Final answer:
The correct equation for the least-squares regression line, based on the given options and correcting for typographical errors, is 'ln(overline{e}_{i}) = 2.305 - 0.101 (time)'.
Step-by-step explanation:
The equation of the least-squares regression line is generally expressed in the form y = a + bx, where y is the predicted value of the dependent variable, 'a' is the y-intercept, and 'b' is the slope of the line.
The correct equation for the least-squares regression line based on the options provided would involve natural logarithm (ln) and the variable 'time' as the independent variable.
Therefore, the equation with 'ln(overline{e}_{i})' on the left side and a linear combination of a constant and 'time' on the right side fits the description.
Scanning through the given options, if we correct any obvious typographical errors in the choices, the correct least-squares regression line equation would look like option (a), which is ln(overline{e}_{i}) = 2.305 - 0.101 (time).