Correlation Coefficient Quiz

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| By Stickrathbrent
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Stickrathbrent
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Questions: 5 | Attempts: 1,044

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• 1.

• 2.

• 3.

• 4.

The coefficient of determination, r, indicates

• A.

The linear relationship between two variables

• B.

The slope of the line of best fit

• C.

How closely the data fit a defined curve

• D.

The sum of the residuals from each data point

A. The linear relationship between two variables
Explanation
The coefficient of determination, r, indicates the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of 1 indicates a perfect positive linear relationship, 0 indicates no linear relationship, and -1 indicates a perfect negative linear relationship. It is a measure of how well the data points fit a straight line, with higher values indicating a stronger linear relationship. Therefore, the correct answer is "the linear relationship between two variables."

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• 5.

Which of the following statements is false?

• A.

The coefficient of determination can have values from –1 to 1.

• B.

The coefficient of determination can be applied to any curve.

• C.

The coefficient of determination can be applied to any straight line.

• D.

The coefficient of determination is the variation in y explained by variation in x, divided by the total variation in y.

• E.

The magnitude of the correlation coefficient determines the strength of the linear relationship

• F.

The sign of the correlation coefficient determines whether the relationship is positive or negative

B. The coefficient of determination can be applied to any curve.
Explanation
The coefficient of determination, also known as R-squared, measures the proportion of the variation in the dependent variable (y) that can be explained by the independent variable (x). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect relationship. The coefficient of determination can only be applied to linear relationships, not curves. Therefore, the statement "The coefficient of determination can be applied to any curve" is false.

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• Current Version
• Mar 20, 2023
Quiz Edited by
ProProfs Editorial Team
• Aug 17, 2014
Quiz Created by
Stickrathbrent

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