Mathematics
Grade 9
15 min
Match correlation coefficients to scatter plots
Match correlation coefficients to scatter plots
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1
Introduction & Learning Objectives
Learning Objectives
Define scatter plots and the correlation coefficient (r).
Identify the direction (positive, negative, or no correlation) of a relationship from a scatter plot.
Describe the strength (strong, moderate, or weak) of a linear relationship shown in a scatter plot.
Estimate the value of the correlation coefficient (r) for a given scatter plot.
Match a given correlation coefficient to the most appropriate scatter plot from a set of options.
Explain the difference in strength and direction between correlation coefficients like r = 0.9 and r = -0.9.
Recognize that a strong correlation does not necessarily mean one variable causes the other.
Does the number of hours you study affect your test scores? 📈 A scatter plot can show us the relationship, and a single nu...
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Key Concepts & Vocabulary
TermDefinitionExample
Scatter PlotA graph that uses dots to represent the values for two different numeric variables. Each dot shows the values of two variables for a single piece of data.A plot where each dot represents a student, with the x-axis showing 'Hours Studied' and the y-axis showing 'Test Score'.
Correlation Coefficient (r)A number between -1 and +1 that measures the direction and strength of the linear relationship between two variables.If the correlation between study hours and test scores is r = 0.85, it indicates a strong, positive linear relationship.
Positive CorrelationWhen one variable tends to increase as the other one increases. The points on the scatter plot generally trend upwards from left to right.As the number of hours you work at a job increa...
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Core Formulas
Range of the Correlation Coefficient (r)
-1 \le r \le 1
The value of 'r' will always be between -1 and 1, inclusive. A value of r = 1 represents a perfect positive linear correlation. A value of r = -1 represents a perfect negative linear correlation. A value of r = 0 means there is no linear correlation.
Interpreting the Sign of r
Sign(r) = Direction
The sign of the 'r' value tells you the direction of the correlation. If r > 0, the correlation is positive (points trend up). If r < 0, the correlation is negative (points trend down).
Interpreting the Magnitude of r
|r| = Strength
The absolute value of 'r' tells you the strength of the correlation. The closer |r| is to 1, the stronger the linear relationship. The closer |r| is to 0,...
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Challenging
[Image of a scatter plot with a moderate positive correlation, but with one outlier point in the bottom-right corner.] If the outlier in the bottom-right corner were removed, what would be the most likely impact on the correlation coefficient (r)?
A.r would increase (become a stronger positive value).
B.r would decrease (become a weaker positive value).
C.r would become negative.
D.r would not change.
Challenging
[Image of a scatter plot showing points that form a clear U-shape (a parabola opening upwards).] Which of the following is the most likely correlation coefficient for this data?
A.r = 0.9
B.r is close to 0
C.r = -0.9
D.r = 0.5
Challenging
A teacher plots student's shoe size versus their score on a history test. The scatter plot shows points scattered randomly all over the graph. The teacher then notices that the student with the highest score also happens to have the largest shoe size, creating a point far to the top right. What is the most likely correlation for the data *before* and *after* noticing this student?
A.Before: r ≈ 0.8; After: r ≈ 0.9
B.Before: r ≈ -0.5; After: r ≈ 0.5
C.Before: r ≈ 0; After: r ≈ 0.4
D.Before: r ≈ 0.4; After: r ≈ 0
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