Question

 

Student enrollment at a university over the past six years is given below.

Year (t)	Enrollment (In 1,000s)
1	6.30
2	7.70
3	8.00
4	8.20
5	8.80
6	8.00

What is the linear trend expression for the above time series?

Select one:

a. T_t = 6.63 – 0.34t

b. T_t = 6.63t + 0.34

c. T_t = 6.63 + 0.34t

d. T_t = 0.77 + 0.59t

e. T_t = 2.06 + 1.44t

Based on the model you determined in the question above, what is the forecast enrollment for year 10?

Select one:

a. 10.06

b. 66.68

c. 10,062.00

d. 100,062.00

e. 100.6

Answer 1

Solution:

We can use excel to find the least-squares regression equation. The excel output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.767383067
R Square	0.588876772
Adjusted R Square	0.486095965
Standard Error	0.599205824
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.057142857	2.057142857	5.729442971	0.074872431
Residual	4	1.436190476	0.359047619
Total	5	3.493333333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	6.633333333	0.557830264	11.89131133	0.000286437	5.084548228	8.182118439
Year (t)	0.342857143	0.143237589	2.393625487	0.074872431	-0.054834159	0.740548445

What is the linear trend expression for the above time series?

Select one:

c. T_t = 6.63 + 0.34t

Based on the model you determined in the question above, what is the forecast enrollment for year 10?

Select one:

a. 10.06