Identify scatterplots associated with the three types of relationships between variables.
Understand that correlation does not imply causation.
Review
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1. Correlation is a statistical measure of the strength of the relationship between two variables—that is, the extent to which scores on the two variables go up or down together. A scatterplot provides a visual representation of the relationship. This scatterplot shows the relationship between study hours per week and GPA.
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2. Two variables are positively correlated if they systematically vary in the same direction, increasing or decreasing together. In this example, a person with a high score on the height variable would also tend to have a high score on the weight variable.
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3. Two variables are negatively correlated if they vary systematically in the opposite direction, with one increasing while the other decreases. In this example of drinking and dexterity (physical coordination), a person with a high score on one variable would tend to have a low score on the other variable.
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4. If two variables have no correlation (zero correlation), a person with a high score on one variable (such as height) is equally likely to have either a high or a low score on the other variable (such as GPA). Knowing one score tells you nothing about the other score.
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5. If two variables are correlated (either positively or negatively), then a person's score on one variable (such as a person’s height) can be used to predict or estimate the likely score on the other variable (such as a person’s arm span).
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6. A correlation between two variables does not indicate that one variable influences the other variable. In other words, correlation does not imply causation. For example, between the years 2002 and 2010, U.S. traffic fatalities fell steadily as the number of doctoral degrees in computer science increased (a negative correlation), but no one believes that the number of computer scientists had anything to do with this reduction in traffic accidents!
Practice 1: Constructing a Scatterplot
Select each of the student names to plot that student’s location on the graph. Then, select the NEXT button and move to Practice 2.
A correlation describes a relationship between two variables. Correlations are usually shown on a graph called a scatterplot. Each point on a scatterplot represents a single person or thing.
We can construct a scatterplot from the scores in this table. As you select each student name, that student's score for each variable is shown as a dotted line, with a point for that student added to the graph at the intersection of the two lines.
Practice 2: The Correlation Coefficient
Select each button to see examples of the three types of scatterplots. Then, select the NEXT button and move to Quiz 1.
The correlation coefficient (r) is a precise measure of the strength of the relationship between the two variables. The relationship can take three forms: positive correlation (r up to +1.0), negative correlation (r as low as –1.0) or no correlation (r near zero).
Quiz 1
Drag each term at the top of the screen to the gray area above the appropriate scatterplot. When all the terms have been placed, select the CHECK ANSWER button.
Quiz 2
Match the terms to the descriptions by dragging each colored circle to the appropriate gray circle. When all the circles have been placed, select the CHECK ANSWER button.
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