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. 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 hourQuestion 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 hourWhile 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.