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 town of Bankrupticut, RI has the following balances at June 30, 2020 in their General Fund: Instructions are below. Tax Revenue Get Out of Jail Free Revenue License & Bribery Revenue Expenditures...
Following are the descriptions of changes in selected accounts and other events for Krimp Caf Pty Ltd. Required (a) Indicate whether each item should be added (A) to or deducted (D) from profit when...
Eastern Merchants shows the following information for its two divisions for year 1: Required Compute divisional operating income for the two divisions. Ignore taxes. How well have these...
McGyver runs a hot air balloon company in Liverpool that takes customers on flights. He hears that Murdock has inherited a hot air balloon from his aunt Penny. McGyver asks to inspect the balloon,...
A Global private bank is aggressively looking to leverage technology to improve customer experience and reduce operational costs. Over the last few years, it has tied up with at least five startups...
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?
What are the two official definitions of dumping ?
Does this assignment include data that supports the decision to increase the company's equity financing?
K Corporation is considering investing in Malaysian security market. The company needs to choose only one from the two securities listed below. The returns are as follows: Return Probability Security...
Inspection of weldments by liquid penetrant inspection is generally used to detect discontinuities such as: 1. A longitudinal surface crack in a weld bead 2. Lack of penetration at root of a fillet...
Planning for his retirement, Nguyen is going to invest $5000 at the beginning of each of the next 20 years. At the end of 20 years, how much will his investment be worth, assuming he earns a return...
What has happened to the value of the South Korean won relative to the U.S. dollar from January to July given the following information?
Coronavirus disease (COVID-19) caused by a new virus results in respiratory illness (like the flu). The disease was first identified in December 2019 and has since spread globally, resulting in the...
The Strahler Stream Order System ranks streams based on the number of tributaries that have merged. It is a top-down system where rivers of the first order are the headwaters (aka outermost...
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...
(i) When should a firm cut dividend pay out rate and increase retention rate to maximize share price? (ii) How can the dividend-discount model handle changing growth rates?
November 2021 (actual) December 2021 (budgeted) January 2022 (budgeted) Cash sales $ 80.000 Credit sales Total sales 240,000 $320,000 $100,000 360,000 $460,000 $ 60,000 180,000 $240,000 Management...
A firm has 200 shareholders, you among them. Each shareholder owns $20 worth of sto addition, Mr. Hostile owns 50 shares (for a firm total of 250 shares) and is trying to fi management. In an attempt...

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