Question

One child in the Mumbai study had height 59 cm and arm span 60 cm. This child’s residual is

a. −3.2 cm.

b. −2.2 cm.

c. −1.3 cm.

d. 3.2 cm.

e. 62.2 cm.

Short answer

The correct option is (a)$-3.2cm$

Step-by-step solution

Given information

The regression line is $\stackrel{⏜}{y}=6.4+0.93x$

Concept

The formula to compute the residual is:

$Residual=(y-\stackrel{⏜}{y})$

Where,

$$\begin{gathered} y=Actualvalue \\ \stackrel{⏜}{y}=Predictedvalue \end{gathered}$$

Explanation

Here, predicted value can be computed as:

$$\begin{gathered} \stackrel{⏜}{y}=6.4+0.93x \\ =6.4+0.93\left(60\right) \\ =62.2 \end{gathered}$$

Now, residual can be calculated as:

$$\begin{gathered} Residual=(y-\stackrel{⏜}{y}) \\ =(59-62.2) \\ =-3.2 \end{gathered}$$

Thus, the residual is$-3.2cm$

Hence, the correct option is (a).