An estimated regression equation was developed relating the top speed for a boat
ID: 3227014 • Letter: A
Question
An estimated regression equation was developed relating the top speed for a boat to the boat's beam and horsepower rating, using the data below.
Compute R2 (to 3 decimals) and R2a (to 2 decimals). Report R2 and Ra2 between 0 and 1.
How good is the fit provided by the estimated regression equation?
Select:
The estimated regression equation provided an excellent fit
The estimated regression equation provided a moderately good fit
The estimated regression equation did not provide a good fit
R2: R2a: Make and Model Calabria Cal Air Pro V-2 Correct Craft Air Nautique 210 Correct Craft Air Nautique SV-211 Correct Craft Ski Nautique 206 Limited Gekko GTR 22 Gekko GTS 20 Malibu Response LXi Malibu Sunsettter LXi Malibu Sunsetter 21 XTi Malibu Sunscape 2 LSV Malibu Wakesetter 21 XTi Malibu Wakesetter VLX Malibu vRide Malibu Ride XTi Mastercraft ProStar 209 Mastercraft X Mastercraft X-2 Mastercraft X-9 MB Sports 190 Plus Svfara SVONE Beam 100.0 91.0 93.0 91.0 96.0 83.0 93.5 98.0 98.0 98.0 98.0 98.0 93.5 93.5 96.0 90.0 94.0 96.0 92.0 91.0 HP 330 330 375 330 375 375 340 340 340 340 320 350 310 310 350 330 330 TopSpeed 45.3 47.3 6.9 6.7 50.1 52.2 47.2 46.0 47.5 47.3 42.5 45.8 2.8 43.2 45.3 47.7Explanation / Answer
The statistical software output for this problem is:
Multiple linear regression results:
Dependent Variable: Top Speed
Independent Variable(s): Beam, HP
Top Speed = 64.965881 + -0.3895895 Beam + 0.051064402 HP
Parameter estimates:
Analysis of variance table for multiple regression model:
Summary of fit:
Root MSE: 1.5953761
R-squared: 0.5972
R-squared (adjusted): 0.5498
R2 = 0.597
R2a = 0.55
The estimated regression equation provided a moderately good fit
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 64.965881 9.0086591 0 17 7.2114929 <0.0001 Beam -0.3895895 0.095789735 0 17 -4.0671321 0.0008 HP 0.051064402 0.013118033 0 17 3.8926875 0.0012