Theme parks are big business. In the United States there are nearly 500 theme and amusement parks which generate over $10 billion a year in revenue. The theme park business is also growing in Europe and Asia. Rides are the main attraction at most parks, and at the center of this attention are the roller coasters. Engineers and designers compete to make them bigger and faster to increase park attendance. Roller coaster fans will wait in line for hours for a speedy, stomach-churning, head spinning 2-minute ride.

What makes a roller coast fast? In this Excel file Roller Coasters are data on some of the fastest roller coasters in the world. The file contains the values for several variables but initially we are interested in the variables speed, drop, and height (the variable definitions are included in the Excel file).

Question 1. Construct a multiple regression model with height and drop as the explanatory variables and speed as the response variable. Enter the values of the model coefficients below.

intercept
height
drop

Question 2. To attract more customers an amusement park owner wants to increase the speed of the park's main roller coaster. Because of design considerations the height of the roller coaster cannot be increased, but the drop can be increased by sending the roller coaster through an underground tunnel. If the drop is increased by 100 feet and the height remains the same, by how much will the speed increase?

miles per hour

Question 3. An amusement park in Japan wants to build a new mega-coaster, which it will name the Cranium Shaker, with a top speed over 110 miles per hour to exceed the speed of the Tower of Terror in Australia. The Cranium Shaker's design has a height of 330 feet and a drop of 415 feet (the drop will go into an underground tunnel). Use the regression model to estimate the top speed of the Cranium Shaker roller coaster.

miles per hour

While the top speed is important, you are also interested in the Duration of the ride. The Duration is affected not only by theLength (feet of track), but also by whether the roller coaster has an inversion (riders are turned upside down). The variableInvert = 1 if the roller coaster has an inversion; Invert = 0 if there is no inversion.

Question 4. Construct a multiple regression model with Length and Invert as the explanatory variables and Duration as the response variable. Select the correct response below. Note reduced submissions for this question.

A.The average duration of a roller coaster without an inversion is approximately 51.9 seconds.

B.For inversion and non-inversion roller coasters with the same length of track, the duration of the inversion roller coaster is approximately 15.3 seconds less than the non-inversion coaster.

C.For inversion and non-inversion roller coasters with the same length of track, the duration of the non-inversion roller coaster is approximately 15.3 seconds less than the inversion coaster.

D.When an inversion and non-inversion roller coaster have the same duration, the inversion roller coaster has approximately 15.4 more feet of track than the non-inversion roller coaster.

E. The average duration of a roller coaster with an inversion is approximately 67.4 seconds.

Speed	Height	Drop
93	310	300
85	235	255
85	245	255
82	205	130
80	209	225
80	230	215
77	208	221
75	205	205
75	200	205
74	207	196
73	170	210
73	202	208
73	179.5	166.5
73	208	205
72	205	194.6
70	188	171
68	173	155
67	195	170
67	110	105
67	203	144
66	127	147
66	120	155
65.6	191.5	177
65	95	151
65	149	144
65	161	155
65	150	150
65	117	115
65	179.5	124
65	156	146
65	150	150
65	143	137
64.8	105	141
63	154	144
63	150	141
63	163	128
62	125	115
62	110	92
55	115	95
55	101.5	100
55	138	138
55	100	90
55	115	95
55	115	95
55	83	75
55	115	95
55	70	95
53	100	95
53	98	88
50	55	52
50	84	78
47	80	75
45	56	47
42	70	64
41	94	66
40	78	72
100	220.5	207.3
80.8	259.2	229.7
71.5	166	178
65.6	191.6	177
60.3	137.8	124.67
56	102	93
56	95	90
80	165	133
80	160	225
78.4	218	214
76	175	215
70	155	80
66.3	122	150
65	157	148
55	70	76
52	92	90
50	70	70
46	70	62
95	318.25	306.75
80.8	262.5	218.1
90	305	300
68	65	180