Problem Analysis:
The task involves interpreting the correlation coefficients ($r$) provided for different datasets and determining the type of correlation (positive, negative, strong, weak) based on the values of $r$. The correlation coefficient $r$ ranges from -1 to 1, where:
- $r = 1$: Perfect positive correlation.
- $r = -1$: Perfect negative correlation.
- $r = 0$: No correlation.
- Values closer to 1 or -1 indicate a stronger correlation, while values closer to 0 indicate a weaker correlation.
Solution:
####
1. Heights and Weights of Athletes
-
Correlation Coefficient ($r$): +0.8915
-
Interpretation:
- The value of $r$ is positive and close to 1.
- This indicates a
strong positive correlation between the heights and weights of athletes.
- As height increases, weight tends to increase as well.
####
2. Number of Absences and Final Grades
-
Correlation Coefficient ($r$): -0.9525
-
Interpretation:
- The value of $r$ is negative and close to -1.
- This indicates a
strong negative correlation between the number of absences and final grades.
- As the number of absences increases, final grades tend to decrease.
####
3. Weight of Cars and Fuel Efficiency
-
Correlation Coefficient ($r$): -0.8685
-
Interpretation:
- The value of $r$ is negative and relatively close to -1.
- This indicates a
strong negative correlation between the weight of cars and their fuel efficiency.
- As the weight of a car increases, its fuel efficiency tends to decrease.
####
4. Year and Annual Admissions
-
Correlation Coefficient ($r$): +0.2780
-
Interpretation:
- The value of $r$ is positive but relatively close to 0.
- This indicates a
weak positive correlation between the year and annual admissions.
- As the year progresses, there is a slight tendency for annual admissions to increase, but the relationship is not very strong.
Final Answers:
1.
Strong positive correlation
2.
Strong negative correlation
3.
Strong negative correlation
4.
Weak positive correlation
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{Strong positive correlation} \\
2. \text{Strong negative correlation} \\
3. \text{Strong negative correlation} \\
4. \text{Weak positive correlation}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of correlation coefficient worksheets.
