Chapter 3, Problem T3.4SPT

To determine

To find: the actual activity level rating for the fish at a temperature of 20 degree Celsius.

Answer to Problem T3.4SPT

87

Explanation of Solution

Given:

  $\begin{array}{c}x\text{=Temperature}\\ y\text{=Activity}\text{level}\text{rating}\end{array}$

Calculation:

Least-squares regression line:

  $\widehat{y}=a+bx$

Calculating the value of a and b using Minitab

  $\begin{array}{c}a=148.62\\ b=-3.2167\end{array}$

General least-squares regression line:

  $\widehat{y}=148.62-3.2167x$

Finding the predicted activity level at 20 degree Celsius by replacing with 20 of x in the equation of the least-squares regression line and calculating:

  $\begin{array}{c}\widehat{y}=148.62-3.2167x\\ =148.62-3.2167\left(20\right)\\ =148.62-64.334\\ =84.286\end{array}$

The predicted activity level rating is 84.286

The actual value would be added with $\widehat{y}$ to the equation

  $\begin{array}{c}y=\text{Resudal}+\widehat{y}\\ =84.286+3\\ =87.286\\ \approx 87\end{array}$

There is it observed that the actual level rating for the fish at a temperature of 20 degree Celsius is approximately 87.

Hence, the correct option is (a)