{.}9768\mathrm{.}777$

$5\mathrm{.}0008\mathrm{.}668$

$5\mathrm{.}0858\mathrm{.}564$

$5\mathrm{.}2988\mathrm{.}351$

$4\mathrm{.}9668\mathrm{.}759$

$4\mathrm{.}8187\mathrm{.}964$

$5\mathrm{.}2448\mathrm{.}519$

$5\mathrm{.}2068\mathrm{.}583$

$5\mathrm{.}0238\mathrm{.}531$

$5\mathrm{.}0508\mathrm{.}916$

$4\mathrm{.}9438\mathrm{.}084$

$5\mathrm{.}0818\mathrm{.}273$

$5\mathrm{.}2338\mathrm{.}389$

$4\mathrm{.}9588\mathrm{.}896$

$4\mathrm{.}7808\mathrm{.}377$

$5\mathrm{.}0898\mathrm{.}853$

$4\mathrm{.}7598\mathrm{.}828$

$5\mathrm{.}0698\mathrm{.}825$

$5\mathrm{.}1788\mathrm{.}314$

$5\mathrm{.}1458\mathrm{.}320$

$4\mathrm{.}8199\mathrm{.}040$

$5\mathrm{.}2538\mathrm{.}278$

$5\mathrm{.}1138\mathrm{.}768$

$5\mathrm{.}2658\mathrm{.}378$

$5\mathrm{.}1888\mathrm{.}371$

$5\mathrm{.}0118\mathrm{.}862$

$4\mathrm{.}7548\mathrm{.}280$

$5\mathrm{.}2128\mathrm{.}552$

$5\mathrm{.}1218\mathrm{.}879$

$5\mathrm{.}2148\mathrm{.}770$

$5\mathrm{.}2878\mathrm{.}161$

$4\mathrm{.}8519\mathrm{.}177$

$5\mathrm{.}0088\mathrm{.}773$

$5\mathrm{.}2378\mathrm{.}474$

$4\mathrm{.}7498\mathrm{.}550$

$4\mathrm{.}8568\mathrm{.}712$

$5\mathrm{.}0918\mathrm{.}127$

$4\mathrm{.}7718\mathrm{.}165$

$5\mathrm{.}1328\mathrm{.}976$

$4\mathrm{.}8408\mathrm{.}628$

$5\mathrm{.}0688\mathrm{.}518$

$4\mathrm{.}9779\mathrm{.}049$

$4\mathrm{.}8368\mathrm{.}363$

$4\mathrm{.}9048\mathrm{.}569$

$4\mathrm{.}8358\mathrm{.}858$

$5\mathrm{.}2808\mathrm{.}381$

$5\mathrm{.}1858\mathrm{.}570$

$5\mathrm{.}2617\mathrm{.}945$

$5\mathrm{.}0947\mathrm{.}044$

$5\mathrm{.}2917\mathrm{.}775$

$4\mathrm{.}8257\mathrm{.}122$

$5\mathrm{.}1757\mathrm{.}396$

$5\mathrm{.}1637\mathrm{.}316$

$4\mathrm{.}8077\mathrm{.}680$

$5\mathrm{.}2787\mathrm{.}702$

$5\mathrm{.}1677\mathrm{.}902$

$4\mathrm{.}8517\mathrm{.}782$

$4\mathrm{.}7187\mathrm{.}821$

$4\mathrm{.}7717\mathrm{.}247$

$5\mathrm{.}1017\mathrm{.}663$

$5\mathrm{.}2748\mathrm{.}016$

$4\mathrm{.}9077\mathrm{.}529$

$4\mathrm{.}8927\mathrm{.}267$

$5\mathrm{.}2497\mathrm{.}647$

$4\mathrm{.}8767\mathrm{.}299$

$5\mathrm{.}0717\mathrm{.}420$

$5\mathrm{.}2877\mathrm{.}798$

$5\mathrm{.}1817\mathrm{.}448$

$5\mathrm{.}0797\mathrm{.}773$

$5\mathrm{.}0607\mathrm{.}384$

$4\mathrm{.}7477\mathrm{.}445$

$4\mathrm{.}8727\mathrm{.}234$

$4\mathrm{.}9547\mathrm{.}354$

$4\mathrm{.}9957\mathrm{.}517$

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

PRE-CALCULUS 4. Which of the following equations represents an ellipse with horizontal minor axis? A. -+ 16y2 = 16 141 =2 D. 10 5. A point moves so that the difference of their distances from (-6,0)...

Q:

MATH 107 Quiz 2 Name Click here to enter text. Each question is worth 5 points. Questions 1 - 5 are multiple choice; you do not need to show your work. Short answers for Questions 6 - 10; show your...

Q:

Make sense of the thoughts of static and dynamic chains, giving an illustration of a circumstance in which they contrast (for example reference to some unacceptable one would get to the wrong...

Q:

Pre-Calculus/Trigonometry | Graded Assignment | Semester A Unit 3 Exam. Part 2 Name: Date: Graded Assignment Semester A Unit 3 Exam, Part 2 When you have nished, please submit this test to the...

Q:

9 Exam: 08.07 Analyzing the Coord X X C A learn.flvs.net/educator/student/examform.cgi?apacecca2*smondelus16*sit=TBpVQAY0pm9aA*5274*0070*passedonce* Q E FLVS Lessons Assessments V Gradebook Email 15...

Q:

I need help with this: Question 1 You just returned from a trip to Venezuela and have 3,000 bolivares fuertes in your pocket. How many dollars will you receive when you exchange this money if the...

Q:

Calculus Questions 1. Question Select your answer. A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point not on the Directrix line. What do you call...

Q:

Need help in C++ Program Problem 1. (20 points) Write a computer program to implement the following algorithm combin- ing the bisection and Newton's method for solving f(r) 0. the function f() and...

Q:

Assignment Case Study The purpose of this assignment is to check your understandings of the readings from (S5chwalbe). You will use this knowledge gained in the readings to display your understanding...

Q:

Marketing Scenario A: You are the marketing manager for a small export/import company operating in El Paso. A client has just contacted you about sourcing (buying) an expensive radio. He wants you to...

Q:

Suppose that And Use properties of definite integrals interval additively, and so on to calculate each of the integrals in problems. (a) (b) (c) f(x) dx=2. | f(x) dx=3, | g(x) dx=-1, g(x) dx = 4....

Q:

Use the Summer Time Supply Corp. data from Problem 12-62A. Requirements 1. Prepare the 2012 statement of cash flows by using the direct method. 2. How will what you learned in this problem help you...

Q:

BE2.8 (LO 2, 3) Included in Gonzalez NVs December 31 trial balance is a note receivable of 12,000. The note is a 4-month, 10% note dated October 1. Prepare Gonzalezs December 31 adjusting entry to...

Q:

WHAT IS the cash flow statement BBINFIT ,AND HOW WE CAN ANALAYSES

Q:

6. last word What would you expect to happen to the proportion of big chain restaurants relative to mom and pop restaurants in a town that lowered its minimum wage? Will the proportion change due to...

Q:

5. Critically evaluate and explain: LO13.2 a. In monopolistically competitive industries, economic profits are competed away in the long run; hence, there is no valid reason to criticize the...

Q:

2. In the small town of Geneva, there are five firms that make watches. The firms respective output levels are 30 watches per year, 20 watches per year, 20 watches per year, 20 watches per year, and...

Previous Question Next Question