Final answer:
The question addresses statistical concepts in high school-level mathematics, involving the identification of variables, scatter plot creation, least-squares line calculation, and correlation coefficient significance assessment, which often requires the use of a calculator or statistical software.
Step-by-step explanation:
The question involves identifying independent and dependent variables, constructing a scatter plot, calculating a least-squares line, finding the correlation coefficient, and determining the significance of the relationship between variables. This is typically covered in a high school-level statistics or algebra course within the mathematics curriculum. The steps include:
- Deciding which variable is independent (typically the one you have control over or that naturally comes first, such as time) and which is dependent (the outcome of interest).
- Drawing a scatter plot to visually assess the relationship between the two variables.
- Calculating the least-squares line, which minimizes the sum of the squares of the distances of the points from the line, and is given by the formula ý = a + bx.
- Finding the correlation coefficient, which measures the strength and direction of a linear relationship between two variables.
- Assessing whether the correlation coefficient suggests a significant relationship.
To perform these calculations, a calculator or computer software that handles statistical functions is necessary. This can help plot the data, perform regression analysis, and calculate the least-squares line and correlation coefficient.