Using the least squares method of linear regression, the following equation was
ID: 528957 • Letter: U
Question
Using the least squares method of linear regression, the following equation was determined to define the line generated by plotting concentration vs. absorbance:
y = 0.0196x - 0.008.
The concentration of chromium in the sample was found to be
(a) 13.11 mg Cr/L.
(b) 2.81 mg Cr/L.
(c) 13.93 mg Cr/L.
B) If one has a Gaussian distribution of data points,
(a) approximately two thirds of the data points lie above the mean, and one third of the data points lie below the mean accounting for all of the data points.
(b) approximately 2/3 of the data points lie within plus or minus two standard deviations of the mean.
(c) Approximately 2/3 of the data points lie within plus or minus one standard deviation of the mean.
A Gaussian distribution of data is symmetric if
(a) 4.5% of measurements lie outside the range defined by 2 standard deviations above the mean, and two standard deviations below the mean.
(b) 4.5% of measurements lie outside the range defined by 2 standard deviations above the mean, and two standard deviations below the mean with 2.25% of the values above 2 standard deviations from the mean and 2.25% of the values below 2 standard deviations from the mean.
(c) 68.3% of the measurements lie within plus or minus one standard deviation from the mean.
Analysis # mg Cr/L ABS 1 5.23 0.095 2 10.52 0.198 3 15.51 0.295 Unknown ? 0.265Explanation / Answer
1) Use the linear regression equation with y = 0.265. Plug in the value of y in the regression equation and obtain
0.265 = 0.0196x – 0.008
===> 0.0196x = 0265 + 0.008 = 0.273
===> x = 0.273/0.0196 = 13.928 13.93
The correct answer is (c) 13.83 mg Cr/L (ans).
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