Explanation Given information: The table representing the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from the fields having the oil that is about to the end of their economic life in terms of approximate economic value (in billions of dollars) at various levels of recovery is as follows: Percent Recovery (%) 10 40 50 80 Economic Value (in billions of dollars) 200 900 1 , 000 2 , 000 Formula used: The regression line is the line which gives the minimum sum-of-square error for the data points ( x 1 , y 1 ) , ( x 2 , y 2 ) , ⋯ , ( x n , y n ) and expressed as, y = m x + b Where, m and b are the regression coefficients and calculated as: m = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 and b = ∑ y − m ( ∑ x ) n Where n is the number of data points. Calculation: Consider that the table representing the approximate economic value (in billions of dollars) at various levels of recovery is as follows: Percent Recovery (%) 10 40 50 80 Economic Value (in billions of dollars) 200 900 1 , 000 2 , 000 Consider the regression line, y = m x + b Where, y is the economic value in billions of dollars, x is the percent of recovery, m is the slope of the line and b is the y -intercept for the line. Here the data points ( x , y ) are ( 10 , 200 ) , ( 40 , 900 ) , ( 50 , 1000 ) and ( 80 , 2000 ) . Now, make the table for the values of xy and x 2 on substituting the values of x and y . Then, the table is as follows: x y xy x 2 10 200 2 , 000 100 40 900 3 , 600 1 , 600 50 1 , 000 50 , 000 2 , 500 80 2 , 000 160 , 000 6 , 400 ∑ ( Sum ) 180 4 , 100 248 , 000 10 , 600 The regression line is computed by calculating the value of slope and intercept

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 1.4, Problem 20E

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To calculate: The regression line and also calculate the economic value (in billions of dollars) at the recovery level of 70% using the obtained regression line when the table representing the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from the fields having the oil that is about to the end of their economic life in terms of approximate economic value (in billions of dollars) at various levels of recovery is as follows:

Percent Recovery (%) 10 40 50 80

Economic Value (in billions of dollars) 200 900 1,000 2,000

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Chapter 1.4, Problem 19E

Chapter 1.4, Problem 21E

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Percent Recovery (%)	10	40	50	80
Economic Value (in billions of dollars)	200	900	1,000	2,000

Solution Summary: The author calculates the economic value (in billions of dollars) at the recovery level of 70% using the obtained regression line.

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