Definition of Line of Best Fit

The line of best fit, also known as a trend line or regression line, is a straight line that best represents the data on a scatter plot.
It gives a general direction, or trend, of the relationship between two variables on the plot.
This line may not pass through every point, but strives to be the line that passes as closely as possible to all.
The equation of the line of best fit can be used to predict future data points within the same trend.

Sketching the Line of Best Fit

There is not a uniquely correct way to draw a line of best fit—it’s an estimation.
The line should have about an equal number of points above and below.
Try to make the total distances of the points above the line equal to the total distances of the points below the line.
Avoid connecting the dots from one to the next. The line of best fit does not need to touch any of the points.
Do not extend the line of best fit beyond the scope of the given data, as this may lead to inaccurate predictions.

You can use the method of least squares to calculate the line of best fit.
This involves finding the line that minimizes the sum of the squares of the vertical distances of the points from the line.
Two key values you’ll need to know for constructing this line are the slope and the y-intercept.
The slope of the line measures the rate of change between the two variables.
The y-intercept indicates the value of the dependent variable when the independent variable is zero.

The line of best fit can be used to make predictions about one variable based on the known value of the other variable.
While the line of best fit provides valuable information, be aware that predictions based on this line should only be made within the scope of the data.
Data beyond the existing range (extrapolations) can be inaccurate as the trend may not remain the same outside the range of available data.
Be aware of outliers. These are data points that do not fit the general trend. They can affect the line of best fit significantly.

Evaluate the goodness of the fit by calculating the correlation coefficient, denoted as r.
The value of r ranges between -1 and 1.
A perfect positive linear relationship (all points lie perfectly on the line) gives r = 1.
A perfect negative relationship (all points lie perfectly on a downward sloping line) has r = -1.
If there is no linear relationship, r is approximately = 0.
A higher absolute value of r indicates a stronger linear relationship between the variables.