Solutions 11: Fitting Linear Models to Data

Solutions to Try Its

1. [latex]54^\circ \text{F}[/latex]

2. 150.871 billion gallons; extrapolation

Solutions to Odd-Numbered Exercises

1. When our model no longer applies, after some value in the domain, the model itself doesn’t hold.

3. We predict a value outside the domain and range of the data.

5. The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.

7. 61.966 years

9. No

11. No

13. Interpolation. About [latex]60^\circ \text{ F}[/latex].

15. C

17. B

19.

21.

23. Yes, trend appears linear because [latex]r=0.\text{985}[/latex] and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.

25. [latex]y=\text{1}.\text{64}0x+\text{13}.\text{8}00[/latex] , [latex]r=0.\text{987}[/latex]

27. [latex]y=-0.962x+26.86, r=-0.965[/latex]

29. [latex]y=-\text{1}.\text{981}x+\text{6}0.\text{197}[/latex] ; [latex]r=-0.\text{998}[/latex]

31. [latex]y=0.\text{121}x - 38.841,r=0.998[/latex]

33. [latex]\left(-2,\text{ }-6\right),\left(1,\text{ }-12\right),\left(5,\text{ }-20\right),\left(6,\text{ }-22\right),\left(9,\text{ }-28\right)[/latex]; [latex]y=-2x - 10[/latex]

35. [latex]\left(\text{189}.\text{8},0\right)[/latex] If 18,980 units are sold, the company will have a profit of zero dollars.

37. [latex]y=0.00587x+\text{1985}.4\text{1}[/latex]

39. [latex]y=\text{2}0.\text{25}x-\text{671}.\text{5}[/latex]

41. [latex]y=-\text{1}0.\text{75}x+\text{742}.\text{5}0[/latex]

43. Yes

45. Increasing

47. [latex]y=-\text{3}x+\text{26}[/latex]

49. 3

51. [latex]y=\text{2}x-\text{2}[/latex]

53. Not linear

55. parallel

57. [latex]\left(-9,0\right);\left(0,-7\right)[/latex]

59. Line 1: [latex]m=-2[/latex]; Line 2: [latex]m=-2[/latex]; Parallel

61. [latex]y=-0.2x+21[/latex]

63.

65. 250

67. 118,000

69. [latex]y=-\text{3}00x+\text{11},\text{5}00[/latex]

71. a) 800 b) 100 students per year c) [latex]P\left(t\right)=100t+1700[/latex]

73. 18,500

75. $91,625

77. Extrapolation.

79.

81. Midway through 2024

83. [latex]y=-1.294x+49.412;\text{ } r=-0.974[/latex]

85. Early in 2022

87. 7,660