Final answer:
Changing the units of measurement of only the independent variable in a regression equation does not affect the slope, but it does affect the intercept and the units of the error term.
Step-by-step explanation:
In a regression equation, changing the units of measurement of only the independent variable does not affect the slope. This is because the slope represents how the dependent variable (y) changes for every one-unit increase in the independent variable (x), on average. If we scale the independent variable, both the numerator and denominator in the slope's 'rise over run' calculation are scaled by the same factor, meaning the actual slope value remains unchanged.
However, changing the units of measurement will affect the other components of the regression equation like the intercept and the units of the error term, if not the presence or nature of it. But it won't affect the dependent variable itself as it is not being scaled. Therefore, the correct answer is the intercept, as it is directly dependent on the unit of the independent variable.