Math Problem Statement

∑x=2582 (Sum of heights), 

∑y=390 (Sum of foot sizes) 

∑x2= 445430 

 ∑y2= 10167.5 

∑xy= 67293.5    Now, we substitute these into the Pearson correlation formula: 

r= n ∑xy− 

∑x∑y/(n∑x2−(∑x)2) (n∑y2−(∑y)2) 

Solution

The Pearson correlation coefficient formula is:

r=n∑xy−(∑x)(∑y)(n∑x2−(∑x)2)(n∑y2−(∑y)2)r = \frac{n \sum xy - (\sum x)(\sum y)}{\sqrt{(n \sum x^2 - (\sum x)^2)(n \sum y^2 - (\sum y)^2)}}

Given values:

  • ∑x=2582\sum x = 2582 (Sum of heights)
  • ∑y=390\sum y = 390 (Sum of foot sizes)
  • ∑x2=445430\sum x^2 = 445430
  • ∑y2=10167.5\sum y^2 = 10167.5
  • ∑xy=67293.5\sum xy = 67293.5
  • nn (sample size) is unknown.

Could you confirm the sample size nn so we can proceed with the calculation?

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Pearson Correlation Coefficient

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

Undergraduate Statistics / High School Advanced Math

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