MR_analysis
Multiple Regression Analysis
16
3. Multiple Regression Analysis
The concepts and principles developed in dealing with simple linear regression (i.e. one explanatory variable) may be extended to deal with several explanatory variables.
We begin with an example of two explanatory variables, both of which are continuous. The regression equation in such a case becomes:
Y = α + β1x1 + β2 x2
It is customary to replace α with β 0, and so all future regression equations would be written as
Y = β0 + β1x1 + β2x2 ……βnxn
Regression with two explanatory variables
During certain surgical operations the surgeon may wish to lower the blood pressure of the patient by administering a drug. After the surgery is over the return to normal of the blood pressure depends on the dose of the drug administered, and the average systolic blood pressure reached during surgery.
A surgeon wishes to study the relationship between the dose of a new drug, the average systolic blood pressure during the operation and time for the blood pressure to come back to normal after administration of the drug has ceased.
The results obtained are in the following table:
(Data from Anaesthesia 1959;14:53-64).
LogDose
B.P.Surg
Case
Recov time 1
5.2
66
7
2
4.17
52
10
18
3
4.1
72
4
3.55
67
4
5
4.74
69
10
6
4.01
71
13
7
5.89
88
21
8
5.27
68
12
9
4.14
59
9
10
5.34
73
65
11
4.7
68
20
12
4.33
58
31
13
2.72
61
23
14
4.79
68
22
15
3.91
69
13
16
4.01
55
9
17
4.37
67
12
18
4.12
67
12
Research Methods – II
Case
LogDose
B.P.Surg
Recov time 19
4.86
68
20
3.96
59
11
8
21
4.01
68
26
22
3.68
63
16
23
4.95
65
23
24
5.2
72
7
25
3.8
58
11
26
3.75
69
8
27
5.53
70
16
3. Multiple Regression Analysis
The concepts and principles developed in dealing with simple linear regression (i.e. one explanatory variable) may be extended to deal with several explanatory variables.
We begin with an example of two explanatory variables, both of which are continuous. The regression equation in such a case becomes:
Y = α + β1x1 + β2 x2
It is customary to replace α with β 0, and so all future regression equations would be written as
Y = β0 + β1x1 + β2x2 ……βnxn
Regression with two explanatory variables
During certain surgical operations the surgeon may wish to lower the blood pressure of the patient by administering a drug. After the surgery is over the return to normal of the blood pressure depends on the dose of the drug administered, and the average systolic blood pressure reached during surgery.
A surgeon wishes to study the relationship between the dose of a new drug, the average systolic blood pressure during the operation and time for the blood pressure to come back to normal after administration of the drug has ceased.
The results obtained are in the following table:
(Data from Anaesthesia 1959;14:53-64).
LogDose
B.P.Surg
Case
Recov time 1
5.2
66
7
2
4.17
52
10
18
3
4.1
72
4
3.55
67
4
5
4.74
69
10
6
4.01
71
13
7
5.89
88
21
8
5.27
68
12
9
4.14
59
9
10
5.34
73
65
11
4.7
68
20
12
4.33
58
31
13
2.72
61
23
14
4.79
68
22
15
3.91
69
13
16
4.01
55
9
17
4.37
67
12
18
4.12
67
12
Research Methods – II
Case
LogDose
B.P.Surg
Recov time 19
4.86
68
20
3.96
59
11
8
21
4.01
68
26
22
3.68
63
16
23
4.95
65
23
24
5.2
72
7
25
3.8
58
11
26
3.75
69
8
27
5.53
70