Absolutely! Let’s solve the worksheet step by step, filling in the blanks and analyzing each scatter plot example.
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Part 1: Fill in the Blanks
1. Correlation – the relationship between two variables in a data set
> *Explanation:* Correlation describes how two variables are related — whether they tend to increase or decrease together, or have no clear pattern.
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2. Correlation coefficient (r) – measures the strength and direction of the relationship between two variables in a data set
> *Explanation:* The correlation coefficient “r” quantifies both how strong the relationship is (close to 0 = weak; close to ±1 = strong) and whether it’s positive (both increase) or negative (one increases as the other decreases).
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3. *r must be between -1 and 1*
> *Explanation:* The value of r always falls in this range. -1 means perfect negative linear correlation, +1 means perfect positive linear correlation, and 0 means no linear correlation.
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Part 2: Analyze Each Scatter Plot Example
We’ll determine:
- Type of correlation (Positive, Negative, or No)
- Estimated r value (based on how tightly clustered the points are around an imaginary line)
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Example 1:
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Observation: Points generally trend upward from left to right →
positive correlation. However, there’s some scatter — not perfectly aligned.
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Estimated r value: Around
0.6 to 0.7 — moderate to strong positive correlation.
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✔ Answer: Positive correlation, r ≈ 0.65
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Example 2:
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Observation: Points are scattered randomly with no clear upward or downward trend →
no correlation.
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Estimated r value: Very close to
0.
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✔ Answer: No correlation, r ≈ 0
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Example 3:
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Observation: Points form a very clear downward-sloping line →
strong negative correlation.
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Estimated r value: Very close to
-1, maybe
-0.95.
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✔ Answer: Negative correlation, r ≈ -0.95
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Example 4:
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Observation: Points form a very tight upward-sloping line →
very strong positive correlation.
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Estimated r value: Close to
+1, maybe
0.95.
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✔ Answer: Positive correlation, r ≈ 0.95
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✔ Final Answers Summary:
Fill-in-the-blanks:
- Correlation – the
relationship between two variables...
- Correlation coefficient (r) – measures the
strength and
direction...
- *r must be between
-1 and
1*
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Examples:
1.
Positive correlation, r ≈
0.65
2.
No correlation, r ≈
0
3.
Negative correlation, r ≈
-0.95
4.
Positive correlation, r ≈
0.95
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Let me know if you’d like to graph these or calculate exact r values using formulas — but for this worksheet, estimation based on visual pattern is what’s expected! 📊
Parent Tip: Review the logic above to help your child master the concept of free scatter plot worksheet.
