Question

what is the correlation coefficient for the data shown in the table?

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$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 0 & 0 \\\\\\hline 1 & 1 \\\\\\hline 4 & 4 \\\\\\hline 5 & 5 \\\\\\hline\\end{array}$$

\\)

options:

• 1
• 0
• 4
• 5

Explanation:

Analyze the data points

The given data points from the table are:

$$ (x, y) \in \{(0, 0), (1, 1), (4, 4), (5, 5)\} $$

Determine the relationship

For every data point in the set, the value of \(y\) is exactly equal to \(x\):

$$ y = x $$

Calculate the correlation coefficient

Since all data points lie perfectly on a straight line with a positive slope (\(m = 1\)), there is a perfect positive linear relationship. Therefore, the Pearson correlation coefficient \(r\) is:

$$ r = 1 $$

Answer:

• 1 (Correct answer)
• 0
• 4
• 5