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

1. 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 =

2. Compute r². (Round your answer to three decimal places.)

r² =

2b. Did the estimated regression equation provide a good fit?

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

(b) The estimated regression equation did not provide a good fit, since r² < 0.55.     

(c) The estimated regression equation provided a good fit, since r² < 0.55.

(d) The estimated regression equation provided a good fit, since r² ≥ 0.55.

3. Predict the price (in dollars) for a bike that weighs 15 pounds. (Round your answer to the nearest dollar.)

Answer 1

The statistic software output for this problem is :

1)

= 28574 - 1439 x

2)

r ² = 0.864

(d) The estimated regression equation provided a good fit, since r² ≥ 0.55.

3)

price = $6989