Math Problem Statement

Use a calculator to verify that

x = 64,

x2 = 1126,

y = 630,

y2 = 88,950, and

xy = 9,720.

Compute r. (Round your answer to four decimal places.)

Solution

To compute rr, we’ll use the formula for the Pearson correlation coefficient:

[ r = \frac{{n \cdot (xy) - (x \cdot y)}}{{\sqrt{[n \cdot x^2 - (x)^2] \cdot [n \cdot y^2 - (y)^2]}}} ]

Given values are:

  • x=64x = 64
  • x2=1126x^2 = 1126
  • y=630y = 630
  • y2=88950y^2 = 88950
  • xy=9720xy = 9720

We need to confirm the values for nn (which represents the number of data pairs). Without this, we can’t fully compute rr. Could you provide the value of nn, or should I assume a specific value?

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation

Formulas

Pearson correlation coefficient formula: r = (n * xy - x * y) / sqrt((n * x^2 - x^2) * (n * y^2 - y^2))

Theorems

Pearson correlation theorem

Suitable Grade Level

Grades 10-12