Question

read the following description of a data set. a states department of education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. as a first step, the department put together a report on a sample of towns in the state. for each town in the sample, the report recorded its population (in thousands), x, and its number of schools, y. the least squares regression line of this data set is: y = 0.373x - 22.068. complete the following sentence: if a town had one thousand more people, the least squares regression line predicts that it would have more schools.

Explanation:

Step1: Identify the regression - line equation

The regression line is $y = 0.373x-22.068$, where $x$ is the population (in thousands) and $y$ is the number of schools.

Step2: Calculate the change in $y$ for a change in $x$

We want to find the change in $y$ when $x$ increases by 1 (since an increase of one - thousand people means $\Delta x = 1$).
The slope of the regression line is $m = 0.373$. In a linear equation $y=mx + b$, the slope $m$ represents the change in $y$ for a unit change in $x$. So when $x$ increases by 1 (one - thousand people), the change in $y$ is given by the slope.

Answer:

0.373 more schools.