Question

U.S. Civilian Labor Force (thousands)
Year	Labor Force		Year	Labor Force
2007	178,978		2012	180,688
2008	179,715		2013	180,211
2009	178,171		2014	181,298
2010	178,710		2015	183,017
2011	179,055		2016	184,700

Click here for the Excel Data File

(a) Make a line graph of the U.S. civilian labor force data.

Line Graph A	Line Graph B	Line Graph C	Line Graph D

• Line Graph 1

• Line Graph 2

• Line Graph 3

• Line Graph 4

(b) Describe the trend (if any) and discuss possible causes.

Trend is  (Click to select)  positive  negative  . There seems to be an  (Click to select)  increase  decrease  in the rate of growth over the past few years.

(c) Fit three trend models: linear, exponential, and quadratic. Which model would offer the most believable forecasts? (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)

• Linearchecked
• Quadraticunanswered
• Exponentialunanswered

(d) Make forecasts using the following fitted trend models for years 2017-2019. (Round your answers to the nearest whole number.)

t	Linear	Quadratic	Exponential
11
12
13

Answer 1

a) Line chart

b) The trend is positive. There seems to be an increase in the rate of growth over the past few years.

c)

Linear model

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.857
R Square	0.734
Adjusted R Square	0.701
Standard Error	1129.635
Observations	10
ANOVA
	df	SS	MS	F
Regression	1	28150554	28150554	22.06028
Residual	8	10208594	1276074
Total	9	38359148
	Coefficients	Standard Error	t Stat	P-value
Intercept	177241.53	771.69	229.68	0.00
time	584.14	124.37	4.70	0.00

Labor Force =  177241.53+  584.14*time period

Quadratic model

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.970
R Square	0.940
Adjusted R Square	0.923
Standard Error	572.111
Observations	10
ANOVA
	df	SS	MS	F
Regression	2	36067975	18033987	55.09749
Residual	7	2291173	327310.5
Total	9	38359148
	Coefficients	Standard Error	t Stat	P-value
Intercept	179935.5	672.9	267.4	0.00
time	-762.9	281.0	-2.7	0.03
time^2	122.5	24.9	4.9	0.00

Labor Force =  179935.5- 762.9*time period + 122.5*time^2

Exponential model

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.857
R Square	0.735
Adjusted R Square	0.702
Standard Error	0.006
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.000857	0.000857	22.17838	0.001523
Residual	8	0.000309	3.86E-05
Total	9	0.001166
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	12.085	0.004	2845.773	0.000	12.076
time	0.003	0.001	4.709	0.002	0.002

Ln(labor Force) = 12.085 + 0.003*time

Laboe force = e0.03*time + 12.089 = 177273*e0.03*time

Out of these models we use quadratic model because R2 is higher for this model compared to the others.

d)

t	Linear	Quadratic	Exponential
11	183667.1	186366.1	246581.1
12	184251.2	188420.7	254090.6
13	184835.4	190720.3	261828.8