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.
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?
Total Fat (g)
|Quarter Pounder with Cheese
|Arch Sandwich Special
|Arch Special with Bacon
|Grilled Chicken Light
Can we predict the number of
total calories based upon the total fat grams?
1. Prepare a scatter plot of
2. Using a strand of
spaghetti, position the spaghetti so that the plotted points are as close
to the strand as possible.
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.
5. Calculate the slope of the
line through your two points.
three decimal places.
6. Write the equation of the
7. This equation can now be used to predict
information that was not plotted in the scatter plot.
Question: Predict the total
calories based upon 22 grams of fat.
Choose two points that you think will
line of best fit.
- If you are looking for values that fall within the plotted values, you
- If you are looking for values that fall outside the plotted values, you
Be careful when
extrapolating. The further away from the plotted
values you go, the less reliable is your prediction.
So who has the
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
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
To answer this question, we need the assistance of a graphing calculator.
See the next lesson.