Question

Consider this scenario: The population of a city increased steadily over a six-year span. The following ordered pairs show the population and the year over the six-year span (population, year) for specific recorded years.

(3,700, 2000),    (3,900, 2001),    (4,800, 2003),    (5,950, 2006)

Use linear regression to determine a function y, where the year y depends on the population x, to five decimal places of accuracy. Use your function to predict when the population will hit 12,000. (Round your answer down to the nearest year.)

The population will hit 12,000 in the year ???? .

Answer 1

The following data are passed:

Population	Year
3700	2000
3900	2001
4800	2003
5950	2006

The independent variable is Population, and the dependent variable is Year. In order to compute the regression coefficients, the following table needs to be used:

	Population	Year	Population*Year	Population2	Year2
	3700	2000	7400000	13690000	4000000
	3900	2001	7803900	15210000	4004001
	4800	2003	9614400	23040000	4012009
	5950	2006	11935700	35402500	4024036
Sum =	18350	8010	36754000	87342500	16040046

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Year = 1990.7116 + 0.0026 * Population

When Population =12000 then

Year = 1990.7116 + 0.0026 * 12000= 2021.9116

The population will hit 12000 in year 2022

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