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: y
Positive Correlation:
Our data increases from left to right. x
Negative Correlation: y
Our data decreases from left to right. x
No Correlation:
y
Our data does not have any pattern.
x
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 3 4 6 8 10 12
Weight
(lbs)
2.5
7.6
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 2 3 4 6 8 10 12
Weight(y) 2.5
7.6
12.5
17.1
24.3
37.9
49.2
54.9
30
20
10
60
50
40
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 m=
𝟑𝟕.𝟗 −𝟏𝟕.𝟏
𝟖−𝟒
=
𝟐𝟎.𝟖
𝟒
= 5.2
Using one of the two points and the point-slope form equation: we get: 𝒚 17.1
= 5.2
( 𝒙 4 ) 𝒚 𝒚
𝟏
= m ( 𝒙 𝒙
𝟏
)
Age Weigh t
1
2
2.5
7.6
3 12.5
4 17.1
6 24.3
8 37.9
10 49.2
𝒚 - 17.1 =5.2
𝒙 – 20.8
12 54.9
𝒚 =5.2
𝒙 – 20.8 +17.1 𝒚 =5.2
𝒙 – 3.7
Procedure 3: Estimate the weight of the 7-monthold panda
Using the found equation of the Trend
Line: 𝒚 =5.2
𝒙 – 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 50 o N.
Latitude Temp
35 46
33
30
52
67
25
43
40
39
76
32
37
44
Procedure 1: Scatter Plot
80
30
20
10
70
60
50
40
20 25 30 35 40 45
Latitude ( o N)
50
Latitude
(x)
35
Temp
(y)
46
33
30
52
67
25
43
40
39
76
32
37
44
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 slope m=
𝟑𝟕−𝟔𝟕
𝟒𝟎−𝟑𝟎
=
−𝟑𝟎
𝟏𝟎
= - 3
Using one of the two points and the point-slope form equation: we get: 𝒚 67 = -3 ( 𝒙 30 ) 𝒚 𝒚
𝟏
= m ( 𝒙 𝒙
𝟏
) 𝒚 𝟔𝟕 =-3 𝒙 + 𝟗𝟎 𝒚 =-3 𝒙 + 90 + 67 𝒚 = -3 𝒙 + 157
(x) (y)
35 46
33 52
30 67
25 76
43 32
40 37
39 44
Procedure 3: Estimate the temperature of the
50 o N:
Using the found equation of the Trend
Line: 𝒚 = -3 𝒙 + 157 and letting x = 50 o N of latitude we get: 𝒚
=-3(
50
)
+𝟏𝟓𝟕 𝒚
= –150 + 157
𝒚
=7
Thus at latitude of
50 o N
the temperature will be about
7 o F.
VIDEOS:
Scatter Plots
https://www.khanacademy.org/math/algebra/line ar-equations-and-inequalitie/graphing-slopeintercept/v/fitting-a-line-to-data
