The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables. Here is the data on percent body fat and preferred amount of salt. Preferred amount of salt x 0.2 0.3 0.4 0.5 0.6 0.8 1.1 Percent body fat y 20 31 22 29 39 22 30 In calculating the preferred amount of salt, the weight of the salt was in milligrams. (a) Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in milligrams. (Round your answers to one decimal place.) ŷ = ? + ? x (b) A mad scientist decides to measure weight in tenths of milligrams. The same data in these units are as follows. Preferred amount of salt x 2 3 4 5 6 8 11 Percent body fat y 20 31 22 29 39 22 30Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in tenths of milligrams. (Round your intercept to one decimal place and your slope to two decimal places.) ŷ = ? + ? x (c) Use both lines to predict the percent body fat from preferred amount of salt for a child with preferred amount of salt 1 when weight is measured in milligrams, which is the same as 10 when weight is in tenths of milligrams. (Round your answers to one decimal place.) in milligrams ? % body fat in tenths of milligrams ? % body fat Are the two predictions the same (up to any roundoff error)? Yes No

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables. Here is the data on percent body fat and preferred amount of salt.

Preferred amount of salt x	0.2	0.3	0.4	0.5	0.6	0.8	1.1
Percent body fat y	20	31	22	29	39	22	30

In calculating the preferred amount of salt, the weight of the salt was in milligrams.

(a) Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in milligrams. (Round your answers to one decimal place.)

ŷ = ? + ? x

(b) A mad scientist decides to measure weight in tenths of milligrams. The same data in these units are as follows.

Preferred amount of salt x	2	3	4	5	6	8	11
Percent body fat y	20	31	22	29	39	22	30

Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in tenths of milligrams. (Round your intercept to one decimal place and your slope to two decimal places.)

ŷ = ? + ? x

(c) Use both lines to predict the percent body fat from preferred amount of salt for a child with preferred amount of salt 1 when weight is measured in milligrams, which is the same as 10 when weight is in tenths of milligrams. (Round your answers to one decimal place.)

in milligrams	?	% body fat
in tenths of milligrams	?	% body fat

Are the two predictions the same (up to any roundoff error)?

Yes No

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