Question

what is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? 1) 1.00 2) 0.93 3) -0.93 4) -1.00

Explanation:

Step1: Observe data trend

As x - values increase, y - values decrease, indicating a negative correlation.

Step2: Assess strength visually

The points seem to follow a relatively straight - line pattern, suggesting a strong correlation.

Step3: Recall correlation coefficient range

The correlation coefficient \(r\) ranges from - 1 to 1, where - 1 is a perfect negative linear correlation, 1 is a perfect positive linear correlation, and 0 is no linear correlation.

Step4: Eliminate non - negative options

Options 1) and 2) can be eliminated since they represent positive correlations.

Step5: Determine strength

Since the points almost lie on a straight line, the correlation is very strong, close to - 1. So the correlation coefficient is approximately - 0.93.

Answer:

1. - 0.93