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. DATA file Enrollment (1,000s) Period (t) Year 2001 6.5 2002 2003 8.4 10.2 12.5 13.3 2004 2005 2006 2007 2008 2009 13.7 17.2 18.1

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1	6.5	16.00	30.25	22.00
2	8.1	9.00	15.21	11.70
3	8.4	4.00	12.96	7.20
4	10.2	1.00	3.24	1.80
5	12.5	0.00	0.25	0.00
6	13.3	1.00	1.69	1.30
7	13.7	4.00	2.89	3.40
8	17.2	9.00	27.04	15.60
9	18.1	16.00	37.21	24.40

	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   =   1.45667
                  
intercept,   ß0 = y̅-ß1* x̄ =   4.71667          

intercept = 4.72

slope = 1.46

MSE=(SSE/(n-2)) = 0.49

c)

Predicted Y at X=   10   is                  
Ŷ =   4.72 +   1.46 *   10   =   19.28