Question

In: Statistics and Probability

Bicycling, the world's leading cycling magazine, reviews hundreds of bicycles throughout the year. Their "Road-Race" category...

Bicycling, the world's leading cycling magazine, reviews hundreds of bicycles throughout the year. Their "Road-Race" category contains reviews of bikes used by riders primarily interested in racing. One of the most important factors in selecting a bike for racing is the weight of the bike. The following data show the weight (pounds) and price ($) for 10 racing bikes reviewed by the magazine.†

Brand Weight Price ($)
FELT F5 17.8 2,100
PINARELLO Paris 16.1 6,250
ORBEA Orca GDR 14.9 8,370
EDDY MERCKX EMX-7 15.9 6,200
BH RC1 Ultegra 17.2 4,000
BH Ultralight 386 13.1 8,600
CERVELO S5 Team 16.2 6,000
GIANT TCR Advanced 2 17.1 2,580
WILIER TRIESTINA Gran Turismo 17.6 3,400
SPECIALIZED S-works Amira SL4 14.1 8,000

(a)

Use the data to develop an estimated regression equation that could be used to estimate the price for a bike given the weight. (Round your numerical values to the nearest integer).

ŷ =

(b)

Compute

r2.

(Round your answer to three decimal places.)

r2

=

Did the estimated regression equation provide a good fit?

The estimated regression equation provided a good fit, since r2 ≥ 0.55.The estimated regression equation did not provide a good fit, since r2 < 0.55.     The estimated regression equation provided a good fit, since r2 < 0.55.The estimated regression equation did not provide a good fit, since r2 ≥ 0.55.

(c)

Predict the price (in dollars) for a bike that weighs 13 pounds. (Round your answer to the nearest dollar.)

$

Solutions

Expert Solution

a)

y^ =28574-1439x

b)

SST=Syy= 52,120,800.0000
SSE =Syy-(Sxy)2/Sxx= 7,102,922.539
SSR =(Sxy)2/Sxx = 45,017,877.4609
Coeffficient of determination R^2 =SSR/SST= 0.864

The estimated regression equation provided a good fit, since r2 ≥ 0.55

c)

predicted price =28574-1439*13 =9867


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