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Question : An engineer collects the following data showing the speed and miles per gallon of a 4 : 2146848

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

88) An engineer collects the following data showing the speed and miles per gallon of a 4-door sedan.

Speed, s |
Miles per Gallon, M |

30 |
17 |

35 |
21 |

40 |
24 |

40 |
25 |

45 |
29 |

50 |
29 |

55 |
33 |

60 |
30 |

65 |
25 |

a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?

b) Find the quadratic regression equation hat(y) = b_{0} + b_{1}x + b_{2}x^{2}.

c) Interpret the coefficient of determination.

89) For the data set below, use a partial F-test to determine whether the variables x_{4} and x_{5} do not significantly help to predict the response variable, y. Use the α = 0.05 level of significance.

x |
x |
x |
x |
x |
Y |

0.9 |
2.7 |
2.6 |
10.8 |
15.2 |
12 |

3.8 |
2.4 |
5.4 |
9.5 |
4.4 |
10.7 |

2 |
2.2 |
7.7 |
10.4 |
1.8 |
10.9 |

5.3 |
2.4 |
7.2 |
9.1 |
1.6 |
10.4 |

4.8 |
2.7 |
6.1 |
11.6 |
5.5 |
10.3 |

8.3 |
2.2 |
8.7 |
10.5 |
5 |
10.4 |

12.7 |
2.1 |
9.1 |
11.3 |
2.3 |
10.4 |

6.3 |
1.8 |
1 |
8.5 |
22.6 |
9 |

14.4 |
2.1 |
3.5 |
10.4 |
11.4 |
8.7 |

9.2 |
1.2 |
5.8 |
8.9 |
6.6 |
8.6 |

90) For the data set below, use a partial F-test to determine whether the variables x_{1} and x_{2} do not significantly help to predict the response variable, y. Use the α = 0.05 level of significance.

x |
x |
x |
x |
y |

24.8 |
66.2 |
13.7 |
3.6 |
60 |

26.5 |
100.4 |
15.8 |
11.5 |
66.4 |

30.7 |
77.9 |
14 |
15.5 |
76.3 |

40 |
83.5 |
8.9 |
8.9 |
77.2 |

33.4 |
69.2 |
10.7 |
18.4 |
82.2 |

41.9 |
83.7 |
9.9 |
21.6 |
84.4 |

25.5 |
112.8 |
10.1 |
16.4 |
87.2 |

33.8 |
68.4 |
6.9 |
25.6 |
88.4 |

23.5 |
69.6 |
7.7 |
15.7 |
90.6 |

39.8 |
63.2 |
6.7 |
30.7 |
93.4 |