Question

Year	Period (t)	Enrollment (1000s)
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. The data shows the enrollment for the college for the nine most recent years. Construct a time-series plot. What type of pattern exists in the data?

b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.  (using Period as the independent variable).
What is SSE; round to 4 decimal places.

c. Using the result from the simple linear regression analysis found in question 6 above, what is the forecasted enrollment for period 21; round to 2 decimal places.

Answer 1

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endiment 12 * DE 2001 2002 2003 2004 2005 2006 Year 2007 2008 2009 >> Linear trend patlean 13 observed O Simple linear regression model foo the teenot line, y = a+bx. the 2000) method of least squares the X= (20 8 estimates of ась аз 6² = & cxigi) - {xirgi n xi² - (2x)2 8.) using excell, 6 - Slope Canon y's, known ai's ) = 1.456667 ar intercept (keo y's, a's) = 4.11667 x - Nm.no 84 10.2 12.5 13-3 31 15. 172 14 y = 4.71667+ 1.456667 *2-

them. 8 y 6.5 - y = 4.71661+14566672 (4-g*) 2 6. 1733 0.1067 7.6300 0.2209 0.4715 9.0867 10-5433 - 0-2500 12 8.4 0.1179 m + 12.0 0.0245 1.4-122 r 13.3 13.7 17.2 18.1 13.4561 14.9133 16.3700 17.8 267 0.6889 0.0747 sums 3.4273 o 30 SSE = = CY-99 ? 3.4273 21 period means year 2021 so x=C2021 -2000) = 2/ = 4.71667 +1.456667 * (21) = 35.30667 = 35.31