The equation of a regression line, unlike the correlation, depends on the units

Question

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.

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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.)

(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 29 22 30 38 23 29

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.)

(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.)

Preferred amount
of salt x 0.2 0.3 0.4 0.5 0.6 0.8 1.1 Percent body fat y 20 29 22 30 38 23

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Explanation / Answer

Ans:

a)

slope,b=(7*109.6-3.9*191)/(7*2.75-3.9^2)=5.5

intercept,a=(191-5.5*3.9)/7=24.2

y'=24.2+5.5x

b)

Slope,b=(7*1096-39*191)/(7*275-39^2)=0.55

intercept,a=24.22

y'=24.22+0.55x

c)when x=1

y'(in milligrams)=5.5*1+24.2=29.7

y'(in tenth of mg)=0.55*10+24.22=29.7

x y xy x^2 y^2 1 0.2 20 4 0.04 400 2 0.3 29 8.7 0.09 841 3 0.4 22 8.8 0.16 484 4 0.5 30 15 0.25 900 5 0.6 38 22.8 0.36 1444 6 0.8 23 18.4 0.64 529 7 1.1 29 31.9 1.21 841 Total= 3.9 191 109.6 2.75 5439

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