Question

Sarah's parents are concerned that the she seems short for her age.

Their doctor has the following record of Sarah's height:
Age (months) 36 48 51 54 57 60Height (cm) 86 90 91 93 94 95
The simple linear regression equation to predict height from age is y = 71.95 + 0.3883(x).

What is the residual at age = 51 months ?
A) 91 cm
B) 91.75 cm
C) -0.75 cm
D) 0.75 cm

Answer 1

Option C

Explanation:

Given that Sarah's parents are concerned that the she seems short for her age.

From the data given we find regression equation connecting age and height is

`y = 71.95 + 0.3883(x).`

Actual observation shows for 51 months her height was 91

Predicted height =

`71.95 + 0.3883(51).\\=91.7533`

Actual height = 91

Residual = observed - actual

= -0.7533

=-0.75

Option C is right