Linear Regression Method Algorithm (Fit y=a+bx Curve)
Regression analysis is basically a set of statistical process for finding relationship among independent variables (explanatory variables) and dependent variable. If we are finding best equation relating these variables then it is known as best fit or curve fitting. When we are finding linear relationship among independent variables and dependent variable then it is called Linear Regression. In linear regression, when there is only one independent variable then the process is known as Simple Linear Regression.
Least Square Regression
The method of least squares is a standard approach in regression analysis to approximate the relation among dependent variable amd independent variables. In the least squares method the unknown parameters are estimated by minimizing the sum of the square of errors between the data and the model.
Simple linear regression has equation having form y = a + bx.
Procedure for Linear Regression (Fitting y = a + bx) using Least Square Method
1. Form normal equations: ∑y = na + b ∑x ∑xy = a∑x + b∑x2 2. Solve normal equations as simulataneous equations for a and b 3. Substitute the value of a and b in y= a + bx which is required line of best fit.
Linear Regression Algorithm (Fitting y = a + bx)
1. Start 2. Read Number of Data (n) 3. For i=1 to n: Read Xi and Yi Next i 4. Initialize: sumX = 0 sumX2 = 0 sumY = 0 sumXY = 0 5. Calculate Required Sum For i=1 to n: sumX = sumX + Xi sumX2 = sumX2 + Xi * Xi sumY = sumY + Yi sumXY = sumXY + Xi * Yi Next i 6. Calculate Required Constant a and b of y = a + bx: b = (n * sumXY - sumX * sumY)/(n*sumX2 - sumX * sumX) a = (sumY - b*sumX)/n 7. Display value of a and b 8. Stop