Final answer:
The true statement is c.) the least-squares line is the process of minimizing the sum of the squared residuals, as it best describes the method used in linear regression to find the line of best fit. This is achieved by making the sum of the squared differences between observed and predicted values as small as possible.
option c is the correct
Step-by-step explanation:
The question of which statement about the least-squares line is true can be answered by understanding the fundamentals of linear regression. In statistics, specifically in the context of linear regression, the least-squares criterion is a method used to find the best-fitting line that minimizes the discrepancies between observed data and the data estimated by a model. Therefore, the correct statement is: c.) the least-squares line is the process of minimizing the sum of the squared residuals.
When we calculate the least-squares regression line, we are indeed attempting to find the line that results in the smallest possible value for the sum of the squares of the errors (SSE), where an error, or residual, is the difference between an observed value and the value predicted by our regression model. The formula for the least-squares regression line is often written as ŷ = a + bx, where ŷ represents the predicted value, a is the y-intercept, b is the slope of the line, and x represents the independent variable.
The method of least-squares regression is powerful because it provides a way to quantify the best fit of a line through a scatter plot of data, allowing for predictions within the scope of the observed data set.