4.3 Correlation Coefficient

Front

What is the correlation coefficient?

Back

The correlation coefficient is a statistic that measures the strength and direction of a linear association between two quantitative variables.

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CCSS.HSS.ID.C.8

Front

What does a correlation coefficient of 0 indicate?

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A correlation coefficient of 0 indicates no correlation between the two variables.

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CCSS.HSS.ID.B.5

Front

What does a positive correlation coefficient signify?

Back

A positive correlation coefficient signifies that as one variable increases, the other variable also tends to increase.

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CCSS.HSS.ID.B.5

Front

What does a negative correlation coefficient signify?

Back

A negative correlation coefficient signifies that as one variable increases, the other variable tends to decrease.

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CCSS.HSS.ID.B.5

Front

What is the range of values for the correlation coefficient?

Back

The correlation coefficient ranges from -1 to +1.

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CCSS.HSS.ID.C.8

Front

What does a correlation coefficient of +1 indicate?

Back

A correlation coefficient of +1 indicates a perfect positive linear relationship between two variables.

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CCSS.HSS.ID.B.5

Front

What does a correlation coefficient of -1 indicate?

Back

A correlation coefficient of -1 indicates a perfect negative linear relationship between two variables.

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CCSS.HSS.ID.B.5

Front

What is the meaning of r² in correlation analysis?

Back

r², or the coefficient of determination, indicates the proportion of variance in the dependent variable that can be explained by the independent variable.

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CCSS.HSS.ID.B.6B

Front

If r² = 0.46, what does this imply about the data?

Back

If r² = 0.46, it implies that 46% of the variance in the dependent variable is explained by the independent variable, indicating a moderate relationship.

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CCSS.HSS.ID.B.6B

Front

What does a weak positive correlation look like on a scatter plot?

Back

A weak positive correlation on a scatter plot shows points that are loosely clustered around an upward sloping line.

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CCSS.HSS.ID.B.5