Question

Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value.”

What was the actual activity level rating for the fish at a temperature of 20°C?

a. 87

b. 84

c. 81

d. 66

e. 3

Short answer

The correct option is (a)$87$

Step-by-step solution

Given information

$x=$Temperature

$y=$Activity level rating

Explanation

Least-squares regression line:

$\stackrel{⏜}{y}=a+bx$

Calculating the value of $a$and $b$using Minitab

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

General least-squares regression line:

$\stackrel{⏜}{y}=148.62-3.2167x$

Finding the expected activity level at $20$degrees Celsius by replacing $x$in the least-squares regression line equation with $20$and calculating:

$$\begin{gathered} y=Resudal+\stackrel{⏜}{y} \\ =84.286+3 \\ =87.286 \\ \approx 87 \end{gathered}$$

The estimated level of activity is $84.286$

The real value would be added to the equation with $y$

$$\begin{gathered} y=Resudal+\stackrel{⏜}{y} \\ =84.286+3 \\ =87.286 \\ \approx 87 \end{gathered}$$

The real level rating for the fish at a temperature of $20$degrees Celsius has been found to be around $87$

Hence, the correct option is (a)