Transcript 5_7 Satter Plots and Trend Lines

5.7 SCATTER PLOTS AND TREND LINES:
Scatter Plot: a graph that relates two
different sets of data by displaying them as
ordered pairs (x, y).
Correlation: The relationship/trend found
in any given data.
Trend line: Line on a scatter plot, drawn
near the points, that shows a correlation
Interpolation: The act of estimating a value
between two known values.
Extrapolation: The act of predicting a value
outside of the range of known values.
Line of Best Fit: Line that shows the most
accurate relationship between two sets of
data.
Correlation Coefficient(r): a number from
-1 to 1 that tells us how closely the
equation models the data.
Causation: A change in one quantity
causes a change in a second quantity.
GOAL:
SCATTER PLOTS:
We must be able to provide domain,
range and ordered pairs.
CORRELATIONS: In any data we can have three
types of correlation:
Positive Correlation:
y
x
Our data increases from left to right.
Negative Correlation:
y
x
Our data decreases from left to right.
No Correlation:
y
x
Our data does not have any pattern.
Correlation Coefficient (r):
Whenever we are given data/information/ordered
pairs, we must be able to provide certain details:
Ex:
Make a scatter plot of the data, provide the
type of relationship it represents and the
approximate weight of a 7-month-old panda.
Weight of a Panda
Age
(months)
1
2
Weight
(lbs)
2.5
7.6
3
4
6
8
10
12
12.5 17.1 24.3 37.9 49.2 54.9
To answer the questions on the panda task we must
do three procedures:
Procedure 1: Create a Scatter Plot
Procedure 2: Write an Equation of the Trend of the
Line
Procedure 3: Estimate the weight of a 7-month-old
panda.
Procedure 1: Scatter Plot
Age (x)
1
Weight(y) 2.5
2
3
4
6
8
10
12
7.6
12.5
17.1
24.3
37.9
49.2
54.9
Weight (lbs)
60
50
40
30
20
10
2
4
6
8
10
12
Age (Months)
Procedure 2: Write an equation of the Trend
Using A(4, 17.1) and B(8, 37.9), points on
the positive correlation line, we find the
slope
𝟑𝟕.𝟗 −𝟏𝟕.𝟏 𝟐𝟎.𝟖
m=
=
= 5.2
𝟖−𝟒
𝟒
Using one of the two points and the
point-slope form equation: 𝒚- 𝒚𝟏 = m(𝒙-𝒙𝟏)
we get: 𝒚- 17.1 =5.2(𝒙 - 4)
𝒚- 17.1 =5.2𝒙 – 20.8
𝒚 =5.2𝒙 – 20.8 +17.1
𝒚 =5.2𝒙 – 3.7
Age
Weigh
t
1
2.5
2
7.6
3
12.5
4
17.1
6
24.3
8
37.9
10
49.2
12
54.9
Procedure 3: Estimate the weight of the 7-monthold panda
Using the found equation of the Trend
Line:
𝒚 =5.2𝒙 – 3.7
and letting x = 7 months,
we get:
𝒚 =5.2(7) – 3.7
𝒚 =36.4 – 3.7  𝒚 =32.7
Thus a 7-month-old panda will
weight about 32.7 lbs.
YOU TRY IT: Use the data below to create a
scatter plot, provide the relationship and
approximate the daily temperature in
January at a latitude of 50o N.
Latitude
35
33
30
25
43
40
39
Temp
46
52
67
76
32
37
44
Temperature (o F)
Procedure 1: Scatter Plot
Latitude
(x)
Temp
(y)
80
35
46
70
33
52
60
30
67
50
25
76
40
43
32
40
37
39
44
30
20
10
20
25
30
35 40
45
Latitude (o N)
50
Negative
Correlation
Trend Line
Procedure 2: Write an equation of the Trend
Using A(30, 67) and B(40, 37), points on the
negative correlation line, we find the
𝟑𝟕−𝟔𝟕 −𝟑𝟎
slope
m=
=
=-3
𝟒𝟎−𝟑𝟎
𝟏𝟎
Using one of the two points and the
point-slope form equation: 𝒚- 𝒚𝟏 = m(𝒙-𝒙𝟏)
we get: 𝒚- 67 = -3 (𝒙 - 30)
𝒚- 𝟔𝟕 =-3𝒙 + 𝟗𝟎
𝒚 =-3𝒙 + 90 + 67
𝒚 = -3𝒙 +157
(x)
(y)
35
46
33
52
30
67
25
76
43
32
40
37
39
44
Procedure 3: Estimate the temperature of the
50oN:
Using the found equation of the Trend
Line:
𝒚 = -3𝒙 +157
and letting x = 50o N of latitude
we get:
𝒚 =-3(50)+𝟏𝟓𝟕
𝒚 = –150 + 157  𝒚 =7
o
50
Thus at latitude of
N the
temperature will be about 7o F.
VIDEOS:
Scatter Plots
https://www.khanacademy.org/math/algebra/line
ar-equations-and-inequalitie/graphing-slopeintercept/v/fitting-a-line-to-data
CLASSWORK:
Page 338-339
Problems: As many as needed
to master the
concept