(a) Explanation Given: The values of x i 's and y j 's are 54, 60, 75, 76, 78, 84, 88, 89, 97, 99 and 50, 66, 80, 68, 71, 80, 95, 85, 94, 86 respectively. Formulae used: Formula 1: The formulae to find the normal equations are, ( ∑ k = 1 n x k 2 ) a + ( ∑ k = 1 n x k ) b = ∑ k = 1 n x k y k ( ∑ k = 1 n x k ) a + n b = ∑ k = 1 n y k Formula 2: Compute the value of a using the below formula. a = n ( ∑ k = 1 n x k y k ) − ( ∑ k = 1 n x k ) ( ∑ k = 1 n y k ) n ( ∑ k = 1 n x k 2 ) − ( ∑ k = 1 n x k ) 2 . Formula 3: Compute the value of b using the below formula. b = ( ∑ k = 1 n y k ) − a ( ∑ k = 1 n x k ) n . Calculation: Here, the value of n = 10 . Construct the table to compute the normal equation. x k y k x k y k x k 2 54 50 2,700 2,916 60 66 3,960 3,600 75 80 6,000 5,625 76 68 5,168 5,776 78 71 5,538 6,084 84 80 6,720 7,056 88 95 8,360 7,744 89 85 7,565 7,921 97 94 9,118 9,409 99 86 8,514 9,801 ∑ k = 1 10 x k = 800 ∑ k = 1 10 y k = 775 (b) To determine To sketch: The least square line using graphing calculator. (c) To determine To predict: The score of a student in the final examination who have scored 95 in the midterm examination.

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 14.5, Problem 1MP

(a)

To determine

To find: The normal equations and the least square line for the given table.

(b)

To determine

To sketch: The least square line using graphing calculator.

(c)

To determine

To predict: The score of a student in the final examination who have scored 95 in the midterm examination.

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Chapter 14.4, Problem 38E

Chapter 14.5, Problem 2MP

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Chapter 14 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Prob. 5MP Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

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