Final answer:
Scatter plots are classified based on the correlation between the variables: a plot with data points moving in the same direction shows a positive correlation, while one with data points moving in opposite directions indicates a negative correlation. A plot with no discernible pattern signifies no correlation.
Step-by-step explanation:
When analyzing scatter plots, we categorize the relationship between the variables based on the direction and strength of the association between them. The categories of correlation are:
- Positive correlation: This occurs when the variables tend to move in the same direction. As one variable increases, the other variable also tends to increase.
- Negative correlation: This happens when the variables move in opposite directions. As one variable increases, the other variable tends to decrease.
- No correlation or Zero correlation: In this case, there is no discernible pattern in the way the variables move relative to each other.
To classify the scatter plots based on the given correlations:
- A scatter plot with data showing a positive correlation, where 0 < r < 1, should be classified as having a positive correlation.
- A scatter plot with data showing a negative correlation, where -1 < r < 0, should be classified as having a negative correlation.
- If a scatter plot shows data with a correlation coefficient of r = 0, it should be classified as having no correlation.
Examples could include the positive correlation between weight and height, the negative correlation between tiredness and hours of sleep, or no correlation between shoe size and hours of sleep.
The sign of the correlation coefficient (positive or negative) indicates the direction of the relationship between the variables. It's also essential to use regression analysis and calculate the correlation coefficient to determine the strength and significance of the relationship.