Question

An anthropologist is interested in the relationship

between fathers' and sons' heights. She collects a
simple random sample of 25 fathers and 25 sons, and
determines that the least-squares regression line is ý = -
2.8+ 1.1x, where ŷ is the predicted height of each son
and x is the height of his father (both measured in
inches).
One father is 72 inches tall, and his son is 75 inches tall.
What is the residual for the son's height?
O -2.8
O-1.4
O 1.1
O 1.4

Answer 1

Answer: B. -1.4

Explanation:

To find the residual, we need to first calculate the predicted height of the son using the given regression equation:

ŷ = -2.8 + 1.1x

where x is the height of the father. For the given father who is 72 inches tall, we have:

ŷ = -2.8 + 1.1(72) = 75.6

So the predicted height of the son is 75.6 inches.

The residual is then calculated by subtracting the predicted height from the actual height of the son:

residual = actual height - predicted height

= 75 - 75.6

= -0.6

Therefore, the residual for the son's height is -0.6, which is closest to answer B after rounding to one decimal place.