Chapter 3: Q T3.6. (page 201)

Scientists examined the activity level of fish at $7$ different temperatures. The 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 given below. Notice that the horizontal axis
on the residual plot is labeled “predicted (F/T).
Which of the following gives a correct interpretation of s in this setting?
(a) For every 1°C increase in temperature, fish activity is predicted to increase by $4.785$ units.
(b) The average distance of the temperature readings from their mean is about $4.785 ° C$
(c) The average distance of the activity level ratings from the least-squares line is about $4.785$ units.
(d) The average distance of the activity level readings from their mean is about $4.785$
(e) At a temperature of $0 ° C$ , this model predicts an activity level of $4.785$

Short Answer

Expert verified

The correct option is (c).

Step by step solution

Given information

Concept

A regression line is a straight line that depicts the relationship between an explanatory variable $x$ and a response variable $y$ By entering any value of $x$ into the equation of the line, you may use a regression line to anticipate the value of $y$ for any value of $x$

Explanation

The standard deviation of the residuals s measures the average size of the prediction mistakes when using the regression line (residuals). We can see that s is $4.785$ from the output above. The average distance between the activity level data and the least-squares line is approximately $4.785$ units, as shown. As a result, option (c) is the proper choice.