In linear regression using the least squares method, which of the following equations best approximates the line of best fit for a set of data points $(x,y)$?

• A. $y=ax-b$
• B. $y=bx$
• C. $y=bx+a$
• D. $y=ax+b$

Answer: (C)

Verified step by step guidance

1. Understand that in linear regression, the goal is to find the line that best fits the data points by minimizing the sum of squared differences between observed values and predicted values.
2. Recall the general form of the linear regression equation: \(y = a x + b\), where \(a\) is the slope of the line and \(b\) is the y-intercept.
3. Recognize that the slope \(a\) represents the change in \(y\) for a one-unit change in \(x\), and the intercept \(b\) represents the value of \(y\) when \(x = 0\).
4. Note that the least squares method calculates \(a\) and \(b\) by solving the normal equations derived from minimizing the sum of squared residuals, ensuring the best linear approximation.
5. Compare the given options and identify that the correct form of the line of best fit is \(y = a x + b\), matching the standard linear regression equation.