Math Problem Statement

Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between X and Y.

Solution

The correlation coefficient rr between XX (year) and YY (high temperature) is approximately r=0.795r = 0.795.

This indicates a strong positive correlation between the two variables.

Would you like further details or have any questions?

Here are 5 related questions:

  1. What does a positive correlation coefficient imply in this context?
  2. How would a correlation coefficient of 1.0 differ from 0.795?
  3. What is the significance of the correlation coefficient in climate studies?
  4. Can correlation alone prove causation between two variables?
  5. What would a correlation coefficient close to 0 indicate about the relationship?

Tip: The closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the two variables.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Linear Regression

Formulas

Correlation coefficient formula: r = Σ[(X - X̄)(Y - Ȳ)] / sqrt[Σ(X - X̄)^2 Σ(Y - Ȳ)^2]

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

Grades 10-12