Final answer:
The purpose of a regression line is to find the best-fit line through a scatter plot that can be used for prediction, not to connect all the points.
Step-by-step explanation:
The answer to the student's question is False. The purpose of a regression line is not to connect all the points in a scatter plot, but rather to find the line that best fits the data and can be used to predict future outcomes. The regression line, also known as the line of best fit, is determined using the least-squares method, where the sum of squared errors (SSE) is minimized. This line represents the estimated statistical relationship between the independent variable (x) and dependent variable (y).
It is important to analyze the scatter plot and the correlation coefficient to determine if linear regression is appropriate for the data set. If the correlation is significant and the scatter plot shows a linear trend, we can confidently use the regression line for predictions within the range of observed values.