Explanation Given: The data, based on annual surveys of 1000-plus adults aged 18 and over, are shown in the following table: Year 2012 2013 2014 2015 Percent Share, y 87 86 84 83 x = 0 represents 2012 . 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 2012 0 87 0 0 2013 1 86 1 86 2014 2 84 4 168 2015 3 83 9 249 Total ∑ x = 6 ∑ y = 340 ∑ x 2 = 14 ∑ x y = 503 Table (1) Consider the least square equation. n b + m ∑ x = ∑ y ⋯ ( 1 ) b ∑ x + m ∑ x 2 = ∑ x y ⋯ ( 2 ) Substitute 4 for n , 6 for ∑ x and 340 for ∑ y in equation ( 1 ) To determine b) The average rate of change in the penetration rate of pay-TV over the years. To determine c) The penetration rate in 2016 .

Finite Mathematics for the Managerial, Life, and Social Sciences

12th Edition

ISBN: 9781337405782

Author: Soo T. Tan

Publisher: Cengage Learning

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Question

Chapter 1.5, Problem 12E

To determine

a)

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

To determine

b)

The average rate of change in the penetration rate of pay-TV over the years.

To determine

c)

The penetration rate in 2016.

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Chapter 1.5, Problem 11E

Chapter 1.5, Problem 13E

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Chapter 1 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences

Ch. 1.1 - What can you say about the signs of a and b if the...Ch. 1.1 - Refer to the accompanying figure. a. Given the...Ch. 1.1 - In Exercises 16, refer to the accompanying figure...Ch. 1.1 - In Exercises 16, refer to the accompanying figure...Ch. 1.1 - In Exercises 16, refer to the accompanying figure...Ch. 1.1 - In Exercises 16, refer to the accompanying figure...Ch. 1.1 - In Exercises 16, refer to the accompanying figure...Ch. 1.1 - In Exercises 16, refer to the accompanying figure...Ch. 1.1 - In Exercises 712, refer to the accompanying...Ch. 1.1 - Prob. 8E

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