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

(c)

Predict the price (in dollars) for a bike that weighs 17 pounds. (Round your answer to the nearest dollar.)

$

Answer 1

a) n = number of bikes = 10

Regression equation is

where a is intercept and b is slope

b = -1439.006

b = -1439 (Round to the nearest integer)

a = 5550 - (-1439.*16)

a = 5550 + 23024

a = 28574

Regression equation is

b)

r = - 0.9294 (Round to 4 decimal)

  (Round to 3 decimal)

Degrees of freedom = n - 2 = 10 - 2 =8

0.55 is r critical value for df = 8 and alpha = 0.10 for two tailed test. (From table of r critical values)

|r| = 0.9294 > 0.55

> 0.55

So we can say that the regression equation is good predictor.

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

c) For x = 17

= 28574 - 1439 * 17

= 28574 - 24463

= 4111

The price for a bike that weighs 17 pounds is $4111