Explanation Given: The following table gives the volume (in billions of pieces) of first-class mail from 2007 through 2011: Year 2007 2008 2009 2010 2011 Value, y 95.9 91.7 83.8 78.2 73.5 x = 1 represents 2007 . Approach: Suppose n data points are given, P 1 ( x 1 , y 1 ) , P 2 ( x 2 , y 2 ) , P 3 ( x 3 , y 3 ) ................. P n ( x n , y n ) Then the least-squares (regression) line for the data is given by the linear equation (function) y = f ( x ) = m x + b Where the constants m and b satisfy the normal equation. n b + ( x 1 + x 2 + ... + x n ) m = y 1 + y 2 + ... + y n n b + m ∑ x = ∑ y ( x 1 + x 2 + ... + x n ) b + ( x 1 2 + x 2 2 + ... + x 3 2 ) m = x 1 y 1 + x 2 y 2 + ... + x n y n b ∑ x + m ∑ x 2 = ∑ x y The equation of the line having slope m is given by, y = m x + b Calculation: The calculation required for obtaining the normal equations are summarized in the following table. Year x y x 2 x y 2007 1 95.9 1 95.9 2008 2 91.7 4 183.4 2009 3 83.8 9 251.4 2010 4 78.2 To determine b) The volume of first-class mail in 2016 .

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ISBN: 9780100478183

Author: Tan

Publisher: YUZU

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Chapter 1.5, Problem 18E

To determine

a)

The equation of the least-squares line for the data.

To determine

b)

The volume of first-class mail in $2016$ .

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Chapter 1.5, Problem 17E

Chapter 1.5, Problem 19E

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a) The equation of the least-squares line for the data.

Solution Summary: The author explains how the equation of the least-squares lines is y=-5.8x+102.