The correct answer is A) Method of Least Squares.

Why “Method of Least Squares” is the Correct Answer:

The “Line of Best Fit” is indeed another name for the “Method of Least Squares.” This method is a mathematical technique used to find the best-fitting linear regression line through a set of data points. Here’s a detailed explanation of why “Method of Least Squares” is the correct choice:

1. Objective of the Method:

The primary objective of the Method of Least Squares is to determine the equation of a straight line that best represents the relationship between two variables in a set of data. This method minimizes the sum of the squared differences (residuals) between the observed data points and the values predicted by the linear regression line.

2. Linear Regression:

The Line of Best Fit is essentially a linear regression line. A linear regression line is represented by the equation:

$Y=aX+b$

where:

• • $Y$ is the dependent variable (the variable being predicted or explained).
  • $X$ is the independent variable (the variable used to make predictions).
  • $a$ is the slope of the line, representing the change in $Y$ for a one-unit change in $X$.
  • $b$ is the intercept, representing the value of  $Y$ when $X$ is zero.

3. Minimizing the Sum of Squares:

The “Least Squares” part of the method refers to the minimization of the sum of the squared differences between the observed values of the dependent variable and the values predicted by the linear regression line.

4. Line of Best Fit:

The term “Line of Best Fit” is often used in a practical context to describe the linear regression line that results from applying the Method of Least Squares. This line represents the best approximation of the relationship between the two variables, as it minimizes the overall error between the observed data and the predicted values.

Why the Other Options Are Not Correct:

B) Moving Average Method:

The Moving Average Method is a different statistical technique used for smoothing time-series data. It involves calculating the average of a certain number of consecutive data points to create a moving average line. While it is used for trend analysis and smoothing, it is not the same as the Method of Least Squares.

C) Semi-Average Method:

The Semi-Average Method is not related to the determination of a regression line. It typically involves calculating the average of two values, which is sometimes used for certain statistical purposes. However, it is not synonymous with the Method of Least Squares.

D) Trend Line Method:

The term “Trend Line” is often used interchangeably with the “Line of Best Fit,” but it can also refer to various methods used to identify and describe trends in data. While a trend line may be the result of a linear regression analysis (Method of Least Squares), it is not a specific mathematical technique like the Method of Least Squares.

In summary, the “Line of Best Fit” is another name for the “Method of Least Squares,” which is a mathematical technique for finding the best-fitting linear regression line through a set of data points. This method minimizes the sum of squared differences between observed and predicted values, resulting in a line that represents the relationship between two variables in the data.

The other options, such as the Moving Average Method, Semi-Average Method, and Trend Line Method, are distinct statistical techniques with different purposes and methodologies.