Math Problem Statement
Compute the linear correlation coefficient between the weight of a car and its miles per gallon. three decimal places Car Weight (lbs) Miles per Gallon
Car 1 3,765 21
Car 2 3,944 17
Car 3 3,530 21
Car 4 3,175 22
Car 5 2,580 27
Car 6 3,730 18
Car 7 2,605 26
Car 8 3,772 17
Car 9 3,310 20
Car 10 2,991 25
Car 11 2,752 26
Solution
The linear correlation coefficient between the weight of a car and its miles per gallon is , indicating a strong negative correlation. This suggests that as the weight of the car increases, the miles per gallon generally decrease.
Would you like further details or have any questions?
Here are some related questions for further exploration:
- How is the strength of a correlation interpreted based on the correlation coefficient?
- What factors might explain the negative correlation between weight and fuel efficiency?
- Can we use this correlation to make predictions about other cars’ fuel efficiency based on their weight?
- What is the importance of examining the correlation before making decisions in vehicle design?
- How would removing one of the outlier data points affect the correlation coefficient?
Tip: Remember, correlation does not imply causation—it only measures the relationship, not the reason one variable affects the other.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Correlation Coefficient
Formulas
Pearson correlation coefficient formula
Theorems
Pearson's correlation theorem
Suitable Grade Level
Grades 11-12
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