Questions: Zhenghan notices a strong correlation between whether a person is a freshman, sophomore, junior, or senior in college and the number of credit hours that a student has registered for. As students' years in college increase, they tend to register for fewer credit hours. Based on this information, the correlation coefficient between years in college and number of credit hours is closest to: +0.70 -0.20 +0.20 -0.70

Zhenghan notices a strong correlation between whether a person is a freshman, sophomore, junior, or senior in college and the number of credit hours that a student has registered for. As students' years in college increase, they tend to register for fewer credit hours. Based on this information, the correlation coefficient between years in college and number of credit hours is closest to: +0.70 -0.20 +0.20 -0.70
Transcript text: Zhenghan notices a strong correlation between whether a person is a freshman, sophomore, junior, or senior in college and the number of credit hours that a student has registered for. As students' years in college increase, they tend to register for fewer credit hours. Based on this information, the correlation coefficient between years in college and number of credit hours is closest to: $+0.70$ $-0.20$ $+0.20$ $-0.70$
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Solution

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Solution Steps

Step 1: Understand the relationship described

Zhenghan observes that as students' years in college increase (from freshman to senior), they tend to register for fewer credit hours. This indicates a negative relationship between years in college and the number of credit hours.

Step 2: Interpret the correlation coefficient

A correlation coefficient measures the strength and direction of a linear relationship between two variables. A positive value indicates a positive relationship, while a negative value indicates a negative relationship. The magnitude (absolute value) indicates the strength, with values closer to 1 or -1 representing stronger relationships.

Step 3: Match the relationship to the correlation coefficient

Since the relationship is negative (as years in college increase, credit hours decrease), the correlation coefficient must be negative. Additionally, the relationship is described as "strong," so the magnitude should be closer to -1. Among the options, \(-0.70\) is the closest to a strong negative correlation.

Final Answer

\(\boxed{-0.70}\)

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