For a least-squares line, the positive and negative residuals always cancel out, so the plain sum of the residuals is zero.

Circle one:   True   False

You fit a calibration line through five standard readings by least squares. What exactly does the least-squares method make as small as it can?

• The sum of the vertical gaps between each point and the line
• The horizontal gaps between the points and the line
• The largest single vertical gap only
• The slope of the line

What exactly does the least squares fit make as small as it can?

• The sum of the squared vertical gaps between points and line
• The horizontal gaps between the points
• The slope of the line

What is a residual?

• The slope of the fitted line
• The vertical distance from one point to the line
• The largest standard value

After fitting a line, you plot each residual against concentration. The points form a clear U shape, curved at both ends. What does this tell you?

• The straight line is the wrong model, the relationship is curved
• The fit is perfect and the residuals are random
• One standard was measured wrong and should be deleted
• The uncertainty of the line is zero

Another fit gives reading equals 1.5 times concentration plus 0.20. A sample reads 1.70. Type the concentration.

Answer: ______________

A colorimeter calibration gives the least-squares line absorbance = 2.5 times concentration + 0.10. A drink sample reads an absorbance of 1.35. What is its concentration in the units of the standards? Round to two decimal places.

Answer: ______________

Your standards run from 1 to 10 ppm and the calibration line fits them almost perfectly. A sample reads far above the top standard, at an absorbance matching about 25 ppm. What should you do?

• Say the result is unreliable and dilute the sample into the standard range
• Trust the line because it fits the standards so well
• Extend the line and report 25 ppm without any comment
• Average 25 ppm with the top standard

Standards were run at 0, 2, 4, 6, and 8 ppm. On your calibration line, where is the uncertainty of a concentration read back from the absorbance the smallest?

• At 4 ppm, the mean of the standard concentrations
• At 0 ppm, the lowest standard
• At 8 ppm, the highest standard
• It is the same everywhere on the line

Residuals curve and your unknown sits at the top end of the standards. What should you do?

• Trust the line since it looks straight
• Delete the curved residuals
• Refit with a curve or narrow the range, and distrust the end reading