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Chapter 3: Q T3.4. (page 215)

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

Expert verified

The correct option is (a)87

Step by step solution

01

Given information

x=Temperature

y=Activity level rating

02

Explanation

Least-squares regression line:

y⏜=a+bx

Calculating the value of aand busing Minitab

a=148.62b=−3.2167

General least-squares regression line:

y⏜=148.62−3.2167x

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

y=Resudal+y⏜=84.286+3=87.286≈87

The estimated level of activity is 84.286

The real value would be added to the equation with y

y=Resudal+y⏜=84.286+3=87.286≈87

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

Hence, the correct option is (a)

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