Final answer:
The second step in solving a quantitative relationship is to identify the variables, which includes deciding on independent and dependent variables, drawing a scatter plot, calculating the least-squares line, and finding the correlation coefficient to understand the relationship between the variables.
Step-by-step explanation:
The second step in solving a quantitative relationship after defining the problem is identifying the variables. Specifically, you need to:
- Decide which variable should be the independent variable and which should be the dependent variable.
- Draw a scatter plot of the data to visualize the relationship between these variables.
- Inspect the scatter plot to determine if there is a relationship between the variables. The presence of a trend, pattern, or correlation in the plot can indicate this.
- Calculate the least-squares line, and place the equation in the form ý = a + bx. This helps in making predictions or understanding the trend mathematically.
- Find the correlation coefficient to measure the strength and direction of the relationship. A significant correlation coefficient indicates a strong relationship between the variables.
- Estimate values using the regression equation, for example, estimating the average height for a specific age.
- Finally, evaluate if a linear model is indeed the best fit for the data or if another model might be more suitable.
Before progressing to these steps, it's crucial to quite precisely identify the unknown quantities. This involves making a written list of what needs to be determined, as well as distinguishing known information from that which must be inferred or calculated. After forming a comprehensive understanding of what is known and what is unknown, you can proceed with solving the equation or system of equations pertinent to the problem at hand, applying physical principles as needed.