Waterskiing and wakeboarding are two popular water-sports. Finding a model that best suits your intended needs, whether it is waterskiing, wakeboading, or general boating, can be a difficult task. WaterSki magazine did extensive testing for 88 boats and provided a wide variety of information to help consumers select the best boat. A portion of the data they reported for 16 boats with a length of between 20 and 22 feet follows. Beam is the maximum width of the boat in inches, HP is the horsepower of the boat's engine, and TopSpeed is the top speed in miles per hour (mph).
Make and Model Beam HP TopSpeed
Calabria Air Pro V2 100 330 45.3
CCAN 210 91 330 47.3
CCAN SV-211 93 375 46.9
CCSN 206 Limited 91 330 46.7
Gekko GTR 22 96 375 50.1
Gekko GTS 20 83 375 52.2
M Response LXi 93.5 340 47.2
M Sunsette LXi 98 400 46
M Wakesetter VLX 98 400 47.3
M vRide 93.5 340 44.5
M Ride XTi 93.5 320 44.5
Mstr ProStar 209 96 350 42.5
Mstr X1 90 310 45.8
Mstr X2 94 310 42.8
Mstr X9 96 350 43.2
MB Sprts 190 Plus 92 330 45.3
a. Using these data, develop an estimated regression equation relating the top speed with the boat's beam and horsepower rating.
b. The Svfara SV609 has a beam of 85 inches and an engine with a 330 horsepower rating. Use the estimated regression equation developed in part (a) to estimate the top speed for the Svfara SV609.
c. Compute and interpret and R2 and R2a.
d. Does the estimated regression equation provide a good fit to the data? Explain.