Fitting Polynomials in Excel: Techniques and Methods

While Excel primarily provides the LINEST function for linear regression, fitting polynomials requires an additional approach. This article covers different methods to achieve polynomial regression in Excel, including using the LINEST function, adding trendlines, and combining the FORECAST and INDEX functions.

Introduction to Polynomial Fitting in Excel

Polynomial fitting is a powerful technique in data analysis that allows you to model non-linear relationships between variables. Unlike the LINEST function, which is tailored for linear equations, you can fit higher order polynomials by manually creating polynomial terms and using the LINEST function or by using chart trendlines.

Method 1: Using the LINEST Function for Polynomial Regression

Begin by organizing your data, placing the x-values in one column, and the corresponding y-values in another. Here’s how you can proceed with a quadratic fit (a 2nd degree polynomial) using the LINEST function:

Prepare Your Data: Assume your x-values are in column A and y-values in column B. Create Polynomial Terms: Add additional columns for the polynomial terms. For a quadratic fit (2nd degree polynomial), add the following columns: Column C for (x^2): i.e., A2^2 Column D for (x): i.e., A2 Column E for the constant term: i.e., 1 Using LINEST: Select a range of cells for the coefficients. For a quadratic fit, you need 3 cells. Enter the following formula as an array formula (press Ctrl Shift Enter): LINEST(B2:B[n], C2:E[n], TRUE, TRUE) Replace [n] with the last row of your data. The output will provide you with the coefficients for the polynomial.

Method 2: Using Excel’s Chart Trendline

Another user-friendly approach is through Excel’s trendline feature:

Create a Scatter Plot: Select your data and insert a scatter plot. Add a Trendline: Click on the data series in the chart. Right-click and select the trendline option. Display Equation: Check the ‘Display Equation on chart’ box to see the line of best fit. Summary: This method is particularly useful when you want to visualize the trend immediately and provides a quick way to get the equation of the polynomial fit.

Method 3: Using the FORECAST and INDEX Functions

For predicting future values based on your polynomial fit, you can use the coefficients obtained from the LINEST method to create a formula:

Write the Polynomial Equation: Based on the coefficients obtained from LINEST, write the polynomial equation. For a quadratic equation Y ax^2 bx c: Create a Formula: In a new cell, use the following formula with the coefficients obtained from LINEST example: a * A2^2 b * A2 c

Conclusion

Excel, despite lacking a direct polynomial fitting function similar to LINEST for linear regression, offers several methods for polynomial fitting. By using the LINEST function, trendlines, or combining the FORECAST and INDEX functions, you can effectively model complex relationships between variables in your dataset.