Problem 2. In order to calibrate a protein analyzer, a regression equation is de
ID: 3392906 • Letter: P
Question
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
Explanation / Answer
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 0.005889Related Questions
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