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A line
of best fit (or "trend"
line) 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. |
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You can examine
lines of best fit with:
1. paper and pencil only
2. a combination of graphing calculator and
paper and pencil
3. or solely with the graphing calculator
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Example:
Is there
a relationship between the fat grams and the total calories
in fast food?
|
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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Paper and Pencil Solution:
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1. Prepare a scatter plot of
the data on graph paper.
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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| 3. Find two points that you think will be
on the "best-fit" line. Perhaps you chose the points (9, 260) and
(30, 530). Different people may choose different points.
4. Calculate the slope of the
line through your two points (rounded to
three decimal places).
5. Write the equation of the
line. This equation can now be used to predict information
that was not plotted in the scatter plot. For example, you
can use the equation to find the total calories based upon 22
grams of fat.
Equation:
Prediction based on 22 grams of fat:
Different people may choose different points and
arrive at different equations. All of them are "correct",
but which one is actually the "best"? To determine the
actual "best" fit, we will use a graphing calculator. |
Graphing Calculator Solution:
1. Enter the data in the calculator
lists. Place the data in L1 and
L2.
STAT, #1Edit,
type values into the lists |
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2.
Prepare a scatter plot of the data.
Set up for the scatterplot.
2nd StatPlot
- choose
the first icon - choices
shown at
right. Choose
ZOOM #9 ZoomStat.
Graph shown below.
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3.
Have the calculator determine the line of
best fit.
STAT → CALC #4 LinReg(ax+b)
Include the
parameters L1,
L2, Y1.
(Y1
comes from
VARS → YVARS, #Function, Y1)
You now have the values of
a and b needed to
write the equation of the actual
line of best fit. See values at
the right.
y = 11.73128088x + 193.8521475
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| 4. Graph
the line of best fit. Simply hit
GRAPH.
To get a predicted value within the
window,
hit
TRACE,
up arrow, and type the desired value. The
screen below shows x = 22.
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