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So which line
is the REAL "line-of-best-fit"? |
In the lesson on
Line of Best Fit (without the graphing calculator), we discovered
that finding the line-of-best-fit may lead to many "different" equations
depending upon the points chosen to construct the line.
Simply stated, the graphing calculator
has the capability of determining which line will actually represent the
REAL line-of-best-fit.
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The directions on this page were
prepared using
the TI-83+/TI-84+ graphing calculator.
Use
of the graphing calculator will help you to
better
understand the concept of line of best fit.
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Let's examine
our fast food problem again with the use of the graphing calculator.
(This example and chart
are from MathBits.com and were used with permission.)
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?
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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 - 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 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.
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Question: Predict the total
calories based upon 22 grams of fat.
ANS:
451.940 calories |
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