Linear Regression Using Least Squares Method - Line of Best Fit Equation

Step-by-Step Tutorial: Linear Regression Using Least Squares Method

Step 1: Introduction to Linear Regression

• Linear regression helps in finding a linear equation that best fits the data points.
• The least squares method is used to calculate the equation of the line that minimizes the distance of data points from the line.

Step 2: Data Setup in Excel

1. Create a table with four columns:
   • Column 1: X values (1, 2, 3, 4, 5, 6, 7)
   • Column 2: Y values (3.8, 9.0, 11.2, 13.6, 16.0, ...)
   • Column 3: Product of X and Y values
   • Column 4: Squared X values

Step 3: Calculation of Sums

1. Calculate the sum of each column:
   • Sum of X values: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
   • Sum of Y values: 61.8
   • Sum of XY values: 314.8
   • Sum of X squared values: 140

Step 4: Calculate Slope (m) and Y-intercept (b)

1. Use the formulas:
   • Slope (m): (n * Σxy - Σx * Σy) / (n * Σx^2 - Σx^2)
   • Y-intercept (b): (Σy - m * Σx) / n

Step 5: Write the Linear Equation

1. The linear equation is in the form: y = mx + b
2. Plug in the calculated values of m and b to get the equation.

Step 6: Validation Using Excel

1. Enter the Y values in column B and X values in column C in Excel.
2. Use Excel functions to calculate:
   • Slope: =SLOPE(B2:B8, C2:C8)
   • Y-intercept: =INTERCEPT(B2:B8, C2:C8)

Step 7: Interpretation and Validation

1. Check the accuracy of the equation by plugging in X values and comparing the predicted Y values with the actual Y values.
2. Excel provides a quick and efficient way to calculate the slope and y-intercept for the linear equation.

Conclusion:

• You have now learned how to perform linear regression using the least squares method to find the line of best fit for your data points.
• This method is useful for creating linear equations that accurately represent experimental data or observations.
• Excel can be a handy tool for quick calculations in linear regression analysis.

By following these steps, you can efficiently calculate the slope and y-intercept for a linear equation using the least squares method and validate the accuracy of the line of best fit.