Final answer:
The least squares method is a statistical technique used in linear regression to determine the best-fit line for a set of data by minimizing the sum of the squared errors (SSE).
Step-by-step explanation:
The least squares method refers to a statistical technique used in linear regression to determine the best-fit line for a set of data. This method minimizes the sum of the squared errors (SSE), that is, it finds the line that makes the vertical distances from the data points to the line (errors) as small as possible, when those distances are squared. The equation of the least-squares regression line has the form ŷ = a + bx, where 'a' is the y-intercept, 'b' is the slope of the line, 'x' represents the independent variable, and ŷ is the predicted value of the dependent variable for a given value of the x variable. The slope 'b' and intercept 'a' estimated by this method are used to make predictions for the y variable given new x values.
Many calculators and software programs, such as Excel, can perform the calculations necessary to find the least-squares regression line. Additionally, the correlation coefficient 'r' can tell us about the strength and direction of the relationship between the x and y variables.