Chapter 3.2, Problem 43E

(a)

To determine

To explain:The interpret the residual for Kiana.

Answer to Problem 43E

The residual of Kiana is 15 walks, it means that the difference between Kiana’s actual walk and predicted value is 15.

Explanation of Solution

Given:

x: Height of a student.

y: Number of steps required to walk the length of a school hallway.

It is given that Kiana took 49 steps to walk the hallway while her height is 67 inches.

The given OLS regression line is:

  $\widehat{y}=113.6-0.921x$

Calculation:

The predicted walk of Kiana behalf of her height, can be calculated as:

  $\begin{array}{c}\widehat{y}=\mathrm{113..60}-0.921\left(67\right)\\ =51.8930\end{array}$

The residual for Kiana, can be calculated as:

  $\begin{array}{c}e=y-\widehat{y}\\ =67-51.8930\\ =15.1070\end{array}$

Interpretation:

The difference or fluctuation between true and predicted value, is known as the residual.

Here, the residual of Kiana is 15.1070, approximately 15 walks, it means that the difference between Kiana’s actual walk and predicted value is 15.

(b)

To determine

To explain:Number of fewer steps do you expect Matthew to take compared to Samantha.

Answer to Problem 43E

The number of fewer expected steps that Matthew will take compared to Samantha inches if Matthew is 10 inches taller than Samantha, is 8 steps.

Explanation of Solution

Given:

As per the above information,

Matthew is 10 inches taller than Samantha.

Calculation:

The number of fewer expected steps that Matthew will take compared to Samantha inches if Matthew is 10 inches taller than Samantha, can be calculated as:

Samantha ‘walk

  ${\widehat{y}}_1=113.6-0.921x$

Matthew ‘walk

  $\begin{array}{c}{\widehat{y}}_2=113.6-0.921\left(10x\right)\\ =113.6-9.21x\end{array}$

The expected walk is:

  $\begin{array}{c}E={\widehat{y}}_1-{\widehat{y}}_2\\ =113.6-0.921x-113.6+9.21x\\ =8.289x\\ \approx 8x\end{array}$