Population data for 1990 – 2016 are shown for the states of TN and VA. a . Devel

Question

Population data for 1990 – 2016 are shown for the states of TN and VA.

a. Develop linear a trend equation for population in each state.

b. By how much is population growing each year in TN? In VA?

c. Predict TN population for 2020.

Year TN VA 1 4894492 6216884 2 4966587 6301217 3 5049742 6414307 4 5137584 6509630 5 5231438 6593139 6 5326936 6670693 7 5416643 6750884 8 5499233 6829183 9 5570045 6900918 10 5638706 7000174 11 5703719 7105817 12 5750789 7198362 13 5795918 7286873 14 5847812 7366977 15 5910809 7475575 16 5991057 7577105 17 6088766 7673725 18 6175727 7751000 19 6247411 7833496 20 6306019 7925937 21 6356671 8025773 22 6397634 8110035 23 6454306 8192048 24 6494821 8262692 25 6544663 8317372 26 6595056 8367587 27 6651194 8411808

Explanation / Answer

Using minitab:

1 Enter the given data in minitab columns

2 Choose Stat > Time Series > Trend Analysis.

3    In Variable, enter TN

4    Under Model Type, choose Linear.

5    Check Generate forecasts and enter 4 in Number of forecasts.

Then click on OK so we get the following output

Trend Analysis for TN

Data TN
Length 27
NMissing 0

Fitted Trend Equation

Yt = 4907550 + 67566*t

Accuracy Measures

MAPE 1
MAD 39314
MSD 2122761012

Forecasts

Period Forecast
28 6799397
29 6866963
30 6934529
31 7002095

Similarly do for the state VA

The minitab output for VA is

Trend Analysis for VA

Data VA
Length 27
NMissing 0

Fitted Trend Equation

Yt = 6146262 + 87619*t

Accuracy Measures

MAPE 0
MAD 22820
MSD 933611065

Forecasts

Period Forecast
28 8599605
29 8687225
30 8774844
31 8862463

a) So for the state TN

Fitted Trend Equation is

Yt = 4907550 + 67566*t

Fitted Trend Equation for VA is

Yt = 6146262 + 87619*t

b) The population growing each year in TN is same as slope of t (coefficient of time ) that is 67566.

The population growing each year in VA is same as slope of t (coefficient of time ) that is 87619

c) We have given that the data from1990 to 2016 so if we put 4 years in 2016 then we get predicted populations.

here we replace 1990 by 1 and 2016 by 27 so we need to put 27+4 = 31 in the trend equations of TN and VA.

So we get predicted value for TN in 2020 as

Yt = 4907550 + 67566*t = Yt = 4907550 + 67566*31 =  7002095

and predicted value for VA in 2020 as

Yt = 6146262 + 87619*t = Yt = 6146262 + 87619*t = 8862463

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