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 0.945-0.945, 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:

  1. How is the strength of a correlation interpreted based on the correlation coefficient?
  2. What factors might explain the negative correlation between weight and fuel efficiency?
  3. Can we use this correlation to make predictions about other cars’ fuel efficiency based on their weight?
  4. What is the importance of examining the correlation before making decisions in vehicle design?
  5. 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