Establish the Lagrange Identity, that for any numbers a1, a2,..., an and b1,b2,..., bn, Use the identity

Question:

Establish the Lagrange Identity, that for any numbers a1, a2,..., an and b1,b2,..., bn,

Use the identity to show that the correlation coefficient is equal to 1 if and only if all of the sample points lie on a straight line (Wright 1992). (Hint: Establish the identity for n = 2; then induct.)

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

See More Books

Question Posted: May 26, 2016 05:22 AM

See More Questions

This exercise involves a well-known inequality known as the triangle inequality (a special case of Minkowski's Inequality). (a) Prove (without using Minkowski's Inequality) that for any numbers a and...
Establish Green's Second Identity: as
If the sample correlation coefficient is equal to 1, is it necessarily true that r = 1? If r = 1, is it necessarily true that r = 1?
/* FILE: FLIX2YOU_data-load.txt */ /* Script to populate tables for FLIX2YOU .. current schema before revision */ /* Written by Gary Heberling on July 2, 2012 */ /* For IST210 world campus Penn State...
Sea Biz Co. has four employees. FICA Social Security taxes are 6.2% of the first $106,800 paid to each employee, and FICA Medicare taxes are 1.45% of gross pay. Also, its FUTA taxes are 0.8% and SUTA...
The Big Sky Company, a wholesale distributor, has recorded an operating loss for each of the past three years. A percentage-ofsales analysis shows that its gross profit is 21.6 percent. The average...
The Chronicle of Higher Education Almanac (Aug. 27,1999) reports that the percentage of undergraduates in the United States receiving federal financial aid is 45% at public four-year institutions and...
Suppose that we modify the model of the firm's investment behavior by assuming that any capital the firm has remaining at the end of the period can be sold at the price p'K (in our model we assumed...
Carroll Corporation has two products, Q and P. During June, the company's net operating income was $26,000, and the common fixed expenses were $56.000. The contribution margin ratio for Product was...
At December 31, 2023, Cord Companys plant asset and accumulated depreciation and amortization accounts had balances as follows: Depreciation is computed to the nearest month and residual values are...
Let X1,..., Xn be a random sample, where X- and S2 are calculated in the usual way (a) Assume now that the X,s have a finite fourth moment, and denote 6 = EX*, 02 - E(xi-e1y,j = 2,3,4 (b)Show that...
Let X be one observation from a n(0, 2) population. Is |X| a sufficient statistic?
Because of the many later developmental transformations that produce the elaborately structured organs, the body plan set up during gastrulation bears little resemblance to the body plan in the...
Locate a scholarly article relevant to how to present your financial plan for opening a Roller Skating Rink (from your draft business plan) to a lending institution--and describe your strategy for...
How would you expect seasonal fluctuations in demand to affect a rental company's decisions about pricing rented products such as wedding dresses or convertible cars? In terms of pricing principles,...
Do we drive technology, or does technology drive us? If technology drives us, what are the risks? The other side of the coin would be that we are able to stay ahead of technological transformations....
How do you explain the differences between the two analyses and what are the implications of using the BCG matrix in practice?
How do leadership styles, such as transformational leadership, shared leadership, and servant leadership, impact team dynamics, member motivation, and overall team effectiveness ?
Why is it important to complete the design process thoroughly?
Explain the operation of the dividends received deduction.
An order for a computer system can specify memory of 4, 8, or 12 gigabytes, and disk storage of 200, 300, or 400 gigabytes. Describe the set of possible orders.
Three events are shown on the Venn diagram in the following figure: Reproduce the figure and shade the region that corresponds to each of the following events. (a) A (b) A B (c) (A B) U C (d) (B U...
A digital scale is used that provides weights to the nearest gram. (a) What is the sample space for this experiment? Let A denote the event that a weight exceeds 11 grams, let B denote the event that...
. Emerson Cammack wishes to purchase an annuity contract that will pay him $7,000 a year for the rest of his life. The Philo Life Insurance Company figures that his life expectancy is 20 years, based...
Integrity Inc. can sell 20-year, $1,000 par value bonds paying semi-annual interests with a 10% coupon. The bonds can be sold for $1,050 each; flotation cost of $50 per bond will be incurred in this...
Duncan Inc. issued 500, $1,200, 8%, 25 year bonds on January 1, 2020, at 102. Interest is payable on January 1. Duncan uses straight-line amortization for bond discounts or premiums. INSTRUCTIONS:...

Establish the Lagrange Identity, that for any numbers a1, a2,..., an and b1,b2,..., bn, Use the identity

Question:

2 n-1 n 72 a,b

Step by Step Answer:

To establish the Lagrange Identity consider the case when n 2 a 1 ...View the full answer

Statistical Inference

Students also viewed these Statistics questions