Bioequivalence and Bioavailability Forum

Dear Ohlbe and ElMaestro,

Thank you very much for the comments and inputs.

❝ In any case it is quite easy to show the interest during method validation: in each validation run you can calculate the calibration curve without weighting and with classical factors such as 1/X and 1/X², then check the back-calculated concentrations and residuals.

I have read the lengthy discussion on other threads on weighting factor in standard calibration curve. I have gone through the paper on Weighted least square linear regression (Almeida et al., 2002) and example plus calculation given by Helmut. I am confused due to my poor knowledge in stats. I copied the example (given by Helmut in year 2008) as below for my question.

Example:
model: y = 1.0000 + 2.0000 * x + error
 ┌────┬──────┬───────┬────────┬───────┬────────┬───────┬────────┐
 │ x  │  y   │  w=1  │  bias  │ w=1/x │  bias  │ w=1/x²│  bias  │
 ├────┼──────┼───────┼────────┼───────┼────────┼───────┼────────┤
 │  1 │  3.7 │  1.13 │ 13.0%  │  1.05 │  5.00% │  1.02 │  2.00% │
 │  2 │  5.6 │  2.07 │  3.50% │  2.01 │  0.50% │  1.99 │ -0.50% │
 │  4 │  9.4 │  3.95 │ -1.25% │  3.92 │ -2.00% │  3.93 │ -1.75% │
 │  8 │ 17   │  7.72 │ -3.50% │  7.74 │ -3.25% │  7.82 │ -2.25% │
 │ 16 │ 34   │ 16.1  │  0.63% │ 16.3  │  1.88% │ 16.5  │  3.13% │
 ├────┴──────┼───────┴────────┼───────┴────────┼───────┴────────┤
 │ intercept │ 1.4250 (+42.5%)│ 1.6109 (+61.1%)│ 1.7133 (+71.3%)│
 │     slope │ 2.0185 (+0.93%)│ 1.9876 (-0.62%)│ 1.9537 (-2.31%)│
 └───────────┴────────────────┴────────────────┴────────────────┘

I would like to know how the values of 1/x and 1/x² were calculated. The x is the input as given in the first column (1,2,4,8,16) ?? I could not get the data as presented in the table.

Kindly let me know the program in R-software that can be used to perform this calculation.

I am really sorry to bring up the old topic again. Also sorry to Helmut for using his example without permission.

Thank you.

Regards,
Ken

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Edit: Table BBcoded. Please use the before posting. [Helmut]