Math Problem Statement

Compute the sample correlation coefficient. (Round your answer to three decimal places.)

Solution

To compute the sample correlation coefficient (r), we need to know the data points for two variables, XX and YY. The formula for the sample correlation coefficient is:

r=nxy(x)(y)(nx2(x)2)(ny2(y)2)r = \frac{n \sum{xy} - \left( \sum{x} \right) \left( \sum{y} \right)}{\sqrt{ \left( n \sum{x^2} - \left( \sum{x} \right)^2 \right) \left( n \sum{y^2} - \left( \sum{y} \right)^2 \right) }}

Where:

  • nn is the number of data points,
  • xx and yy are the individual data points for the two variables,
  • xy\sum{xy} is the sum of the products of corresponding values of xx and yy,
  • x\sum{x} and y\sum{y} are the sums of the values of xx and yy,
  • x2\sum{x^2} and y2\sum{y^2} are the sums of the squares of the values of xx and yy.

Could you please provide the data points for xx and yy, or upload a file with them?

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Data Analysis

Formulas

r = (n Σxy - (Σx)(Σy)) / sqrt((n Σx^2 - (Σx)^2) * (n Σy^2 - (Σy)^2))

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

College-Level Statistics or Advanced High School