Math Problem Statement
accurately match these values of r with the accompanying 5 scatter plots : 0.767, 1, -1, -0.767, and -0.396.
accurately match these values of r with the accompanying 5 scatter plots: 0.767, 1, -1, -0.767, and -0.396.
Solution
To match the correlation coefficients (r-values) , , , , and with the given scatter plots, let's first understand what the r-values represent:
- r = 1: This indicates a perfect positive linear relationship. The points should lie on a straight line with a positive slope.
- r = -1: This indicates a perfect negative linear relationship. The points should lie on a straight line with a negative slope.
- r = 0.767: This suggests a strong positive correlation, but not perfect. The points should generally follow a positive trend but may have some scatter.
- r = -0.767: This suggests a strong negative correlation, but not perfect. The points should generally follow a negative trend but may have some scatter.
- r = -0.396: This indicates a weaker negative correlation. There is still a downward trend, but the points will be more scattered.
Scatterplot Observations:
- Scatterplot 1: The points show a negative linear relationship. This indicates a strong negative correlation, likely r = -1.
- Scatterplot 2: The points are scattered with no clear trend, but there appears to be a slight negative correlation. This likely corresponds to r = -0.396.
- Scatterplot 3: The points are scattered, but there's a slight positive trend, corresponding to a lower positive correlation. This should correspond to r = 0.767.
- Scatterplot 4: The points lie on a straight line with a positive slope, indicating a perfect positive correlation, r = 1.
- Scatterplot 5: The points have a general negative trend with some scatter, likely indicating r = -0.767.
Final Matching:
- Scatterplot 1:
- Scatterplot 2:
- Scatterplot 3:
- Scatterplot 4:
- Scatterplot 5:
Would you like further details or have any questions on correlation and scatter plots?
Relative Questions:
- What does a correlation coefficient of 0 imply about the scatter plot?
- How can outliers affect the value of r in a scatter plot?
- What is the difference between positive and negative correlations?
- How can we visually identify if a scatter plot has a weak or strong correlation?
- Can non-linear relationships have a high correlation coefficient?
Tip:
The closer the r-value is to 1 or -1, the stronger the linear relationship. A value near 0 suggests little to no linear relationship.
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Math Problem Analysis
Mathematical Concepts
Correlation Coefficient
Scatter Plots
Linear Relationships
Formulas
Correlation coefficient formula
Linear equation y = mx + b
Theorems
Pearson's Correlation Coefficient
Suitable Grade Level
Grades 10-12