Question

a) Calculate the slope and y-intercept for these data. b) Calculate the total sum of squares (SST). c) Partition the sum of squares into the SSR and SSE. a) Calculate the slope and y-intercept for these data. y = + x (Round to four decimal places as needed.)

Answer 1

	X	Y	X * Y	X2	Ŷ	SSE =Σ(Y - Ŷ)2	SST = Σ(Yi - Y̅ )2	SSR = Σ( Ŷ - Y̅ )2	Residual = ( Y - Ŷ )
	3	5	15	9	4	1	6.76	2.56	1
	2	0	0	4	2	4	5.76	0.16	-2
	3	4	12	9	4	0	2.56	2.56	0
	1	1	1	1	0	1	1.96	5.76	1
	2	2	4	4	2	0	0.16	0.16	0
Total	11	12	32	27	12	6	17.2	11.2	0

X̅ = Σ (Xi / n ) = 11/5 = 2.2
Y̅ = Σ (Yi / n ) = 12/5 = 2.4

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X² - (ΣX)² )
b = ( 5 * 32 - 11 * 12 ) / ( 5 * 27 - ( 11 )²)
b = 2.0000

a =( ΣY - ( b * ΣX ) ) / n
a =( 12 - ( 2 * 11 ) ) / 5
a = -2.0000
Equation of regression line becomes Ŷ = - 2 + 2 X

Part b)

SST = Σ(Yi - Y̅ )² = 17.2

Part c)

SSR = Σ( Ŷ - Y̅ )² = 11.2

SSE =Σ(Y - Ŷ)² = 6