Final answer:
The best fitting line is the one that minimizes the sum of the squared errors of prediction, also known as the least-squares regression line. It is calculated using the least-squares criterion, which finds the specific line where the sum of all errors squared is the smallest. The equation of this line can be represented as ŷ = a + bx.
Step-by-step explanation:
The correct description of the best fitting line, also known as the least-squares regression line, is the line that minimizes the sum of the squared errors of prediction. When we talk about the sum of squared errors (SSE), we refer to the total of all errors squared, where an error is the difference between the observed value and the predicted value based on the regression line.
By minimizing these squared errors, the least-squares regression line provides the best approximation for the data set depicted on a scatter plot.
The least-squares criterion for the best fit involves finding the values of the intercept (a) and slope (b) that make the SSE as small as possible. The equation of the line of best fit can be expressed as ŷ = a + bx, where ŷ is the estimated value of the dependent variable.
It is crucial to understand that while a regression line is useful for making predictions within the data set, it should not be used to make predictions for values outside the range of the data. Additionally, identifying any potential outliers is important as they can significantly affect the regression line.
Therefore answer is d. the line are even the line that minimizes the sum of errors of prediction.