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.

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.

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 0.9 when weight is measured in milligrams, which is the same as 9 when weight is in tenths of milligrams. (Round your answers to one decimal place.)

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

Yes

No   

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 23 31 39 22 29

Explanation / Answer

(A) here the linear regression line to be calculated with the help of the given table

so lets say line equation is y = a +bx

and a and b = line constants.

so by formulas

a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

all the values are given above and putting all these values from the table, we get

a = [195 * 2.75 - 3.9 * 110.9] / [7 * 2.75 - 3.92]

a = 25.67

Here,

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [7 * 110.9 - 3.9 * 195] / [ 7 * 2.75 - 3.92] = 3.910

Here regression line is

y^ = 3.91 x + 25.7

(b) Here as we change weight to miligrams then slope will be reduced by 10 times.

y^ = 0.391x + 25.7

(c) x = 0.9 in mg

y^ = 3.91 * 0.9 + 25.7 = 29.2 % fat

in tenths of millingrams

y^ = 0.391 * 9 + 25.7 = 29.2% body fat

yes, the prediction are the same

amount of salt (x) body fat (y) x^2 xy 0.2 20 0.04 4 0.3 31 0.09 9.3 0.4 23 0.16 9.2 0.5 31 0.25 15.5 0.6 39 0.36 23.4 0.8 22 0.64 17.6 1.1 29 1.21 31.9 Sum 3.9 195 2.75 110.9

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.