Question

Consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the population x and the year y over the ten-year span in the form (x, y) for specific recorded years. Use linear regression to determine a function y, where the year depends on the population. Round to three decimal places of accuracy. (2500, 2001), (2650, 2002), (3000, 2004), (3500, 2007), (4200, 2011) Predict when the population will hit 15,000.

Answer 1

`y = 0.00587x +1986.406`

Explanation:

Given that the population of a city increased steadily over a ten-year span. The following ordered pairs show the population x and the year y over the ten-year span in the form (x, y) for specific recorded years.

x y

2500 2001

2650 2002

3000 2004

3500 2007

4200 2011

Slope 0.005865485

Intercept 1986.406413

So regression line is

`y = 0.00587x +1986.406`

When population = 15000

`0.00587(17000)+1986.406\\=2074.389`