Question

Which of the following properties are associated with variables? Choose all that apply.

a. They pass data between activities.
b. They have directions like In, Out, In/Out.
c. They require a defined scope.
d. There must be at least one activity in the designer panel to create variables.

Answer 1

In mathematical and statistical contexts, variables can have different properties. The independent variable is controlled or manipulated while the dependent variable is observed. Scatter plots and regression analysis are used to determine the relationship between variables, with the correlation coefficient indicating the strength and direction of this relationship.

Step-by-step explanation:

When discussing variables in the context of mathematics and particularly in statistical analysis, several properties are typically associated with them:

• Independent and dependent variables: The independent variable is the one that is being manipulated or controlled, while the dependent variable is the one that is being measured or observed as it responds to the independent variable.
• Scatter plot: This graphical representation demonstrates the relationship between two variables. On the scatter plot, data points are plotted to see if there is a linear relationship between the variables.
• A regression analysis can be performed to find the line of best fit and calculate the correlation coefficient, which indicates the strength and direction of the linear relationship between two variables.
• The correlation coefficient is a statistical measure that reflects the correlation between variables. Its value ranges from -1 to 1, where +1 indicates a perfect positive linear correlation, -1 indicates a perfect negative linear correlation, and 0 indicates no linear correlation.

Given these properties, let's explore the scenarios:

1. In the case of studying elderly drivers and motor vehicle fatalities, the age of drivers would be the independent variable, and the number of fatalities per 100,000 drivers would be the dependent variable.
2. The number of family members would be the independent variable, and the weekly grocery bill would be the dependent variable.
3. For insurance companies, the age of the applicant is the independent variable while the life insurance premiums are the dependent variable.
4. Power consumption is the independent variable and the utility bills represent the dependent variable.
5. Level of education would be the independent variable with the crime rate in a population being the dependent variable.

These examples illustrate how independent and dependent variables are used to explore relationships between different properties in mathematical studies.