Question

1. the table shows the heights and the lengths of several rectangles. what does the correlation coefficient indicate about the strength of the linear association between the height and the length of these rectangles? a. weak, negative correlation c. weak, strong correlation b. strong, negative correlation d. strong, positive correlation

Explanation:

Step1: Analyze the data trend

As height increases, length does not follow a clear increasing or decreasing pattern. For example, when height is \(10\) (first occurrence), length is \(16\); when height is \(10\) (second occurrence), length is \(45\).

Step2: Recall correlation coefficient rules

A correlation coefficient close to \(0\) indicates a weak correlation. Since there is no consistent upward (positive) or downward (negative) trend, we check the options.

• Option a: Weak, negative correlation. There is no strong downward trend.
• Option b: Strong, negative correlation. No strong downward trend.
• Option c: Weak, strong correlation. Incorrect description (should be weak or strong, not both).
• Option d: Strong, positive correlation. No strong upward trend.

Answer:

a. Weak, negative correlation