Question

TRUE OR FALSE : The residual is the difference between the actual value of a dependent variable and the value predicted by the estimated regression line.

Answer 1

Answer is TRUE

let us consider the following data

x	y
61	77
43	47
39	46
66	81
66	76
64	75
44	49
77	95
58	72
77	91

The estimated regression of y ( dependent variable) on x (independent variable) is

Solving for a and b we get

a= - 6.15

b= 1.29

(Note : this example is just for explanation , so calculation is not shown )

Thus we get , estimate of regression equation is

- 6.15 +1.29 x

From this equation , for each x we will get a predicted value of y , and residual is given by

x	y
61	77	72.54	4.46
43	47	49.32	-2.32
39	46	44.16	1.84
66	81	78.99	2.01
66	76	78.99	-2.99
64	75	76.41	-1.41
44	49	50.61	-1.61
77	95	93.18	1.82
58	72	68.67	3.33
77	91	93.18	-2.18

Thus residual is the difference between the actual value of dependent variable and value predicted by regression line .