5. Determine if each set of data is best represented by a linear, quadratic, exponential, or sinusoidal regression equation. Where possible, state the coefficient of determination r, for each equation. (6 marks) Table 1: X -3 -2 -1 0 2 3 0 -4.5 -4.5 0 4.5 4.5 Linear equation coefficient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yeso): Best type of equation: Table 2: X -2 -1 0 1 2 3 -6 -2 0 2 4 6 Linear equation coefficient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yeso): Best type of equation: Table 3: X -3 0 1 2 3 9 0 4 9 Linear equation coefficient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yeso): Best type of equation: Table 4: x -3 -2 -1 0 3 0.125 | 0.25 0.5 8Table 4: X -3 -2 -1 0 1 2 3 0.125 0.25 0.5 1 2 4 8 Linear equation coefficient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yeso): Best type of equation: Page 5 of 7 VVS: 30-2 A8 21/22 Sem 6. The Niagara Sky Wheel is a Ferris wheel in 70 4 Niagara Falls, Ontario. Instead of seats, visitors 60 ride in capsules which they enter and exit at the lowest point of the ride. The graph to the right 40 models the height of a particular capsule over height (m) the course of a ride. 30 - 20 10 24 time (min) a. State the value of each characteristic of the graph above and explain what it represents in the context of the question. i) amplitude (2 marks)8. The table below provides the average monthly temperature in Niagara, Ontario over the course of a year. Month Temperature C 1 January -0.4 2 February 1.3 3 March 5.9 4 April 12.8 5 May 19.4 6 June 24.5 7 July 27.4 8 August 26 9 September 21.9 10 October 15.1 11 November 8.7 12 December 2.7 a. Determine the equation of a sinusoidal regression function y = asin (bx + c) + d that best models the data. Express the values of a, b, c, and d to the nearest tenth. (2 marks) b. Use the sinusoidal regression equation above (with rounded values) to predict the average temperature, to the nearest tenth, in Niagara next March. (1 mark) C. Most tourists visit Niagara during months when the average temperature is 17 .C and higher. Determine the month of the year when the temperature first reaches 17 .C. (1 mark)