Question

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.)

$

Answer 1

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