When working with data in Google Sheets or Microsoft Excel, one of the most common tasks is to find a relationship between two variables, which is often done using the line of best fit. The line of best fit, also known as a regression line, is a straight line that best represents the data in a scatter plot. It helps to identify trends and make predictions based on the relationship between the variables. This line is not just a visual tool; it is calculated using a method known as least squares regression. In this article, we will dive into how Excel and Google Sheets calculate the line of best fit, focusing on the computational method behind it.
The least squares method is the foundation for calculating the line of best fit. This method minimizes the sum of the squared differences between the observed values (the actual data points) and the predicted values (the values on the line). In simpler terms, it finds the line that reduces the distance between the data points and the line itself as much as possible. By minimizing the squared errors, the least squares method ensures that the line is as close as possible to all the points in the data set.
To understand this more clearly, let’s break it down. Suppose you have a set of data points, each represented by an X value (independent variable) and a Y value (dependent variable). The goal is to find a straight line of the form y = mx + b, where:
• y is the predicted value,
• m is the slope of the line,
• x is the independent variable, and
• b is the y-intercept.
The line of best fit is determined by calculating the values of m and b that minimize the sum of squared errors, where each error is the vertical distance between a data point and the line. The formula for the slope (m) and intercept (b) can be derived using calculus, but the process is typically hidden from the user in both Excel and Google Sheets, which automate it for convenience.
In Excel, you can calculate the line of best fit in a couple of ways. One common method is to use the LINEST function, which returns an array of statistics for a linear regression. The LINEST function computes the slope, intercept, and other statistical values such as the standard error and the coefficient of determination (R-squared), which indicates how well the line fits the data. The syntax for the LINEST function is:
=LINEST(known_y’s, known_x’s)
In this formula:
• known_y’s represents the range of dependent values (Y values),
• known_x’s represents the range of independent values (X values).
Once you have the slope (m) and intercept (b) from the LINEST function, you can manually plot the line of best fit on a scatter plot or use it for predictions.
Excel also provides a simpler way to calculate the line of best fit through its charting tools. When you insert a scatter plot, you can add a trendline by right-clicking on any data point and selecting “Add Trendline.” In the options, you can choose a linear trendline, which will automatically calculate the line of best fit using the least squares method. Excel even allows you to display the equation of the line on the chart, giving you the slope and intercept directly on the graph.
Google Sheets offers a similar process for calculating the line of best fit. The simplest way is by using the LINEST function in the same manner as in Excel. The syntax is almost identical:
=LINEST(Y_range, X_range)
Just as in Excel, the LINEST function in Google Sheets will return the slope and intercept, which can then be used to plot the line of best fit or for prediction purposes. Google Sheets also allows you to insert a scatter plot and add a trendline. To do this, select the chart, click on the three vertical dots in the top right corner of the chart, and choose “Edit chart.” From there, you can select “Customize,” then “Series,” and check the box for “Trendline.” Google Sheets will automatically calculate the line of best fit and display it on the graph.
Both Excel and Google Sheets use the least squares method to determine the best fitting line. The underlying computational method is the same in both applications, relying on statistical principles to find the line that best represents the data. This makes these tools powerful for quickly analyzing data and identifying trends, particularly when you are working with large datasets where manually calculating a regression line would be time-consuming.