Explanation:

To understand why the sum of squares of residuals or errors should be minimum for the best-fitted trend line, let's first define what a residual or error is in the context of a trend line.

Residual or Error:
In regression analysis, the residual or error is the difference between the observed values and the predicted values by the trend line. It represents the deviation of each data point from the trend line and is an indicator of how well the trend line fits the data.

Sum of Squares of Residuals:
The sum of squares of residuals is the sum of the squared differences between the observed values and the predicted values. It is calculated by squaring each residual and summing them up. The sum of squares of residuals measures the overall goodness of fit of the trend line.

Objective:
The objective of fitting a trend line to a set of data points is to minimize the deviation or error between the observed values and the predicted values. Therefore, the best-fitted trend line is the one that minimizes the sum of squares of residuals.

Reasoning:
If the sum of squares of residuals is positive or negative, it indicates that the trend line is not a good fit for the data. A positive sum of squares of residuals means that the trend line is underestimating the observed values, while a negative sum of squares of residuals means that the trend line is overestimating the observed values.

On the other hand, if the sum of squares of residuals is minimum, it means that the trend line is minimizing the deviation between the observed values and the predicted values. It represents the best compromise between accuracy and simplicity in representing the data. Therefore, option 'B' - Minimum is the correct answer.

Conclusion:
In summary, the best-fitted trend line is the one for which the sum of squares of residuals is minimum. This indicates that the trend line minimizes the deviation between the observed values and the predicted values, making it a good fit for the data.