Question

25 multiple choice 2 points
the table below shows the number of people who were living in a village from 2005
to 2010.

what is the meaning of the slope of the line of best fit for these data?
the maximum number of people that could live in the villagethe original number of people that were living in the villagethe annual increase in the number of people that were living in the village

Explanation:

In a linear regression model (line of best fit) for time - series data (where \(x\) represents time, here years), the slope \(m\) of the line \(y = mx + b\) has a specific interpretation.

The general formula for the slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). When \(x\) represents time (in years) and \(y\) represents the number of people, \(x_2−x_1 = 1\) (since we are looking at annual changes). So \(m=y_2 - y_1\), which is the change in the number of people per year.

The maximum number of people in the village would not be related to the slope (it would be an upper - bound value, perhaps a limit in a non - linear model). The original number of people is the \(y\) - intercept (\(b\) in the equation \(y=mx + b\), when \(x = 0\) if \(x\) is re - scaled).

Answer:

the annual increase in the number of people that were living in the village