Population data for 1990 – 2016 are shown for the states of TN and VA. a. Develo
ID: 3260166 • Letter: P
Question
Population data for 1990 – 2016 are shown for the states of TN and VA. a. Develop a linear 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
Answer:
Population data for 1990 – 2016 are shown for the states of TN and VA. a. Develop a linear 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.
Result for TN
Regression Analysis
r²
0.992
n
27
r
0.996
k
1
Std. Error
47880.914
Dep. Var.
TN
ANOVA table
Source
SS
df
MS
F
p-value
Regression
7,477,730,701,814.4200
1
7,477,730,701,814.4200
3261.71
5.19E-28
Residual
57,314,547,332.7621
25
2,292,581,893.3105
Total
7,535,045,249,147.1800
26
Regression output
confidence interval
variables
coefficients
std. error
t (df=25)
p-value
95% lower
95% upper
Intercept
4,907,549.7977
18,953.5347
258.925
2.20E-44
4,868,514.2622
4,946,585.3332
Year
67,565.9615
1,183.0565
57.111
5.19E-28
65,129.4111
70,002.5120
Predicted values for: TN
95% Confidence Interval
95% Prediction Interval
Year
Predicted
lower
upper
lower
upper
Leverage
31
7,002,094.605
6,956,532.632
7,047,656.578
6,893,465.255
7,110,723.956
0.213
The regression line is
Y = 4,907,549.7977+67,565.9615*year
population growing each year in TN = 67,565.9615
for the year 2020, the year value is 31.
predicted population for TN in 2020 =7,002,094.605
Result for VA
Regression Analysis
r²
0.998
n
27
r
0.999
k
1
Std. Error
31753.739
Dep. Var.
VA
ANOVA table
Source
SS
df
MS
F
p-value
Regression
12,575,183,322,094.2000
1
12,575,183,322,094.2000
12471.67
2.91E-35
Residual
25,207,498,767.0161
25
1,008,299,950.6806
Total
12,600,390,820,861.2000
26
Regression output
confidence interval
variables
coefficients
std. error
t (df=25)
p-value
95% lower
95% upper
Intercept
6,146,262.3134
12,569.6348
488.977
2.75E-51
6,120,374.6659
6,172,149.9608
Year
87,619.3877
784.5812
111.677
2.91E-35
86,003.5123
89,235.2630
The regression line is
Y = 6,146,262.3134 +87,619.3877 *year
population growing each year in VA = 87,619.3877
Regression Analysis
r²
0.992
n
27
r
0.996
k
1
Std. Error
47880.914
Dep. Var.
TN
ANOVA table
Source
SS
df
MS
F
p-value
Regression
7,477,730,701,814.4200
1
7,477,730,701,814.4200
3261.71
5.19E-28
Residual
57,314,547,332.7621
25
2,292,581,893.3105
Total
7,535,045,249,147.1800
26
Regression output
confidence interval
variables
coefficients
std. error
t (df=25)
p-value
95% lower
95% upper
Intercept
4,907,549.7977
18,953.5347
258.925
2.20E-44
4,868,514.2622
4,946,585.3332
Year
67,565.9615
1,183.0565
57.111
5.19E-28
65,129.4111
70,002.5120
Predicted values for: TN
95% Confidence Interval
95% Prediction Interval
Year
Predicted
lower
upper
lower
upper
Leverage
31
7,002,094.605
6,956,532.632
7,047,656.578
6,893,465.255
7,110,723.956
0.213