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50.	Estimate whether the following pairs of scores for X and Y reflect a positive relationship, a negative relationship, or no relationship. Hint: Note any tendency for pairs of X and Y scores to occupy similar or dissimilar relative locations

Construct a scatterplot for X and Y. Verify that the scatterplot does not describe a pronounced curvilinear trend.

The scatterplot above shows the relationship between the X and Y values. From the plot, it is evident that as \( X \) increases, \( Y \) tends to decrease. This suggests a **negative relationship** between the two variables, as higher values of \( X \) are associated with lower values of \( Y \).

Additionally, the data points do not form a pronounced curvilinear pattern, so the relationship appears to be linear rather than curvilinear.

Would you like more details or have any further questions?

Here are five related questions for further exploration:
1. How can we calculate the correlation coefficient to quantify the strength of the relationship between \( X \) and \( Y \)?
2. How would a linear regression line look on this scatterplot?
3. What other types of relationships (positive or curvilinear) might occur between variables, and how can they be identified?
4. What happens if we add more data points to this scatterplot? Would the negative trend still hold?
5. How can we test if the relationship between \( X \) and \( Y \) is statistically significant?

**Tip:** The correlation coefficient \( r \) ranges from -1 to 1. A value near -1 indicates a strong negative linear relationship, while a value near 1 indicates a strong positive relationship.

Estimate whether the following pairs of scores for X and Y reflect a positive relationship, a negative relationship, or no relationship. Hint: Note any tendency for pairs of X and Y scores to occupy similar or dissimilar relative locations. Construct a scatterplot for X and Y. Verify that the scatterplot does not describe a pronounced curvilinear trend.

Explore how to construct a scatterplot to analyze the relationship between X and Y values. Determine if there is a negative or positive linear relationship using core concepts such as correlation coefficients and linear regression. Suitable for students in Grades 10-12.

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