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 ($) for 10 racing bikes reviewed by the magazine.t Brand Weight Price ($) FELT FS 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 ?. (Round your answer to three decimal places.) Did the estimated regression equation provide a good fit? The estimated regression equation did not provide a good fit, since r? 2 0.55. The estimated regression equation did not provide a good fit, since r2 < 0.55. O The estimated regression equation provided a good fit, since r2 2 0.55. O The estimated regression equation provided a good fit, since 2 < 0.55. (c) Predict the price (in dollars) for a bike that weighs 14 pounds. (Round your answer to the nearest dollar.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![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 ($) for 10 racing bikes reviewed by the magazine.t
Brand
Weight
Price ($)
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).
%3D
(b) Compute r. (Round your answer to three decimal places.)
,2 =
Did the estimated regression equation provide a good fit?
The estimated regression equation did not provide a good fit, since r > 0.55.
The estimated regression equation did not provide a good fit, since r- < 0.55.
The estimated regression equation provided a good fit, since r 2 0.55.
The estimated regression equation provided a good fit, since r < 0.55.
(c) Predict the price (in dollars) for a bike that weighs 14 pounds. (Round your answer to the nearest dollar.)
$](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fccbe0e-690a-4599-ae28-c1fea38612a2%2Ff706363d-0358-44b3-9fd6-71aaed256c3b%2Ffk2ub75_processed.png&w=3840&q=75)
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