Math Problem Statement
Solution
To solve the problem of determining the sample correlation coefficient (r) for the given data, let’s outline the steps:
Formula for Correlation Coefficient:
Where:
- : Number of data points
- : Sum of all -values (temperatures)
- : Sum of all -values (electricity usage)
- : Sum of the product of and for each row
- : Sum of the squares of -values
- : Sum of the squares of -values
Steps:
- Extract the given data:
- Temperature (), Electricity Use (), and the product ().
- Calculate:
- .
- Plug the values into the formula and compute .
- Round the result to three decimal places.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Relationships
Formulas
Sample Correlation Coefficient Formula: r = (n * Σxy - Σx * Σy) / sqrt((n * Σx^2 - (Σx)^2) * (n * Σy^2 - (Σy)^2))
Theorems
Linear Correlation Coefficient Theorem
Suitable Grade Level
Grades 10-12
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