Is a Line of Best Fit Always Straight?
Line of best fit is typically assumed to be straight in linear regression analysis. However in more complex regression techniques like polynomial regression, the line of best fit can take on curved forms to better fit the data.
Thus, the line of best fit is not always required to be straight.
In fact, depending on the nature of the data the line of best fit can take various forms including linear, quadratic, exponential or logarithmic. For the example provided, let’s fit a quadratic curve to the dataset representing the growth of a bacterial colony over time:
Time (hours) |
Bacterial Count |
---|---|
1 |
100 |
2 |
200 |
3 |
400 |
4 |
800 |
5 |
1600 |
General equation for a quadratic curve is:
y = ax2 + bx + c
We can use the given data points to solve for the coefficients a, b and c.
Using the first data point (1, 100):
100 = a(1)2 + b(1) + c
100 = a + b + c..(1)
Using the second data point (2, 200):
200 = a(2)2 + b(2) + c
200 = 4a + 2b + c …(2)
Using the third data point (3, 400):
400 = a(3)2 + b(3) + c
400 = 9a + 3b + c…(3)
Now, we have a system of three equations (1), (2) and (3) to solve for a, b and c.
Solving this system will give us the coefficients of the quadratic curve equation, which will represent the growth pattern of the bacterial colony over time.
Line of Best Fit
Line of Best Fit: A Line of best fit is a fundamental concept of statistics used to analyze the relationship between two variables. It helps predict the values of one variable based on the values of another variable(given).
Line of best fit is a straight line drawn through a scatter plot of data points that best represent their distribution by minimizing the distances between the line and these points. It results from regression analysis and serves to illustrate the relationship among the data. This line is also a predictive tool, useful for forecasting trends, such as market indicators and price movements.
In this article, we will learn about the Line of Best Fit, how to calculate the line of best fit, solved examples, and other in detail in this article.
Table of Content
- What Is a Line of Best Fit?
- Line of Best Fit in Regression
- Line of Best Fit in Statistics
- Line of Best Fit Formula
- How to Calculate the Line of Best Fit?
- Is a Line of Best Fit Always Straight?
- Where Line of Best Fit is Used?
- Line of Best Fit Examples
- Line of Best Fit – Practice Questions