Final answer:
The Least Squares Method is used to find the best-fit line by minimizing the sum of the squared errors, producing the regression line equation ŵ = a + bx. The method is part of the linear regression analysis and includes calculating the correlation coefficient.
Step-by-step explanation:
The mathematical technique that involves finding the solution that minimizes the sum of the squares of the residuals is known as the Least Squares Method. This method is widely used to determine the best-fit line or regression line for a set of data points by minimizing the sum of the squared errors (SSE). The process is a form of linear regression where the SSE is made as small as possible, which in turn leads to the calculation of the optimal line of best fit with the equation ŵ = a + bx.
To perform this calculation, one typically enters the set of (x, y) data into a calculator or software and uses the regression function to compute the least-squares regression line. This line can then be used to make predictions about the relationship between the independent variable, x, and the dependent variable, y. However, it is important to note that predictions should only be made within the range of the provided data set.
When performing calculations, it is also common to consider the correlation coefficient, symbolized by r, which indicates the strength and direction of the relationship between the variables.
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