APFIVE Experimental Procedure: A researcher studying sample measurements records the weight of a substance in 5 trials as given in the table above. The researcher then performs a simple linear regression to model weight as a function of the trial number but calculates the slope by summing the observed weights and dividing by the number of trials instead of using the covariance of trial number and weight. What is the experimental mistake in the slope calculation?
| Trial | Weight (g) |
|---|---|
| 1 | 10.1 |
| 2 | 10.5 |
| 3 | 10.9 |
| 4 | 11.3 |
| 5 | 11.7 |
The student should have performed a quadratic regression instead of a linear regression due to the non-linear nature of the data.
The student misapplied the formula for the slope by using the arithmetic mean of the weights directly without subtracting the mean of the trial numbers; the correct slope calculation requires using the covariance formula.
The error is in using trial numbers as the independent variable, which is not appropriate in this context.
The mistake stems from rounding errors in the weight measurements, causing the regression to yield an inaccurate slope.
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