Question

Consider the following set of ordered pairs. x 2 7 1 4 30 y 6 9 5 8 6 Assuming that the regression equation is y = 4.491 +0.679x and that the SSE = 1.0189, construct a 95% confidence interval for the slope. Click here to see the t-distribution table, page 1 Click here to see the t-distribution table, page 2 Construct a 95% confidence interval for the slope. LCL = and UCL = (Round to three decimal places as needed.)

Answer 1

	X	Y	X * Y	X2	Ŷ	Sxx =Σ (Xi - X̅ )	Syy = Σ( Yi - Y̅ )	Sxy = Σ (Xi - X̅ ) * (Yi - Y̅)
	2	6	12	4	5.8491	1.96	0.64	1.12
	7	9	63	49	9.2453	12.96	4.84	7.92
	1	5	5	1	5.1698	5.76	3.24	4.32
	4	8	32	16	7.2075	0.36	1.44	0.72
	3	6	18	9	6.5283	0.16	0.64	0.32
Total	17	34	130	79	34.0000	21.2	10.8	14.4

X̅ = Σ (Xi / n ) = 17/5 = 3.4
Y̅ = Σ (Yi / n ) = 34/5 = 6.8

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X² - (ΣX)² )
b = ( 5 * 130 - 17 * 34 ) / ( 5 * 79 - ( 17 )²)
b = 0.6792

a =( ΣY - ( b * ΣX ) ) / n
a =( 34 - ( 0.6792 * 17 ) ) / 5
a = 4.4906
Equation of regression line becomes Ŷ = 4.4906 + 0.6792 X

Confidence Interval

$P = (Syy - b* Sry)/n – 2


52 = (10.8 -0.6792 * 14.4)/5 – 2


S2 = 0.3398

S = 0.5829


b-ta/2(S/(x) <B<b+ta/2(S)/ (SI)

Critical value  
ta/2 = t 0.05/2 = 3.182
( From t table )

0.6792-t 0.05/2(0.5829/ (21.2)) <B<0.6792+t 0.052 (0.5829)/ (21.2))

95% confidence interval is 0.276 < $\beta$ < 1.082.