Linear Regression Slope Calculation Error
The table below shows the weight of a substance recorded over five trials. A researcher attempts to create a linear regression model for weight as a function of the trial number. To find the slope of the regression line, the researcher calculates the sum of the weights and divides by the number of trials. Which of the following best describes the error in this procedure?
| Trial | Weight (g) |
|---|---|
| 1 | 10.1 |
| 2 | 10.5 |
| 3 | 10.9 |
| 4 | 11.3 |
| 5 | 11.7 |
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 student should have performed a quadratic regression instead of a linear regression due to the non-linear nature of the data.
The mistake stems from rounding errors in the weight measurements, causing the regression to yield an inaccurate slope.
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