Suppose that a scatter diagram depicts a relationship between two variables that can be summarized by a straight line. The correlation coefficient is computed and results in a value of –0.73. Which of the following statements is NOT true?

Question

BlackTom AI · Accepted Answer

A correlation of r = −0.73 indicates a moderately strong negative linear association: as one variable increases, the other tends to decrease.

1) Relevant concepts
- The Pearson correlation coefficient r ranges from −1 to +1. The sign indicates direction (negative = inverse, positive = direct) and the absolute value |r| indicates strength (values near 1 are strong, near 0 are weak). Correlation measures linear association, not causation.

2) Step-by-step reasoning
- r = −0.73: the negative sign implies an inverse relationship; therefore increases in one variable are generally associated with decreases in the other.
- |r| = 0.73: this is substantially larger than 0.5, so the linear relationship is moderate-to-strong.
- The problem states the scatter can be summarized by a straight line, which supports the interpretation of r as reflecting linear association.

3) Intermediate “calculations”/interpretations
- Determine direction: r < 0 ⇒ inverse association.
- Determine strength: |r| = 0.73 ⇒ moderately strong linear relationship.
- Range check: −1 ≤ r ≤ 1, so r = −0.73 is a valid correlation.

4) Why the correct choice is correct
- The statement "In general, an increase in one variable is associated with an increase in the other variable." asserts a positive (direct) association. That contradicts r = −0.73, which indicates an inverse (negative) association. Therefore this statement is NOT true, making it the correct selection for the question asking which statement is NOT true.

5) Why the other options are incorrect (i.e., they are true)
- "In general, an increase in one variable is associated with a decrease in the other variable." True because r is negative.
- "Even though the correlation coefficient is less than zero, it still communicates the strength of the linear relationship." True: the magnitude |r| measures strength regardless of sign.
- "There is a linear relationship between the two variables." True given the scatter is summarized by a straight line and the nonzero r indicates linear association.

6) Conclusion
The statement "In general, an increase in one variable is associated with an increase in the other variable." is NOT true for r = −0.73, which matches the provided answer.

Suppose that a scatter diagram depicts a relationship between two variables that can be summarized by a straight line. The correlation coefficient is computed and results in a value of –0.73. Which of the following statements is NOT true?单项选择题

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