Table Of Contents
What is the Line of Best Fit?
A straight line that is drawn on a scatter plot and lies near the majority of the data points is known as the line of best fit. It is often used to estimate data on a graph. The line of best fit is used to demonstrate a pattern or correlation between the dependent and independent variables. It can be expressed either mathematically or visually. The image illustrates what a line of best fit looks like.
The formula to determine the equation of the line of best fit is represented as:
b= -mx + y.
Where,
‘x’ and ‘y’ are variables
‘m’ is the slope
Rapid Recall
A straight line that is located at the closest proximity to the data points on a scatter plot is called the line of best fit.
Rapid Recall
Solved Examples
Example 1:
The table below illustrates the daily temperatures and the number of lattes sold at a cafe for eight randomly selected days. Draw the line of best fit using the given data.
Solution:
Observe the table and plot the points on a coordinate plane:
(30, 45), (36, 43), (44, 36), (51, 35), (60, 30), (68, 27), (75, 23), (82, 17).
Now, draw a straight line in such a way that it is close to as many data points as possible.
Then, the line of best fit will be as follows:
Example: 2
The table shows the ticket prices of various movies in a mall and the average number of people attending each movie per day. If this trend continues then what will be the number of people attending the show if the cost of ticket is $23?
Solution:
The table gives the number of people attending the show and the cost of the movie tickets.
You are asked to estimate the number of people attending if the cost of a ticket is $23.
Enter the given data into the calculator and solve in linear regression mode:
For the given data, find the equation of the line of best fit using a graphing calculator and then solve for y, when x equals 23.
The equation for the line of best fit is:
y = -4.9x + 1042
Substitute x=23 and solve for y,
y = -4.9 × 23 + 1042
= 929.3
Hence, approximately 929 people will attend the show if the cost of a movie ticket is $23.
Example 3:
The table below shows the number of blueberries and their respective weights. Draw a line of best fit for the given data.
Solution:
As per the question, the given data points are (0,0), (1, 0.8), (2, 1.50), (3, 2.20), (4, 3.0), (5, 3.75).
Plot the points on a coordinate plane.
Now, draw a straight line in such a way that it is close to as many data points as possible.
Then, the line of best fit will be as follows.
A line of best fit may or may not pass through any of the data points. However, it should be at a minimum distance possible from each data point.
The line of best fit is a result of regression analysis and a tool for forecasting indicators and price changes.
A scatter plot is a type of plot that uses dots to demonstrate the relationship between two different variables.