(a) Explanation Given: The amount of red meat and poultry consumed in United States is listed as follows: Year U.S. Red Meat Consumption (in billions of pounds) U.S. Poultry Consumption (in billions of pounds) 2005 47.385 34.947 2010 45.931 35.201 2014 43.887 36.107 Table 1 Formula used: The formula for linear regression equation is given by y = a + b x , where a and b are given by the following two formulas. b ( slope ) = n ∑ x y − ( ∑ x ) ( ∑ y ) n ∑ x 2 − ( ∑ x ) 2 a ( intercept ) = ∑ y − b ( ∑ x ) n Where, b = slope of the line, a = y -intercept of the line, x = values of the first data set and y = values of the second data set. Calculation: The linear regression functions r ( x ) that represent red meat consumption in billions of pounds x years after 2005 is obtained as follows. Consider years as a first data set x and red meat consumption as a second data set y . Consider the year 2005 as a reference year, the modified data values for the consumption of red meat in U.S. listed in Table 1. Year x U.S. Red Meat Consumption (in billions of pounds) y 0 47.385 5 45.931 9 43.887 Table 1 From Table 1, it is observed that the total number of data values is n = 3 . Use the above mention formula and set the regression function r ( x ) = a + b x that represents red meat consumption in billions of pounds x years after 2005. Use the data values in Table 1 and construct the following Table 2. x y x 2 x y 0 47.385 0 0 5 45.931 25 229.655 9 43.887 81 394.983 ∑ x = 14 ∑ y = 137.203 ∑ x 2 = 106 ∑ x y = 624.638 Table 2 From Table 2, it is clear that n = 3 , ∑ x = 14 , ∑ y = 137.203 , ∑ x 2 = 106 and ∑ x y = 624.638 . Now use the above mention formula and obtained the slope of the line as follows. Substitute n = 3 , ∑ x y = 624.638 , ∑ x = 14 , ∑ y = 137.203 and ∑ x 2 = 106 in b ( slope ) = n ∑ x y − ( ∑ x ) ( ∑ y ) n ∑ x 2 − ( ∑ x ) 2 . b ( slope ) = 3 ( 624.638 ) − ( 14 ) ( 137.203 ) 3 ( 106 ) − ( 14 ) 2 = 1873.914 − 1920.842 318 − 196 = − 46.928 122 = − 0.384655737 Thus, the slope of the regression function r ( x ) is b = − 0.384655737 . Use the intercept formula to obtain the intercept of the regression function. Substitute n = 3 , ∑ x = 14 , ∑ y = 137.203 , and b = − 0.384655737 in a ( intercept ) = ∑ y − b ( ∑ x ) n . a ( intercept ) = ( 137.203 ) − ( − 0.384655737 ) ( 14 ) 3 = 137 (b) To determine To estimate: The time when the poultry consumption will equal to the red meat consumption in U.S.

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter 6.1, Problem 75E

(a)

To determine

The linear regression functions r(x) and p(x) that represent red meat consumption and poultry consumption, respectively, in billions of pounds x years after 2005.

(b)

To determine

To estimate: The time when the poultry consumption will equal to the red meat consumption in U.S.

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Chapter 6.1, Problem 74E

Chapter 6.1, Problem 76E

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Chapter 6 Solutions

College Algebra: Graphs and Models (6th Edition)

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Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Solve graphically. x y = 6, y = 2x Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Solve using the elimination method. Also determine...Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Solve using the elimination method. Also determine...Ch. 6.1 - Solve using the elimination method. 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[2 4 0 9]Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - Prob. 8E Ch. 6.3 - Prob. 9E Ch. 6.3 - Prob. 10E Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 24E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 26E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 28E Ch. 6.3 - Prob. 29E Ch. 6.3 - Prob. 30E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 40E Ch. 6.3 - Use Gaussian elimination or GaussJordan...Ch. 6.3 - Prob. 42E Ch. 6.3 - Prob. 43E Ch. 6.3 - Prob. 44E Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.3 - Prob. 49E Ch. 6.3 - Prob. 50E Ch. 6.3 - Prob. 51E Ch. 6.3 - Prob. 52E Ch. 6.3 - In Exercises 53 and 54, three solutions of the...Ch. 6.3 - Prob. 54E Ch. 6.3 - Prob. 55E Ch. 6.3 - Prob. 56E Ch. 6.3 - Prob. 57E Ch. 6.3 - Prob. 58E Ch. 6.3 - Prob. 59E Ch. 6.3 - Prob. 60E Ch. 6.3 - Prob. 61E Ch. 6.3 - Prob. 62E Ch. 6.4 - Prob. 1E Ch. 6.4 - Prob. 2E Ch. 6.4 - Prob. 3E Ch. 6.4 - Prob. 4E Ch. 6.4 - For Exercises 520, let...Ch. 6.4 - Prob. 6E Ch. 6.4 - Prob. 7E Ch. 6.4 - Prob. 8E Ch. 6.4 - Prob. 9E Ch. 6.4 - Prob. 10E Ch. 6.4 - Prob. 11E Ch. 6.4 - Prob. 12E Ch. 6.4 - Prob. 13E Ch. 6.4 - For Exercises 520, let...Ch. 6.4 - For Exercises 520, let...Ch. 6.4 - Prob. 16E Ch. 6.4 - Prob. 17E Ch. 6.4 - Prob. 18E Ch. 6.4 - Prob. 19E Ch. 6.4 - Prob. 20E Ch. 6.4 - Prob. 21E Ch. 6.4 - Prob. 22E Ch. 6.4 - Prob. 23E Ch. 6.4 - Prob. 24E Ch. 6.4 - Prob. 25E Ch. 6.4 - Prob. 26E Ch. 6.4 - Prob. 27E Ch. 6.4 - Prob. 28E Ch. 6.4 - Produce. 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Then find the...Ch. 6.7 - Graph the system of inequalities. Then find the...Ch. 6.7 - Prob. 58E Ch. 6.7 - Prob. 59E Ch. 6.7 - Graph the system of inequalities. Then find the...Ch. 6.7 - Find the maximum value and the minimum value of...Ch. 6.7 - Find the maximum value and the minimum value of...Ch. 6.7 - Prob. 63E Ch. 6.7 - Prob. 64E Ch. 6.7 - Prob. 65E Ch. 6.7 - Maximizing Income. Golden Harvest Foods makes...Ch. 6.7 - Prob. 67E Ch. 6.7 - Prob. 68E Ch. 6.7 - Prob. 69E Ch. 6.7 - Prob. 70E Ch. 6.7 - Prob. 71E Ch. 6.7 - Prob. 72E Ch. 6.7 - Minimizing Transportation Cost. An airline with...Ch. 6.7 - Minimizing Transportation Cost. Suppose that in...Ch. 6.7 - Maximizing Profit. It takes Fena Tailoring 3 hr of...Ch. 6.7 - Maximizing Profit. Cambridge Metal Works...Ch. 6.7 - Minimizing Nutrition Cost. Suppose that it takes...Ch. 6.7 - Prob. 78E Ch. 6.7 - Prob. 79E Ch. 6.7 - Prob. 80E Ch. 6.7 - Prob. 81E Ch. 6.7 - Prob. 82E Ch. 6.7 - Prob. 83E Ch. 6.7 - Prob. 84E Ch. 6.7 - Prob. 85E Ch. 6.7 - Graph the system of inequalities. y x + 1, y x2 Ch. 6.7 - Prob. 87E Ch. 6.7 - Prob. 88E Ch. 6.7 - Prob. 89E Ch. 6.7 - Prob. 90E Ch. 6.7 - Prob. 91E Ch. 6.8 - Prob. 1E Ch. 6.8 - Prob. 2E Ch. 6.8 - Prob. 3E Ch. 6.8 - Prob. 4E Ch. 6.8 - Prob. 5E Ch. 6.8 - Prob. 6E Ch. 6.8 - Prob. 7E Ch. 6.8 - Prob. 8E Ch. 6.8 - Prob. 9E Ch. 6.8 - Prob. 10E Ch. 6.8 - Prob. 11E Ch. 6.8 - Prob. 12E Ch. 6.8 - Prob. 13E Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Prob. 16E Ch. 6.8 - Prob. 17E Ch. 6.8 - Prob. 18E Ch. 6.8 - Prob. 19E Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Prob. 21E Ch. 6.8 - Prob. 22E Ch. 6.8 - Prob. 23E Ch. 6.8 - Prob. 24E Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Prob. 26E Ch. 6.8 - Prob. 27E Ch. 6.8 - Prob. 28E Ch. 6.8 - Prob. 29E Ch. 6.8 - Prob. 30E Ch. 6.8 - Prob. 31E Ch. 6.8 - Prob. 32E Ch. 6.8 - Prob. 33E Ch. 6.8 - Prob. 34E Ch. 6.8 - Prob. 35E Ch. 6 - Determine whether the statement is true or false....Ch. 6 - Prob. 2MC Ch. 6 - Prob. 3MC Ch. 6 - Prob. 4MC Ch. 6 - Prob. 5MC Ch. 6 - Prob. 6MC Ch. 6 - Prob. 7MC Ch. 6 - Prob. 8MC Ch. 6 - Prob. 9MC Ch. 6 - Prob. 10MC Ch. 6 - Prob. 11MC Ch. 6 - Prob. 12MC Ch. 6 - Prob. 13MC Ch. 6 - Prob. 14MC Ch. 6 - Prob. 15MC Ch. 6 - Prob. 16MC Ch. 6 - Prob. 17MC Ch. 6 - Prob. 18MC Ch. 6 - Prob. 19MC Ch. 6 - Prob. 20MC Ch. 6 - Prob. 21MC Ch. 6 - Prob. 1RE Ch. 6 - Prob. 2RE Ch. 6 - Prob. 3RE Ch. 6 - Prob. 4RE Ch. 6 - Prob. 5RE Ch. 6 - Prob. 6RE Ch. 6 - Prob. 7RE Ch. 6 - Prob. 8RE Ch. 6 - Prob. 9RE Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Prob. 15RE Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Prob. 19RE Ch. 6 - Prob. 20RE Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Solve the system of equations using Gaussian...Ch. 6 - Prob. 25RE Ch. 6 - Coins. 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Jackson is taking a test...Ch. 6 - Decompose into partial fractions. 5(x+2)2(x+1)Ch. 6 - Prob. 61RE Ch. 6 - Prob. 62RE Ch. 6 - Prob. 63RE Ch. 6 - Prob. 64RE Ch. 6 - Prob. 65RE Ch. 6 - Prob. 66RE Ch. 6 - Prob. 67RE Ch. 6 - Prob. 68RE Ch. 6 - Prob. 69RE Ch. 6 - Prob. 1T Ch. 6 - Prob. 2T Ch. 6 - Prob. 3T Ch. 6 - Prob. 4T Ch. 6 - Prob. 5T Ch. 6 - Prob. 6T Ch. 6 - Prob. 7T Ch. 6 - Prob. 8T Ch. 6 - Prob. 9T Ch. 6 - Prob. 10T Ch. 6 - Prob. 11T Ch. 6 - Prob. 12T Ch. 6 - Prob. 13T Ch. 6 - Prob. 14T Ch. 6 - Prob. 15T Ch. 6 - Prob. 16T Ch. 6 - Prob. 17T Ch. 6 - Prob. 18T Ch. 6 - Prob. 19T Ch. 6 - Prob. 20T Ch. 6 - Prob. 21T Ch. 6 - Prob. 22T Ch. 6 - Prob. 23T Ch. 6 - Prob. 24T Ch. 6 - Prob. 25T

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The linear regression functions r ( x ) and p ( x ) that represent red meat consumption and poultry consumption, respectively, in billions of pounds x years after 2005.

Solution Summary: The author explains the linear regression functions r(x), and p left, that represent red meat consumption and poultry consumption, respectively, in billions of pounds years after 2005.