Drawing a Line of Best Fit from Given Data

Line of Best Fit:

Line of best fit, or trend line, is a straight line drawn on a scattergram to estimate the relationship between two sets of data.
It is not an exact fit, but gives the general trend of the data points.
It can be used to predict values of one variable given values of the other, this is known as interpolation or extrapolation.

Plotting Points:

When creating a scattergram, one set of data values corresponds to the x-axis (horizontal) and the other set corresponds to the y-axis (vertical).
Points on the scattergram represent individual pairs of data.

Drawing the Line:

To draw the line of best fit, you should firstly consider the overall pattern of data points on your scatterplot.
The line of best fit should be drawn so that it is as close as possible to all the data points, minimizing the vertical distances between the points and the line.
If the majority of points are below the line, equal number of points should be above the line. Similarly, if many points are to the right of the line, an equal number should be to the left.

Reliability of Predictions:

The line of best fit is more reliable for interpolation (predicting within the range of given data) than extrapolation (predicting beyond the given data).
Extrapolation is less reliable as it assumes that the observed trend will continue beyond the range of the collected data, which may not be the case.
Outliers can significantly affect the position and gradient of the line of best fit, making predictions less reliable.

Analysing the Line of Best Fit:

The line of best fit can suggest a relationship or correlation between two variables.
A line of best fit with a positive gradient suggests a positive correlation, i.e., as one variable increases, so does the other.
A negative gradient suggests a negative correlation, i.e., as one variable increases, the other decreases.
Remember, correlation does not imply causation. It measures the strength of a relationship, but does not mean one variable affects the other.

Keep in mind, accurately drawing and interpreting the line of best fit is crucial to making meaningful conclusions and predictions from a scatterplot.