a. Explanation Given: The given data is, Year( t ) 0 1 2 3 4 5 6 7 Spending( y ) 1.38 1.44 1.49 1.56 1.61 1.67 1.74 1.78 Formula used: Suppose that there are n data points 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 line for the given data is given by linear equation y = m x + b . The constants m and b satisfy the normal equations, ( x 1 2 + x 2 2 + x 3 2 + … + x n 2 ) m + ( x 1 + x 2 + x 3 + … + x n ) b = x 1 y 1 + x 2 y 2 + x 3 y 3 + … + x n y n (1) And, ( x 1 + x 2 + x 3 + … + x n ) m + n b = y 1 + y 2 + y 3 + … + y n (2) Calculation: From the given data, it is observed that x = 0 corresponds to 2008. Form the new table is as shown below, x 0 1 2 3 4 5 6 7 y 1.38 1.44 1.49 1.56 1.61 1.67 1.74 1.78 That is, x 1 = 0 , x 2 = 1 , x 3 = 2 , x 4 = 3 , x 5 = 4 , x 6 = 5 , x 7 = 6 , x 8 = 7 and y 1 = 1.38 , y 2 = 1.44 , y 3 = 1.49 , y 4 = 1.56 , y 5 = 1.61 , y 6 = 1.67 , y 7 = 1.74 , y 7 = 1.78 . Thus observe that n = 7 . Substitute the data points in the normal equation (1) and obtain as, [ ( 0 2 + 1 2 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 ) m + ( 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 ) b ] = [ ( 0 ) ( 1.38 ) + ( 1 ) ( 1.44 ) + ( 2 ) ( 1 b. To determine To estimate: The rate of change in the projected global defense spending from 2008 through 2015. c. To determine To find: The expected global spending on defense in 2018.

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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Chapter 8.4, Problem 26E

To determine

To find: The equation of least-squares line.

To determine

To estimate: The rate of change in the projected global defense spending from 2008 through 2015.

To determine

To find: The expected global spending on defense in 2018.

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Chapter 8.4, Problem 25E

Chapter 8.4, Problem 27E

Chapter 8 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 8.1 - What is a function of two variables? Give an...Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Let f(x, y) = x2+ 2xy x + 3. Compute f(1, 2),...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Let h(s, t) = s ln t t ln s. Compute h(1, e),...

Ch. 8.1 - Prob. 8E Ch. 8.1 - Let g(r, s, t) = res/t. Compute g(1, 1, 1), g(1,...Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 14E Ch. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 16E Ch. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - In Exercises 19-24, sketch the level curves of the...Ch. 8.1 - Prob. 22E Ch. 8.1 - In Exercises 1924, sketch the level curves of the...Ch. 8.1 - Prob. 24E Ch. 8.1 - Find an equation of the level curve of f (x, y) =...Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - POISEITLLES LAW Poiseuilles Law states that the...Ch. 8.1 - COST FUNCTION FOR A LOUDSPEAKER SYSTEM Acrosonic...Ch. 8.1 - Prob. 38E Ch. 8.1 - REVENUE FUNCTIONS FOR DESKS Country Workshop...Ch. 8.1 - Prob. 40E Ch. 8.1 - 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The equation of least-squares line.

Solution Summary: The author explains how the least-squares line is given by linear equation y=mx+b. The constants m and b satisfy the normal equations.

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To find: The equation of least-squares line.

To estimate: The rate of change in the projected global defense spending from 2008 through 2015.

To find: The expected global spending on defense in 2018.

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Chapter 8 Solutions