Math Notebook
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.
 Is
there a
relationship
between the
fat grams
and the total
calories
in fast food?
Total
Fat (g)
Total Calories
Hamburger
9
260
Cheeseburger
13
320
Quarter-Pounder
21
420
Big Mac
30
560
Grilled Chicken
20
440
Grilled Chx w/ Chz
25
510
Fish Fillet
28
560
Crispy Chicken
25
500
Chicken Nuggets
30
600
Quarter Pounder w/
Chz
31
530
Arch Special w/
Bacon
34
590
 Positive
Correlation: y tends to increase
as x increases
 Negative
Correlation: y tends to
decrease as x increase
 Relative
to no correlation: no apparent
correlation

Can we predict the number of total calories based
upon the total fat grams?
 Step
1: Create a Scatter plot

Step 2: Using a straight edge, position
the straight edge so that the plotted
points are as close to the strand as
possible.
 Step
3: Then, find two points that you
think will be on the "best-fit" line.
I
picked the the points (9, 260) and (30,
530).
You may choose different points.
. Step 4: Calculate the slope of the line
through your two points (rounded to
three decimal places; thousandths place)

Does anyone remember our slope
formula?
 Step
5: Write the equation of the line

This equation can now be
used to predict
information that was not
plotted in the scatter plot.

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.
 We
chose two points to form our line-ofbest-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?
 Kendra
likes to watch crime scene
investigation shows on television. She
watched a show where investigators used a
shoe print to help identify a suspect in a
case.
 She questioned how possible it is to predict
someone’s height is from his shoe print.
 To
investigate, she collected data on shoe
length (in inches) and height (in inches)
from 10 adult men.
x = Shoe Length
Y = Height
12.6
74 inches
11.8
65 inches
12.2
71 inches
11.6
67 inches
12.2
69 inches
11.4
68 inches
12.8
70 inches
12.2
69 inches
12.6
72 inches
11.8
71 inches
Create a scatter plot of
this data
 Is
there a relationship between shoe
length and height?
 How
would you describe the
relationship? Do the men with longer
shoe lengths tend be taller?
 When
two variables “x” and “y” are
linearly related, you can use a line to
describe their relationship.
 You
can also use the equation of the line
to predict the value of the y-variable
based on the value of the x-variable.
 The
equation of a line y = 25.3 +3.66x might
be used to describe the relationship
between shoe length and height,
 Where x represents shoe length and y
represents height.
 To predict the height of a man with a shoe
length of 12, you would substitute 12 in for
“x” in the equation of the line and then
calculate the value of “y”