In analyzing statistical data, which do you think is more likely: a correlation coefficient of 0.9 or a correlation coefficient of 1.0? Explain.
Imagine that you have plotted many data points on an xy-plane. Your points seem to align into a clear best-fit line. Do you think this best-fit line can help you make predictions about future data? Explain your answer, and give one or more examples to support it.
You're studying how well students remember vocabulary after they stop studying a new language. The first student you study remembers 95% of the French words she learned 3 months later, but only 70% of the words 12 months later.
Before studying more students, you wonder: Is a decreasing linear model or an exponential decay model likely to be a better fit for data about remembering? Decide which model you think will be better. Explain your reasoning.
