Answer:
1. The explanatory variable is age(years). TRUE
2. Since the points do not consistently decrease it is a weak correlation. FALSE
3. The slope of the liner regression line used to model the data will be negative. TRUE
4. The point (32, 17) represents someone who is 32 years old and has 17 pairs of shoes. TRUE
5. The explanatory variable is the number of pairs of shoes. FALSE
6. There is a positive correlation between a person's age in years and the number of pairs of shoes they own. FALSE
Step-by-step explanation:
Variables
In a scatter plot, the explanatory variable is the independent variable and is typically plotted along the horizontal axis (x-axis), while the response variable is the dependent variable and is plotted along the vertical axis (y-axis). So, in this case:
- The explanatory variable is age (years).
- The response variable is the number of pairs of shoes.
The x-coordinate of an (x, y) point on the given scatter plot represents the age of the person (in years), and the y-coordinate represents the number of pairs of shoes that person owns. Therefore, the point (32, 17) represents someone who is 32 years old and owns 17 pairs of shoes.
Correlation
Correlation shows how two variables are related and is about whether the data points on a scatter plot lie close to a straight line.
Correlation can be:
- Positive (both variables increase together).
- Negative (the independent variable increases as the dependent variable decreases).
- No correlation (no apparent relationship).
The strength of the correlation is not determined by the consistency of individual points increasing or decreasing, but by how closely the points cluster around a straight line.
- If the points are tightly clustered around a line, the correlation is strong, even if individual points do not perfectly increase or decrease in a consistent manner.
- If the points are widely scattered around the line, the correlation is weak.
In the given scatter plot, as age increases, the number of pairs of shoes decreases, and the data points tightly cluster around the line of best fit. Therefore, the correlation between a person's age in years and the number of pairs of shoes they own is strongly negative, resulting in a negative slope for the linear regression line used to model the data.
