Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians use the least squares method to arrive at the geometric equation for the line, either through manual calculations or by using software.
A straight line will result from a simple linear regression analysis of two or more independent variables. A multiple regression involving several related variables can produce a curved line in some cases.
Key Takeaways
- Universal Relationship Indicator: A line of best fit minimizes the distance between it and some data.
- Essence of Understanding: The line expresses a relationship in a scatter plot of different data points.
- Predictive Marvel: It is an outcome of regression analysis and serves as a crucial prediction tool for indicators and price movements.
- Market Compass: In finance, the line of best fit identifies trends and correlations in market returns, whether between assets or over time.
Understanding the Line of Best Fit
The line of best fit estimates a straight line that minimizes the distance between itself and where observations fall in some data set. It depicts a trend or correlation between the dependent variable and independent variable(s).
Line of best fit is a key concept in regression analysis, which measures the relationship between one or more independent variables and a resulting dependent variable. Professionals in a wide range of fields, from science and public service to financial analysis, use regression.
Line of Best Fit and Regression Analysis
To perform a regression analysis, a statistician gathers data points containing dependent and independent variables. For example, the dependent variable could be a firm’s stock price and the independent variables could be the Standard & Poor’s 500 index and the national unemployment rate, under the assumption that the stock is not listed in the S&P 500. The data set could be the results for these three attributes over the past 20 years.
This data might be depicted as a scatter plot with points that either follow a visible pattern or don’t. If a pattern is apparent, a line of best fit can be sketched to minimize the distance of those points from that line. Using the least squares method, the most commonly used technique in regression analysis, ensures accuracy.
Calculating the Line of Best Fit
A regression with two independent variables will produce a formula with the basic structure:
y = c + b1(x1) + b2(x2)
Here, y is the dependent variable, c is a constant, b1 is the first regression coefficient (slope), and x1 is the first independent variable. The second coefficient and variable are b2 and x2, respectively. Drawing from earlier, the stock price would be y, the S&P 500 would be x1, and the unemployment rate would be x2.
Finding the Line of Best Fit
Multiple methods exist to estimate a line of best fit. The crudest involves visually estimating such a line on a scatter plot. The precise and widely accepted method is the least squares method, minimizing the sum of the residuals of points from the plotted curve.
Is a Line of Best Fit Always Straight?
By definition, a line is straight, but a best fit curl can describe the relationship when variables produce more complicated patterns. It’s possible for this curve to be quadratic, cubic, or even exponential. Simpler descriptions are preferable, offering more clarity.
Application in Finance
For financial analysts, estimating a line of best fit quantifies the relationship between variables like a stock’s price and its earnings per share (EPS). With regression analysis, stock price behaviors or other factors’ tendencies can be projected, helping guide investment decisions.
Bottom Line
A line of best fit minimizes the distance between itself and observed data. It’s indispensable in regression analysis for inferring relationships between dependent and explanatory variables. In finance, economists and analysts use the line of best fit for econometric studies and technical analysis tools.
Related Terms: regression, least squares method, multiple regression, predictive analysis.
