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Scatter Plots
Lesson objectives Teachers' notes
1. Students will be able to determine whether data has a positive, negative, or no correlation.
2. Students will be able to construct a scatter plot and determine the line of best fit.
3. Students will be able to use a line of best fit to make predictions.
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Teachers' notesLesson objectives
Subject:
Topic:
Grade(s):
Prior knowledge:
Crosscurricular link(s):
Algebra 1
Representing Data Scatter Plots
79
Outlier, xaxis, yaxis
Type text here
Lesson notes:
Common Core State Standard(s):SID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
c. Fit a linear function for a scatter plot that suggests a linear association.
College Career Readiness Standard(s):PSD402 Manipulate data from tables and graphs.
PSD602 Analyze and draw conclusions based on information from figures, tables, and graphs.
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Scatter Plot
a graph of paired data in which the data values are plotted as (x, y) coordinatesdependent variable (yaxis)
independent variable (xaxis)
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Correlation
• the degree to which two variables are associated
Positively Associated DataA relationship in paired data in
which the two sets of data tend to increase together.
(follows a pattern from the lower left to the upper right)
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Negatively Associated DataA relationship in paired data in
which one variable's values tend to increase when the other decreases,
and vice versa. (follows a pattern from the upper left to
the lower right)
Negatively Associated Data
Correlation
• the degree to which two variables are associated
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Approximately No CorrelationA relationship in paired data in which
there is no apparent pattern.
n
Correlation
• the degree to which two variables are associated
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Drag each scatter plot to the correct data correlation description.
Positively Associated
Negatively Associated
Approximately No Correlation
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Best Fit Line
A line of best fit is a straight line drawn through as many points as possible with approximately the same number of points above the line as there are below the line.
Positive Correlation
Negative Correlation
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Draw the line of best fit for the given scatter plot.
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What do you think?
The data below shows the relationship of hours 7th graders study a week and the grades they receive on a math test.
Hours Studying Math per Week
Percentage on Math Test
.25
.75
1
1.25
1.5
2.5
2.5
20
25
40
40
50
55
60
Based on the given information, about how many hours would a student need to spend studying per week to get an A (90% or better) on the math test?
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Now, let's use a best fit line to better answer this question...
Step 1:Graph the data.
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Reflection Questions
1. Why might you want to use a line of best fit?
2. What is the hardest part about finding the best fit line?
3. How sure are you that your best fit line will yield an accurate prediction?
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Is this a good line of best fit?
Why or why not?
Drag to reveal the answer
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Use the data and place the line of best fit.
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Which graph has the line of best fit?
What is wrong with the other graph?
This line just goes through the first and last data point. It does not have an equal number of points above and below the graph.
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Which graph has the line of best fit?
What is wrong with the other graph?
The data shows a negative correlation, but the line depicts a positive correlation.
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1
3
4
5
6
7
8
MAR MAY JUL SEP NOVAPR JUN AUG OCT DECFEBJAN
NUMBER OF SIBLINGS
SCATTER PLOT
BIRTHDAY MONTH
(drag the blue & green dots to graph the data for each class period)
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NO CORRELATION
* THE NUMBER OF SIBLINGS AND THE MONTH THAT YOU WERE BORN IN ARE NOT RELATED.
* THERE IS NO PATTERN
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6
5
7
8
9
10
11
12
60 62 64 66 6861 63 65 675856
HEIGHT IN INCHES
SHOE SIZE
SCATTER PLOT
4
(drag the blue & green dots to graph the data for each class period)
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POSITIVE CORRELATION
* TYPICALLY, THE TALLER A PERSON IS, THE BIGGER SHOE SIZE THAT PERSON WILL WEAR.
* THERE IS A PATTERN. Y INCREASES AS X INCREASES.
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3
2
4
5
6
7
8
9
60 62 64 66 6861 63 65 675856
HEIGHT IN INCHES
NUMBER OF LIMBOS
SCATTER PLOT
1
(drag the blue & green dots to graph the data for each class period)
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NEGATIVE CORRELATION
* TYPICALLY, THE TALLER THE PERSON IS, THE FEWER SUCCESSFUL LIMBOS THEY WILL HAVE.
* THERE IS A PATTERN.Y DECREASES AS X INCREASES
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Class Discussion
Can you think of any situations that model no correlation, positive
correlation or negative correlation?
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15 Scatter PlotsVocabulary Words:• scatter plot
• correlation
• line of best fit (trend line)
• positive correlation
• negative correlation
• no correlation
is a line that best represents the data on a scatter plot
- shows relationships between two sets of data
the relationship between two variables
the data displayed on the graph resembles a line rising from left to right
the data displayed on the graph resembles a line falling from left to right
the data displayed on the graph neither resembles a line rising nor falling from left to right
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15 Scatter Plots
Given the examples, what is the correlation?(positive, negative, or no correlation)
Pick a Picture
A Correlation can be Predicted without Having to Observe the Data in a Table or Graph.
TestYourself
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IncorrectIncorrectCorrect
IncorrectIncorrectCorrect
15 Scatter Plots
• Time spent studying and the grade on your test.
• Your grade point average and the number of A’s you receive.
NegativeNegative NoneNonePositivePositive
NegativeNegative NoneNonePositivePositive
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15 Scatter Plots
• The size of a person and the number of fingers he has
IncorrectNegativeNegativeIncorrectPositivePositive CorrectNoneNone
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15 Scatter Plots
• The weight and height of each member of a soccer team.
................
................
................
................
................
...........
IncorrectIncorrectCorrect NegativeNegative NoneNonePositivePositive
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IncorrectPositivePositive CorrectNegativeNegative
15 Scatter Plots
• The size of a car or truck and the number of miles per gallon of gasoline it can travel.
IncorrectNoneNone
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IncorrectNegativeNegative
15 Scatter Plots
• The number of telephones using the same cell phone number and the number of calls you receive.
IncorrectPositivePositive CorrectNoneNone
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15 Scatter Plots• The speed of a runner and the number of races he/she wins.
IncorrectIncorrectCorrect NegativeNegative NoneNonePositivePositive
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15 Scatter Plots
Test Yourself....write these down & answerDo the data sets have a positive, negative, or no correlation?
1. The minimum wage and the year
2. The amount of precipitation and the day of the week
3. The amount of germs on your hands and the number of times you wash your hands in a day
positive
no correlation
negative
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15 Scatter Plots
Correlation can also be shown in scatter plot using graphs for visual reference.
A trend line can be shown which is the line of best fit through the data points.
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15 Scatter Plots
Positive correlation; both data sets increase together.
Negative correlation; as one data set increases, the other decreases.
No correlation; as one data set increases, the other decreases.
Correlation as one data set increases, the other decreases.
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r = + 1.0 Strong Positive As X goes up, Y always also goes up
r = + 0.5 Weak Positive As X goes up, Y tends to usually also go up
r = 0 No Correlation X and Y are not correlated
r = 0.5 Weak Negative As X goes up, Y tends to usually go down
r = 1.0 Strong Negative As X goes up, Y always goes down
15 Scatter PlotsCorrelation Coefficient Relationship Between X & Y
"r" Value Interpretation
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© 2008 SMART Technologies ULC. All rights reserved.
Extraordinary made simple TM
Scatter Plots
Grade:
Subject:
8
Math
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True False
Scatter plots can be used to see relationships between 2 sets of data.
1 True or False
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Yes No
Is a line drawn through scatter plot data points to determine the direction of the relationship called a trend line?
2 Yes or No
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3 If a trend line has an upward direction, the relationship between the data topics can be described as a...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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4 If a trend line has a downward direction, the relationship between the data topics can be described as a...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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5 If a trend line cannot be drawn, the data topics can be described as having...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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6 The amount of time you have to spend with friends and the number of chores you have to do would have a...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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7 The amount of time you spend studying and your score on a test would likely have a...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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8 The number of cars you wash at a school car wash and the money you raise would have a...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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9 Your height and how much time you spend exercising would have...
A Negative Correlation
B No Correlation
C Positive Correlation
D Undefined Correlation
Multiple choice
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10 The size of an animal and how much food it needs each day would have a...
A Negative Correlation
B No Correlation
C Undefined Correlation
D Positive Correlation
Multiple choice
