Define the least-squares problem

Assignment Help Engineering Mathematics
Reference no: EM131760976

Question: (Lotka's law and least squares) Lotka's law describes the frequency of publication by authors in a given field. It states that X aY = b, where X is the number of publications, Y the relative frequency of authors with X publications, and a and b are constants (with b > 0) that depend on the specific field. Assume that we have data points (Xi, Yi), i = 1, . . . , m, and seek to estimate the constants a and b.

1. Show how to find the values of a, b according to a linear leastsquares criterion. Make sure to define the least-squares problem involved precisely.

2. Is the solution always unique? Formulate a condition on the data points that guarantees unicity.

Reference no: EM131760976

Questions Cloud

Discuss about the maximum number of servings : (An optimal breakfast) We are given a set of n = 3 types of food, each of which has the nutritional characteristics described in Table.
Describes why seller adds a finance charge to cash price : describes why a seller adds a finance charge to the cash price when calculating the installment price?
What is the interpretation of given vector : Assume that the grade matrix G is well approximated by a rankone matrix sq?, with s ? Rn and q ? Rm (you may assume that both s, q have non-negative components)
Decides to invest money each month into pension fund : A young man decides to invest money each month into a pension fund, starting on his 30th birthday and ending on his 60th birthday.
Define the least-squares problem : Show how to find the values of a, b according to a linear leastsquares criterion. Make sure to define the least-squares problem involved precisely.
Attention to building robust engagement strategy : The author of Nonprofit Finance for Hard Times asserts “organizational stability requires attention to building a robust engagement strategy focused on young"
Climate of trust and performance evaluation : Effective teams have adequate resources, effective leadership a climate of trust and a performance evaluation and reward system that reflects team contributions
Review problem on permutation matrices : (Permutation matrices) A matrix P ? Rn,n is a permutation matrix if its columns are a permutation of the columns of the n × n identity matrix.
Net income after taxes to average owners equity : Find the ratio of net income after taxes to average owners’ equity.

Reviews

Write a Review

Engineering Mathematics Questions & Answers

  Find jobs arrive at workstation at a rate of four per hour

Consider a factory that processes a single job type. Orders are processed one at a time in a serial processing configuration. One of the workstations requires.

  Find the equivalent lump-sum amount at eoy nine

If a nominal interest rate of 8% is compounded continuously, determine the unknown quantity in each of the following situations.

  Review the case peterson v hewlett-packard co

Employee sued employer for religious discrimination and alleged religious harassment after being terminated for repeatedly refusing to remove biblical passages.

  What is the x-intercept of tangent line

What is the x-intercept of this tangent line? Use this fact to draw the tangent line and find the volume of the solid generated by rotating the top half

  Determining the parallel-pipe system

For the parallel-pipe system of Fig, each pipe is cast iron, and the pressure drop p1 - p2 = 3 lbf/in2. Compute the total flow rate between 1 and 2 if the fluid is SAE 10 oil at 20°C.

  Find a recurrence relation and give initial conditions

Find a recurrence relation and give initial conditions for the number of bit strings of length n that contain at least 3 consecutive zeroes

  How many spam e-mails one can expect to have wade

Overnight one's inbox collects e-mails which one check sin the morning. Question is about how many spam e-mails one can expect to have wade through.

  Develop system equations for the steady-state probabilities

Develop the system equations for the steady-state probabilities for a single operator servicing three machines. What type of difficulties will have to be.

  How much of x must be produced to make a profit

A firm manufactures product x and can sell any amount at a price of £25 a unit. The firm has to pay fixed costs of £200 plus a marginal cost of £20.

  Calculate the first fundamental form of s

Let S be the surface parametrized by X: U → R3, where X(u, v)=(u, v, u2 - v2), Calculate the first fundamental form of S in terms of (u, v)

  Which option is better and by how much

Assume you needed $10 000 on April 1, 2006, and two options were available: Your banker would lend you the money at an annual interest rate of 7.0%, compound.

  Show the effect of the quota on the market for swordfish

The waters off the North Atlantic coast were once teeming with fish. But because of overfishing by the commercial fishing industry.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd