Line of Best Fit
When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight line for purposes of predicting values that may not be displayed on the plot.
Such a straight line is called the “line of best fit.”
It may also be called a “trend” line.
A line of best fit is a straight line that best represents the data on a scatter plot.
This line may pass through some of the points, none of the points, or all of the points.
Materials for examining line of best fit: graph paper and a strand of spaghetti
Is there a relationship between the fat grams and the total calories in fast food?
Let’s find out!
1. Prepare a scatter plot of the data.
2. Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.
Our assistant, Bibs, helps position
the strand of spaghetti.
3. Find two points that you think will be on the “best-fit” line.
4. We are choosing the points (9, 260) and (30, 530). You may choose different points.
Predicting:
– If you are looking for values that fall within the plotted values, you are interpolating.
– If you are looking for values that fall outside the plotted values, you are extrapolating. Be careful when extrapolating. The further away from the plotted values you go, the less reliable is your prediction.
So who has the REAL “line-of-best-fit”?
In step 4 above, we chose two points to form our line-of-best-fit. It is possible, however, that someone else will choose a different set of points, and their equation will be slightly different.
Your answer will be considered CORRECT, as long as your calculations are correct for the two points that you chose. So, if each answer may be slightly different, which answer is the REAL “line-of-best-fit?
To answer this question, we need the assistance of a graphing calculator. See the next lesson.