Question

Find the regression equation using the following set of data with y as the response variable.

x	y
40.2	82.2
54.2	111.8
43	84.3
30.7	68.5
33	90.8
42.8	78.5
30.9	71.7
28.6	69.8
36.6	83.1
41.1	93.9
26.6	63.9
45.5	95.5

What is the correlation coefficient? use three decimal places.
r =  

What is the regression line equation. Use each value to three decimal places.

ˆyy^ =  +  x

What is the predicted value of the response variable, when using a value of 32.1 as the explanatory variable. ? Write answer accurate to one decimal place.
ˆyy^ =  

Answer 1

	X	Y	X * Y	X2	Y2
	40.2	82.2	3304.44	1616.04	6756.84
	54.2	111.8	6059.56	2937.64	12499.24
	43	84.3	3624.9	1849	7106.49
	30.7	68.5	2102.95	942.49	4692.25
	33	90.8	2996.4	1089	8244.64
	42.8	78.5	3359.8	1831.84	6162.25
	30.9	71.7	2215.53	954.81	5140.89
	28.6	69.8	1996.28	817.96	4872.04
	36.6	83.1	3041.46	1339.56	6905.61
	41.1	93.9	3859.29	1689.21	8817.21
	26.6	63.9	1699.74	707.56	4083.21
	45.5	95.5	4345.25	2070.25	9120.25
Total	453.2	994	38605.6	17845.36	84400.92

Part a)

r = 0.868

Equation of regression line is Ŷ = a + bX


b = 1.461
a =( Σ Y - ( b * Σ X) ) / n
a =( 994 - ( 1.4606 * 453.2 ) ) / 12
a = 27.671
Equation of regression line becomes Ŷ = 27.671 + 1.461 X

When X = 32.1
Ŷ = 27.671 + 1.461 X
Ŷ = 27.671 + ( 1.461 * 32.1 )
Ŷ = 74.6