Least Square Method Formula
The Least Square Method formula is used to find the best-fitting line through a set of data points by minimizing the sum of the squares of the vertical distances (residuals) of the points from the line. For a simple linear regression, which is a line of the form y=ax+b, where y is the dependent variable, x is the independent variable, a is the slope of the line, and b is the y-intercept, the formulas to calculate the slope (a) and intercept (b) of the line are derived from the following equations:
- Slope (a) Formula: a=n(∑xy)−(∑x)(∑y) / n(∑x2)−(∑x)2
- Intercept (b) Formula: b=(∑y)−a(∑x) / n
Where:
- n is the number of data points,
- ∑xy is the sum of the product of each pair of x and y values,
- ∑x is the sum of all x values,
- ∑y is the sum of all y values,
- ∑x2 is the sum of the squares of x values.
These formulas are used to calculate the parameters of the line that best fits the data according to the criterion of the least squares, minimizing the sum of the squared differences between the observed values and the values predicted by the linear model.
Least Square Method
Least Square Method: In statistics, when we have data in the form of data points that can be represented on a cartesian plane by taking one of the variables as the independent variable represented as the x-coordinate and the other one as the dependent variable represented as the y-coordinate, it is called scatter data. This data might not be useful in making interpretations or predicting the values of the dependent variable for the independent variable where it is initially unknown. So, we try to get an equation of a line that fits best to the given data points with the help of the Least Square Method.
In this article, we will learn the least square method, its formula, graph, and solved examples on it.
Contact Us