Problem 2 In order to calibrate a protein analyzer a regress

Problem 2. In order to calibrate a protein analyzer, a regression equation is determined between three independent variables and the dependent variable which is the protein. Each variable is measured for 15 samples with the following results:

Sample

A

B

C

Protein

1

-55.8

68.8

-42.2

11.3

2

-54.1

60.8

-41.7

13.0

3

-51.0

54.8

-40.6

13.7

4

-48.9

53.8

-38.5

13.8

5

-51.4

56.7

-41.0

13.9

6

-48.9

54.2

-37.9

13.9

7

-53.9

56.9

-43.0

14.2

8

-53.5

56.1

-43.5

14.2

9

-50.7

54.7

-40.3

14.2

10

-52.9

53.9

-42.4

14.4

11

-54.5

54.7

-44.2

14.9

12

-49.7

50.0

-39.7

15.0

13

-48.4

45.5

-39.8

15.7

14

-52.4

50.5

-43.8

15.8

15

-48.4

40.1

-40.0

17.0

Find the regression equation using A, B and C as the independent variables and Protein as the dependent variable.

Sample	A	B	C	Protein
1	-55.8	68.8	-42.2	11.3
2	-54.1	60.8	-41.7	13.0
3	-51.0	54.8	-40.6	13.7
4	-48.9	53.8	-38.5	13.8
5	-51.4	56.7	-41.0	13.9
6	-48.9	54.2	-37.9	13.9
7	-53.9	56.9	-43.0	14.2
8	-53.5	56.1	-43.5	14.2
9	-50.7	54.7	-40.3	14.2
10	-52.9	53.9	-42.4	14.4
11	-54.5	54.7	-44.2	14.9
12	-49.7	50.0	-39.7	15.0
13	-48.4	45.5	-39.8	15.7
14	-52.4	50.5	-43.8	15.8
15	-48.4	40.1	-40.0	17.0

Solution

Multiple regression is solved using a software like excel.

Paste the above data in excel, and Go to DATA , select DATA ANALYSIS, select REGRESSION, select the Y range (Protein) and X range (A, B and C columns). Click OK.

Regression equation is given by the estimates of coefficients of A, B and C, and intercept term.

Result of regression:

We use the Coefficients column.

Equation:

Proteins = 18.02108 + 0.04219*A - 0.2029*B - 0.22957*C

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990961
R Square	0.982003
Adjusted R Square	0.977095
Standard Error	0.198127
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	3	23.56154	7.853845	200.076	7.09E-10
Residual	11	0.431797	0.039254
Total	14	23.99333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	18.02108	1.339609	13.4525	3.57E-08	15.07262	20.96954	15.07262	20.96954
A	0.04219	0.122827	0.343488	0.737707	-0.22815	0.31253	-0.22815	0.31253
B	-0.2029	0.02708	-7.49243	1.21E-05	-0.2625	-0.14329	-0.2625	-0.14329
C	-0.22957	0.106978	-2.14594	0.055035	-0.46503	0.005889	-0.46503	0.005889