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The population of a country is expected to drop by 30% over the next 50 years as the percent of its citizens that are elderly increases. Projections for the country's population through 2050 are shown in the table.Year, t200520102020203020402050Population, P (in millions)127.8127.3124.1117.6109.5100.6(b) Use the regression feature of a graphing utility to find a linear model for the data. (Round your numerical values to two decimal places.) P = (c) Identify the slope of the model from part (b). (Round your answer to two decimal places.)(d) Use the linear model to predict the population in 2015, 2035, and 2060. (Round your answers to one decimal place.)Are these predictions reasonable?

Question

The population of a country is expected to drop by 30% over the next 50 years as the percent of its citizens that are elderly increases. Projections for the country's population through 2050 are shown in the table.

Year, t 2005 2010 2020 2030 2040 2050
Population, P (in millions) 127.8 127.3 124.1 117.6 109.5 100.6

(b) Use the regression feature of a graphing utility to find a linear model for the data. (Round your numerical values to two decimal places.)
P =
 


(c) Identify the slope of the model from part (b). (Round your answer to two decimal places.)



(d) Use the linear model to predict the population in 2015, 2035, and 2060. (Round your answers to one decimal place.)

Are these predictions reasonable?
 

 

check_circleAnswer
Step 1

Output:

In Excel, enter the data in cells A1 to A7 (t) and B1 to B7 (P); the first row is for labels.

Go to Data > Data Analysis > Regression.

Enter Input Y Range as $B$1:$B$7 and Input X Range as $A$1:$A$7.

Click on the box for Labels.

Click OK.

The regression output will be obtained.

To get the fi...

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.977452148
R Square
0.955412701
Adjusted R Square
0.944265876
2.574705729
Standard Error
Observations
6
ANOVA
Significance F
df
SS
MS
F
Regression
1
568.191895
568.191895 85.71164609
0.000756877
Residual
4
26.51643836
6.629109589
Total
5
594.7083333
Lower 95.0%Upper 95.0%
Coefficients
1356.072603
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
133.753117
10.1386243
0.00053282 984.7144156
1727.43079 984.7144156
1727.43079
Intercept
0.066021713-9.258058441 0.000756877 -0.794538538 -0.427927215 -0.794538538 -0.4279272 15
0.611232877
t
Scatterplot with fitted line
140
120
100
80
60
40
20
C
2000
2010
2020
2030
2040
2050
2060
t
help_outline

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SUMMARY OUTPUT Regression Statistics Multiple R 0.977452148 R Square 0.955412701 Adjusted R Square 0.944265876 2.574705729 Standard Error Observations 6 ANOVA Significance F df SS MS F Regression 1 568.191895 568.191895 85.71164609 0.000756877 Residual 4 26.51643836 6.629109589 Total 5 594.7083333 Lower 95.0%Upper 95.0% Coefficients 1356.072603 Standard Error t Stat P-value Lower 95% Upper 95% 133.753117 10.1386243 0.00053282 984.7144156 1727.43079 984.7144156 1727.43079 Intercept 0.066021713-9.258058441 0.000756877 -0.794538538 -0.427927215 -0.794538538 -0.4279272 15 0.611232877 t Scatterplot with fitted line 140 120 100 80 60 40 20 C 2000 2010 2020 2030 2040 2050 2060 t

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