Question

interpret the least squares regression line of this data set. faced with budget cuts, a state commission is looking into closing some of its public libraries. to help minimize the negative impact of the closures, the commission gathered data on local school and library facilities. the number of schools, x, and the number of libraries, y, were recorded for each town. the least squares regression line for the data set is: y = 0.434x + 0.975. use it to complete the following sentence: if a town had one more school, the least squares regression line predicts that it would have more libraries.

Explanation:

Step1: Identify the slope of regression line

The equation of the least - squares regression line is $y = 0.434x+0.975$, where the slope is $m = 0.434$.

Step2: Interpret the slope

In a linear regression model $y=mx + b$, the slope $m$ represents the change in $y$ for a one - unit change in $x$. Here, $x$ is the number of schools and $y$ is the number of libraries. So, for a one - unit increase in the number of schools ($x$), the number of libraries ($y$) is predicted to increase by the value of the slope.

Answer:

0.434