Final answer:
Without the scatter plot and more context, we cannot definitively choose between the two lines of best fit proposed by the students. The best-fit line is typically calculated with the least-squares method and is represented in a scatter plot showing the relationship between the independent and dependent variables.
Step-by-step explanation:
To determine which line of best fit is the best for the data, we need the context from a scatter plot and the corresponding statistical measurement. Without the actual scatter plot, we cannot definitively choose between Student A's and Student B's equations. However, we can infer some details based on the information provided that relates to creating a line of best fit for a set of data.
The line of best fit is usually computed using the least-squares regression method, which minimizes the sum of the squares of the vertical distances of the points from the line. Data points are represented on a scatter plot and the line of best fit or a least-squares regression line is drawn to represent the relationship between the two variables being studied.
For example, the equation ŷ = -173.51 + 4.83x given in the reference is a result of such a calculation, which will have corresponding values for r (correlation coefficient) and r² (coefficient of determination), the latter being an indicator of how well the model explains the variability of the data.
Regarding Y2 and Y3, they are lines that have the same slope as the line of best fit but are shifted up or down by a certain amount. They are often used to assess the reliability of predictions and to identify outliers, as they represent a specific number of standard deviations from the best-fit line.