Download Parts of a Scatter Plot

Semester B: Unit 2:Scatter Plots
Lesson1: Interpret Scatter Plots
Scatter Plot: a graph in which 2 variables are plotted along the x and y axis. The
purpose of a scatter plot is to show the relationship between the 2 variables
Parts of a Scatter Plot:
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If you are given a table, you can plot the points on a graph to create a scatter plot.
The first point is the x coordinate and the second point is the y coordinate.
Example:
Relationships on a Scatter Plot: you can determine what kind of relationship exists
(if there is one) between the 2 variables.
Example: As the tree gets older, the height increases
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Example: As the number of people in a family increases, the time spent cleaning
the house decreases
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Examples and Notes from Class:
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Lesson 2: Draw Scatter Plots
First Variable: plot on the x axis.
Second Variable: plot on the y axis
Draw a Scatter Plot:
1. Determine the label for the x and y axis.
2. Determine a scale for each axis (the scale does NOT have to be the same on
each axis)
The scale is the number you count by and label on the axis
3. Determine a title for the Scatter Plot
4. Plot the points on the graph
Example:
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Notes from Class:
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Lesson 3: Correlation of Scatter Plots
Positive Correlation: both variables are increasing
Example: As temperature increases, sales of ice cream cones increases
Negative Correlation: one variable increases and one variable decreases
Example: as the cost of an ice cream cone increases, the number sold decreases
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No Correlation: there is no relationship between the 2 variables
Example: there is no relationship between and number of flavors of ice cream and
the number of cones sold
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Determine the Correlation from a Table: follow the pattern for the x and y values
Example:
Chart A: x values are increasing in a pattern of 1; y values show no pattern
No Correlation
Chart C: x values increasing in a pattern of 1; y values decreasing in a pattern of 2
Negative Correlation
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Notes and Examples from Class
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Lesson 4: Linear and Non-Linear Scatter Plots
Perfect Linear Association: when variables change at a constant rate. The pattern
of change is constant for both variables. When you connect the points, it will be a
straight line. (This does NOT mean that the pattern is the same for both variables,
just constant)
Example:
Non-Perfect Linear Association: the points will generally fall in a straight line, but
not exactly.
Example:
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Non-Linear Association: the data appears as a curved instead of a straight line.
The pattern of both variables is not constant (it may be constant for 1 variable).
There is a relationship between the 2 variables, but it is not linear
Example:
x variable: increases by 1
y variable: increases at first, then decreases
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Notes and Examples from Class
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Lesson 6: Clusters and Outliers
Cluster: group of points that are close together
Example: most of the points are in a group near each other. This scatter plot
shows a negative correlation
Example: there is 1 cluster. This scatter plot shows a positive correlation
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Outlier: a point that does not fall in the main pattern of a scatter plot. On a graph,
an outlier is not close to the other points.
Example:
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Notes and Examples from Class:
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Lesson 7: Identify a Line of Best Fit for a Scatter Plot
Line of Best Fit: line that shows the general direction of the points on a scatter
plot
Example:
Examples of Poorly drawn Lines of Best Fit:
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Notes and Examples from Class:
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Lessons 8: Define the Equation for the Line of Best Fit for a Scatter Plot
Step 1: draw the line of best fit: a straight line that falls in the middle of the
data and represents the data as best it can
Step 2: choose 2 points on the line of best fit the go directly through the line or
the 2 points closest to the line
Step 3: use the coordinates of the 2 points chosen in step 2 and the slope formula
to find the slope of the line
Step 4: substitute the slope and the x and y values of 1 point into y = mx + b.
Solve the equation for b
Step 5: write the equation of the line in slope intercept form,
substituting the slope for m and the y-intercept for b: y = mx + b
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Example:
Steps 1 and 2: Draw the Line
of Best Fit & choose
2 points on the line
Step 3:
Find the
slope using
2 points
chosen in
step 2
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Step 4: Use the point (1, 950) for x and y and the slope 150 for m. Substitute into
y = mx + b to find the value of b
Step 5: Write the equation of the line of best fit in slope-intercept form: y = mx +b
m = 150, b = 800
y = 150x + 800
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Notes and Examples from Class:
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Lesson 9: Calculate the Correlation Coefficient for a Data Set
Correlation Coefficient: shows how closely two sets of data are related. It uses a
value between -1 and +1.
Values closer to +1 (like 0.9 or 0.88) show the data has a positive correlation:
(both variables are increasing)
Values closer to -1 (like -0.95 or -0.89) show the data has a negative correlation:
(one variable is increasing, one variable is decreasing)
Value of 0 means there is no correlation between the variables
To find the Correlation Coefficient, you must complete a Correlation Table
Example:
Step 1: find the mean (average) of the x and y values
Step 2: subtract each x value from the mean (represented by the variable a)
subtract each y value from the mean (represented by the variable b)
Step 3: calculate a • b; a2 and b2
Step 4: find the sums of a • b; a2 and b2
Step 5: use the formula to calculate the correlation coefficient
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Formula for the Correlation Coefficient:
Substitute 51 for a • b,
10 for a2
and
329.2 for b2
51 ÷ 57.38 = .89
Correlation Coefficient = .89 shows a strong, positive relationship. You can see
that from the scatter plot as well. The dots are relatively close together.
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Notes and Examples from Class
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