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| Math
A |
Line
of Best Fit
(without graphing
calculator)
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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.
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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
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Is there a
relationship between the fat grams
and the total calories in fast food?
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|
Sandwich |
Total Fat (g) |
Total Calories |
| Hamburger |
9 |
260 |
| Cheeseburger |
13 |
320 |
| Quarter Pounder |
21 |
420 |
| Quarter Pounder with Cheese |
30 |
530 |
| Big Mac |
31 |
560 |
| Arch Sandwich Special |
31 |
550 |
| Arch Special with Bacon |
34 |
590 |
| Crispy Chicken |
25 |
500 |
| Fish Fillet |
28 |
560 |
| Grilled Chicken |
20 |
440 |
| Grilled Chicken Light |
5 |
300 |
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Can we predict the number of
total calories based upon the total fat grams?
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.
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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.
5. Calculate the slope of the
line through your two points.
rounded to
three decimal places.
6. Write the equation of the
line.
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.
ANS:
427.141 calories |
Choose two points that you think will form the
line of best fit.
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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. |
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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.
We can answer the question "Who has the
REAL line-of-best-fit?" , with the assistance of a graphing calculator.
See the next lesson.
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