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Next, the student (a) adds a linear trendline in Excel, (b) has Excel calculate the slope of her line of best fit, and (c) has Excel calculate the standard error in the slope.

I have three questions:

- Why doesn't the standard error in the slope use the individual y uncertainties as inputs to its calculation? What is the theoretical basis for using a standard error calculation that ignores the individual y measurement errors/uncertainties?

- Does the standard error in the slope fail to represent something crucial about the uncertainty in the slope, due to the fact that the standard error calculation ignores the individual y measurement uncertainties?

- Assume the student uses the equation from the top line (below) to calculate manually the slope of her best fit line. She then uses the rules of uncertainty propagation to propagate the individual y measurement uncertainties through this equation. In so doing, she obtains a value of uncertainty in the slope. How would this value compare to the Excel-calculated standard error in the slope?