3.81.* The least squares property of the mean states that the data fall closer to y than...

Question:

3.81.* The least squares property of the mean states that the data fall closer to ¯y than to any other number

c, in the sense that the sum of squares of deviations about the mean is smaller than the sum of squares of deviations about

c. That is,

If you have studied calculus, prove this property by treating f

(c) =
(yi − c)2 as a function of c and deriving the value of c that provides a minimum. (Hint: Take the derivative of f

(c) with respect to c and set it equal to zero.)

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

Step by Step Answer:

Related Book For book-img-for-question

Statistical Methods For The Social Sciences

ISBN: 9780134507101

5th Edition

Authors: Alan Agresti

See More Books

Question Posted: Sep 19, 2024 02:21 PM

See More Questions

You are the VP of Human Resources for a company with 250 employees. You have both outside sales representatives and inside sales representatives that work primarily by phone. James is an outside...
Describe the error. The graph of h (x) = 6 - 2x / 3 - x has the line x = 3 as a vertical asymptote Because 3 x = 0 when x = 3.
Diewold Company has two departments, Milling and Assembly. The company uses a job-order cost system and computes a predetermined overhead rate in each department. The Milling Department bases its...
3.81.* The least squares property of the mean states that the data fall closer to y than to any other number c, in the sense that the sum of squares of deviations about the mean is smaller than the...
Edney Manufacturing Company has $2 billion in sales and $0.6 billion in fixed assets. Currently, the companys fixed assets are operating at 80% of capacity. a. What level of sales could Edney have...
Exercise 4-4 Accruals and Deferrals For the following situations, indicate whether each involves a deferred expense (DE), a deferred revenue (DR), an accrued liability (AL), or an accrued asset (AA)....
According to Statistical Abstract of the United States, 2015, the mean salary (in dollars) of secondary school teachers in the United States varied among states with a five-number summary of (a) Find...
5.77.* To construct a confidence interval for a proportion , it is not necessary to substitute for the unknown value of in the formula for the true standard error of . A less approximate method...
Exhibit 6.12 shows a simplified statement of cash flows for a period. Numbers appear on 11 of the lines in the statement. Other lines are various subtotals and grand totals; ignore these in the...
4) E-Mart Stores uses people and computerized scanners to add arriving shipments into its inventory and to deduct units sold from its inventory. E-Mart's production function is Q = KL, where Q...
A client would like to quit smoking, so the therapist suggests hypnosis. The client undergoes hypnosis and finds that it does help. Which state of consciousness was the client in during the hypnosis?...
A lottery system has balls numbered 1 to 55 and randomly selects 7 of the lottery balls. There is only one prize of $7,900,000.00 which is awarded only if a lottery player selects the correct set of...
1.114 Goldilocks Effect: Read to Your Kids! (Part 2) Exercise 1.13 introduces a study in which 27 four-year-old children are presented with stories three different ways: audio only, illustrated, and...
Jeanette is conducting an experimental study of memory. She has recruited a sample of A-Level students and given them a word-learning task. They first do the task while music is playing and then in...
In what ways was Anderson a transformational leader in order to execute his strategy for Best Buy, how did he combine transformational with transactional leadership? In what ways did Anderson exhibit...
Select the correct answer for each of the following questions. 1. On December 31, 20X3, Saxe Corporation was merged into Poe Corporation. In the business combination, Poe issued 200,000 shares of its...
Consider the logistic-normal model, logit( i ) = + x i + u i . For small , show that it corresponds approximately to a mixture model for which the mixture distribution has var( i ) = [ i (1 i )]...
Altham (1978) introduced the discrete distribution where c(?, ?) is a normalizing constant. Show that this is in the exponential family. Show that the binomial occurs when ? = 0. [Altham noted that...
Suppose that given u, Y is Poisson with E(Y | u) = u , where may depend on predictors. Suppose that u is a positive random variable with E(u) = 1 and var(u) = . Show that E(Y) = and var(Y) = + 2...

3.81.* The least squares property of the mean states that the data fall closer to y than...

Question:

- (vi-c).

Step by Step Answer:

Statistical Methods For The Social Sciences

Students also viewed these Business questions