Question

Scientists examined the activity level of fish at 7 different temperatures. Fish activity was rated

on a scale of 0 to 10 (0 means no activity). The temperature was measured in degrees Celsius. The LSRL is yhat 148.617-3.217x where yhat is the predicted fish activity and x is the temperature in degrees Celsius. The standard deviation of the residuals is found to be s = 4.785 units.

Which of the following gives a correct interpretation of s in this setting?

A. For every 1 degC increase in temperature, fish activity is predicted to increase by 4.785 units.
B. The average distance of the activity level ratings from the least-squares line is about 4.785 units.
C. The average distance of the temperature readings from their mean is about 4.785 degC.
D. The average distance of the activity level readings from their mean is about 4.785 units.
E. At a temperature of 0 degC, this model predicts an activity level of 4.785 units

Answer 1

The standard deviation of the residuals, s, indicates that the average distance of the activity level ratings from the least-squares regression line is about 4.785 units, reflecting how well the regression line fits the observed data.

Step-by-step explanation:

The correct interpretation of the standard deviation of the residuals, s, in this setting is B. The average distance of the activity level ratings from the least-squares line is about 4.785 units. This means that, on average, the observed fish activity levels deviate from those predicted by the least-squares regression line by 4.785 units. It provides a measure of how well the regression line fits the data. If s is smaller, the fit is better; if larger, the fit is not as good. Options A, C, D, and E all describe different concepts that are not related to s, the standard deviation of the residuals.