MGMT 305 - SOLUTIONSTOSUGGESTEDPROBLEMS_CHAPTER14 2. a. 35...

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SOLUTIONS TO SUGGESTED PROBLEMS-_ CHAPTER 14 2. a. b. There appears to be a linear relationship between x and y . c. Many different straight lines can be drawn to provide a linear approximation of the relationship between x and y ; in part d we will determine the equation of a straight line that “best” represents the relationship according to the least squares criterion. d. Summations needed to compute the slope and y -intercept are: 2 19 116 ( )( ) 57.8 ( ) 30.8 i i i i i x y x x y y x x Σ = Σ = Σ - - = - Σ - = 1 2 ( )( ) 57.8 1.8766 30.8 ( ) i i i x x y y b x x Σ - - - = = = - Σ - b y b x 0 1 232 18766 38 30 3311 = - = - - = . ( . )( . ) . . . y x = - 30 33 188 e. . . ( ) . y = - = 30 33 188 6 19 05 14 - 1 0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 8 9 x y
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100 105 110 115 120 125 130 135 61 62 63 64 65 66 67 68 69 x y Simple Linear Regression 4. a. b. There appears to be a linear relationship between x and y . c. Many different straight lines can be drawn to provide a linear approximation of the relationship between x and y ; in part d we will determine the equation of a straight line that “best” represents the relationship according to the least squares criterion. d. Summations needed to compute the slope and y -intercept are: 2 325 585 ( )( ) 110 ( ) 20 i i i i i x y x x y y x x Σ = Σ = Σ - - = Σ - = 1 2 ( )( ) 110 5.5 20 ( ) i i i x x y y b x x Σ - - = = = Σ - b y b x 0 1 117 5 65 2405 = - = - = - (5. )( ) . . . y x = - + 2405 55 e. . . . . ( ) y x = - + = - + = 2405 55 2405 55 63 106 pounds
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Simple Linear Regression 5. a. 0 500 1000 1500 2000 2500 1 1.5 2 2.5 3 3.5 4 4.5 Baggage Capacity Price ($) b. Let x = baggage capacity and y = price ($). There appears to be a linear relationship between x and y . c. Many different straight lines can be drawn to provide a linear approximation of the relationship between x and y ; in part (d) we will determine the equation of a straight line that “best” represents the relationship according to the least squares criterion. d. Summations needed to compute the slope and y -intercept are: 2 29.5 11,110 ( )( ) 2909.8889 ( ) 4.5556 i i i i i x y x x y y x x Σ = Σ = Σ - - = Σ - = 1 2 ( )( ) 2909.9889 638.7561 4.5556 ( ) i i i x x y y b x x Σ - - = = = Σ - 0 1 1234.4444 (638.7561)(3.2778) 859.26 b y b x = - = - = - 859.26 638.76 y x = - + e. A one point increase in the baggage capacity rating will increase the price by approximately $639. f. 859.26 638.76 859.26 638.76(3) $1057 y x = - + = - + =
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6. a. 0 5 10 15 20 25 30 50.00 70.00 90.00 110.00 130.00 150.00 170.00 190.00 Salary Bonus b. Let x = salary and y = bonus. There appears to be a linear relationship between x and y . c. Summations needed to compute the slope and y -intercept are: 2 1420 160 ( )( ) 1114 ( ) 6046 i i i i i x y x x y y x x Σ = Σ = Σ - - = Σ - = 1 2 ( )( ) 1114 .18425 6046 ( ) i i i x x y y b x x Σ - - = = = Σ - 0 1 16 (.18425)(142) 10.16 b y b x = - = - = - 10.16 .18 y x = - + d. $1000 increase in salary will increase the bonus by $180. e
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MGMT 305 - SOLUTIONSTOSUGGESTEDPROBLEMS_CHAPTER14 2. a. 35...

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