Question

Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply. Select all that apply:

a. yˆ=38,000+2500x
b. yˆ=38,000−3500x
c. yˆ=−38,000+2500x
d. yˆ=38,000−1500x

Answer 1

Answer:

a. yˆ=38,000+2500x

d. yˆ=38,000−1500x

Step-by-step explanation:

The least squares regression line for the population change of a small country has the following format:

$y^{^} = a + bx$

In which a is the initial population and b is the number of habitants for which the population increases/decreases a year.

Let's see each case

a. yˆ=38,000+2500x

The population starts at 38000 and increases by 2500 a year. This is a feasible assumption.

b. yˆ=38,000−3500x

The population starts at 38000 and increases by 3500 a year. By the year 2015, the population will be negative. This is not a feasible assumption.

c. yˆ=−38,000+2500x

The population cannot start at a negative value. So this is not a feasible assumption.

d. yˆ=38,000−1500x

The population starts at 38000 and decreases by 1500 a year. This is a feasible assumption.