Question

Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College for the nine most recent years.

Click on the datafile logo to reference the data.

Year	Period (t)	Enrollment (1,000s)
2001	1	6.5
2002	2	8.1
2003	3	8.4
2004	4	10.2
2005	5	12.5
2006	6	13.3
2007	7	13.7
2008	8	17.2
2009	9	18.1

(a)	Choose the correct time series plot.
	(i) (ii) (iii) (iv)
	- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1
	What type of pattern "significantly" exists in the data? (Use 1% level of significance when needed)
	- Select your answer -Only randomnessRandomness & Linear trendRandomness & SeasonalityRandomness, Linear trend & SeasonalityItem 2
(b)	Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
	If required, round your answers to two decimal places.
	y-intercept, b0 =
	Slope, b1 =
	MSE =
(c)	What is the forecast for year 10?
	Do not round your interim computations and round your final answer to two decimal places.
(d)	Use the Holt's method with smoothing constants of 0.3 for alpha and 0.6 for gamma. Find the equation of the forecast line and the MSE for this method.
	If required, round your answers to two decimal places.
	y-intercept, b0 =
	Slope, b1 =
	MSE =
(e)	What is the forecast for year 10?
	Do not round your interim computations and round your final answer to two decimal places.
(f)	Which of the following methods perform better with respect to MSE? - Select your answer -RegressionHolt's with alpha=0.3, gamma=0.6Holt's with alpha=0.2, gamma=0.2

Answer 1

a)

Linear Trend

b)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	45	108	60	130.7	87.40
mean	5.00	12.00	SSxx	SSyy	SSxy

sample size ,   n =   9          
here, x̅ = Σx / n=   5.00   ,     ȳ = Σy/n =   12.00  
                  
SSxx =    Σ(x-x̅)² =    60.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   87.4          
                  
estimated slope , ß1 = SSxy/SSxx =   87.4   /   60.000   =   1.4567
                  
intercept,   ß0 = y̅-ß1* x̄ =   4.7167          
                  
so, regression line is   Ŷ =   4.7167   +   1.4567   *x

period	demand	forcast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	6.5	6.173333	0.33	0.33	0.11
2	8.1	7.630	0.47	0.47	0.22
3	8.4	9.087	-0.69	0.69	0.47
4	10.2	10.543	-0.34	0.34	0.12
5	12.5	12.000	0.50	0.50	0.25
6	13.3	13.457	-0.16	0.16	0.02
7	13.7	14.913	-1.21	1.21	1.47
8	17.2	16.370	0.83	0.83	0.69
9	18.1	17.827	0.27	0.27	0.07

MSE=   Σ(et)²/n =    0.38

c)

Predicted Y at X=   10   is                  
Ŷ =   4.71667   +   1.456667   *   10   =   19.28

THANKS

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