Question

2. Given the following data determine

a. the correlation coefficient

b. The straight-line equation using the least square method

c. Find the standard error.

X= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Y=2.5, 4.8, 6.5, 7.9, 9.7, 11.1, 12.7, 14.7, 16, 17.4.

Answer 1

	X	Y	X * Y	X2	Ŷ	(Y - Ŷ)2
	1	2.5	2.5	1	2.9855	0.2357
	2	4.8	9.6	4	4.6176	0.0333
	3	6.5	19.5	9	6.2497	0.0627
	4	7.9	31.6	16	7.8818	0.0003
	5	9.7	48.5	25	9.5139	0.0346
	6	11.1	66.6	36	11.1461	0.0021
	7	12.7	88.9	49	12.7782	0.0061
	8	14.7	117.6	64	14.4103	0.0839
	9	16	144	81	16.0424	0.0018
	10	17.4	174	100	17.6745	0.0754
Total	55	103.3	702.8	385	187332.0118	0.5359

Part a)

r = 0.999

Part b)

Equation of regression line is Ŷ = a + bX


b = 1.632
a =( Σ Y - ( b * Σ X) ) / n
a =( 103.3 - ( 1.6321 * 55 ) ) / 10
a = 1.353
Equation of regression line becomes Ŷ = 1.3533 + 1.6321 X

Part c)

Standard Error of Estimate S = √ ( Σ (Y - Ŷ )² / n - 2) = √(0.5359 / 8) = 0.2588