Question

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. A regression analysis was completed and the value for s was found to be 3.05.

Which of the following is the best interpretation of s?
The average residual is about 3.05 pretzels.
The average residual is about 3.05 centimeters.
The average handspan of a student is 3.05 centimeters.
The average number of pretzels a student could grab is 3.05 pretzels.

Answer 1

The value 's' indicates the typical deviation of the actual data points from the values predicted by the regression line, with 's = 3.05' in this context meaning the actual number of pretzels grabbed deviates from the predicted number by about 3.05 pretzels.

Step-by-step explanation:

The value 's' in regression analysis represents the standard deviation of the residuals, which quantifies the typical amount by which the actual data points deviate from the values predicted by the regression line. It does not reflect the average residual, as residuals can be both positive and negative, tending to cancel each other out when averaged. Instead, 's = 3.05' indicates on average, the actual number of pretzels grabbed deviates from the predicted number by about 3.05 pretzels.