1) The table below shows the calibration data for the concentration determinatio

Question

1) The table below shows the calibration data for the concentration determination of a newly developed instrument. Please carry out a linear regression manually based on least-squares analysis for this chart. (14 points) a) Determine the linear regression equation, and the corresponding confidence limits of the slope and intercept at the 95% confidence level. b) You want to determine the concentration of the analyte in your sample. You carry out one measurement, and the signal of the instrument is 133.39. What is the analyte concentration, and what is the confidence interval at the 95% confidence level? c) You find that the confidence interval in b) is too high and decide to take more measurements of your sample. The results of these measurements are: 133.21, 133.49, 134.5, 132.99, 133.55. What is the analyte concentration, and what is the confidence interval at the 95% confidence level? Are there outliers in this data set?

Explanation / Answer

Hello! The least-squares analysis is a mathematical analysis. So, I highly recommend you do this question in the math section. However, I'll give you the solution for the linear regression equation and the concentration of the analyte with 133.39. Here we go:

Linear regression:

(You can do this in Excel. I did it in my calculator)

c = 10.022 + 0.227 Si

R2 = 0.9692

For Si = 133.39, c = 40.50

For Si = 133.21, c = 40.46

For Si = 133.49, c = 40.52

For Si = 134.5, c = 40.75

For Si = 132.99, c = 40.41

For Si = 133.55, c = 40.54

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