Below is a regression analysis of the number of burglaries in 2006 (response variable) on the student enrollment (explanatory variable) for 17 randomly-selected four-year public universities in the United States. Assume that the conditions for regression inference have been satistied.
Predictor Coef SE Coef T P
Constant 4.43 10.41 0.43 0.677
Enrollment 0.0018751 0.0005724 3.28 0.005
S= 22.5012 R-Sq= 41.7% R-Sq (adj ) =37.8%
Which of the following is an appropriate interpretation of the number 22.5012?
(a) The standard deviation of the response variable "student enrollment" is 22.5012.
(b) The standard deviation of th explanatory variable "number of burglaries" is 22.5012. )
(c) The typical distance between observed values for student enrollment and values for enrollment predicted by the regression equation is about 22.5012.
(d) The typical distance between observed values for number of burglaries and values for number of burglaries predicted by the regression equation is about 22.5012.
(e) The sum of the squared deviations between the observed number of burglaries and the number of burglaries predicted by the regression equation is about 22.5012

d. The typical distance between observed values for number of burglaries and values for number of burglaries predicted by the regression equation is about 22.5012.

Step-by-step explanation:

In a regression output, the S which is the standard error of the regression, gives us the absolute measure of the average distance from which the observed data point falls from the line of regression. S is in the unit of the response variable or the dependent variable. The response variable is the number of burglaries in 2006. Based on this explanation, option d is the best and right answer for this question.