Scatter Plots Notes and Worksheets - Lindsay Bowden - Free Printable

I will solve the problem by first completing the definitions at the top of the worksheet and then analyzing each of the four example scatter plots to determine their correlation type and estimate the r value.

Step 1: Complete the Definitions

Looking at the top section, I need to fill in the blanks for the definitions of "correlation" and "correlation coefficient (r)".

- Correlation: This is defined as the relationship between two variables in a data set.
- Correlation Coefficient (r): This measures the strength and direction of the relationship between two variables. The value of 'r' must be between -1 and 1.

So, the completed definitions are:
- correlation - the relationship between two variables in a data set
- correlation coefficient (r) - measures the strength and direction of the relationship between two variables in a data set
- *r must be between -1 and 1*

Step 2: Analyze the Example Scatter Plots

Now, I will analyze each of the four example scatter plots based on the definitions provided in the table above.

#### Example 1:
- The points show a general upward trend from left to right, indicating a positive correlation.
- However, the points are somewhat scattered and not tightly clustered around an imaginary line, suggesting a moderate correlation.
- Based on the guide, since it's positive but not very strong, the r value should be between 0 and 1, likely around 0.5 to 0.7.

#### Example 2:
- The points are very scattered with no discernible pattern or trend.
- This indicates no correlation.
- Therefore, the r value is approximately 0.

#### Example 3:
- The points show a clear downward trend from left to right, indicating a negative correlation.
- The points are tightly clustered around an imaginary straight line, suggesting a strong correlation.
- Since it's a strong negative correlation, the r value should be close to -1, perhaps around -0.9.

#### Example 4:
- The points show a very clear upward trend from left to right, indicating a positive correlation.
- The points are tightly clustered around an imaginary straight line, suggesting a very strong correlation.
- Since it's a strong positive correlation, the r value should be close to 1, perhaps around 0.9.

Final Answer

Here is the completed solution for the worksheet:

Definitions:
- correlation - the relationship between two variables in a data set
- correlation coefficient (r) - measures the strength and direction of the relationship between two variables in a data set
- *r must be between -1 and 1*

Examples:

1. Positive Correlation, estimated r value: ~0.6
* *Reasoning: The points trend upwards, indicating a positive relationship, but they are moderately spread out, suggesting a moderate strength.*

2. No Correlation, estimated r value: ~0
* *Reasoning: The points are randomly scattered with no clear upward or downward trend.*

3. Negative Correlation, estimated r value: ~-0.9
* *Reasoning: The points trend sharply downwards, indicating a strong negative relationship, and they are tightly clustered.*

4. Positive Correlation, estimated r value: ~0.9
* *Reasoning: The points trend sharply upwards, indicating a strong positive relationship, and they are tightly clustered.*