The following data were collected from a protein assay. Concentration (mg Optica

Question

The following data were collected from a protein assay. Concentration (mg Optical densit 0 12 16 Unknown1 Unknown 2 0 0.037 0.087 0.116 0.172 0.097 0.123 Identify the dependent and the independent variables. Perform linear regression on the data provided. (hint: only use the data with known concentrations) Does a linear relationship exist between the dependent and independent variables? (10/100) o use R 2 range of R 2 (0 to 1) o if R2-zero, means there is there is no relationship . What would be the concentration of the two unknown samples?

Explanation / Answer

a]

Here Optical density is Independent Variable and Concentration is dependent variable

b]

Multiple regression using minitab:

Step 1) First enter the given data set in minitab columns.

Step 2) Click on Stat>>>Regression>>>General regression...

Response: select Concentration

Model: select Optical Density

Then click on OK

then click on Option.

Confidence level for all interval: put 95

Types of confidence interval: Two-sided.

then click on OK and again Click on OK

So we get the following minitab output

MTB > GReg 'Concentration' = 'Optical Density';
SUBC>   Constant;
SUBC>   Confidence 95.0;
SUBC>   Tolerance 1.0E-12;
SUBC>   Coding -1;
SUBC>   TEquation;
SUBC>   TCoef;
SUBC>   TSummary.

General Regression Analysis: Concentration versus Optical Density

Regression Equation

Concentration = 0.266945 + 93.8478 Optical Density

Coefficients

Term             Coef     SE Coef        T      P
Constant            0.2669 0.48216   0.5536 0.618
Optical Density 93.8478 4.72902 19.8451 0.000

Summary of Model

S = 0.634979     R-Sq = 99.24%        R-Sq(adj) = 98.99%
PRESS = 3.48057 R-Sq(pred) = 97.82%

C]

here R-Sq = 99.24% hence there is linear relationship between dependent and independent variables

D]

here predicts concentration for optical density = 0.097 and 0.123

Concentration = 0.266945 + 93.8478 Optical Density

                        = 0.266945 + 93.8478 * 0.097 = 9.37

And for 0.123

Concentration = 0.266945 + 93.8478 Optical Density

                        = 0.266945 + 93.8478 * 0.123 = 11.81

Done...

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