No calculation required. what test would be used to predict what the tuition will be in 20 years if it has gone up the past five years?

If you have the data, you would probably use a correlation coefficient.

To predict the tuition for the next 20 years, you can use a time series analysis technique. One common method is the exponential smoothing method, specifically the Holt-Winters method.

Here are the steps to use the Holt-Winters method to predict future tuition:

1. Gather the historical tuition data for the past five years, noting the tuition amount for each year. This data will be used to build the forecasting model.
2. Plot the historical tuition data on a graph to visualize the pattern or trend it follows. This will help you determine if there are any seasonality or trend effects.
3. Apply the Holt-Winters method, which considers three components: the level component (average value), the trend component (rate of increase), and the seasonality component (if applicable). Based on the historical data, the method will estimate these components and forecast future values.
4. Once you have estimated these components, you can use them to predict the tuition for the next 20 years.

It's important to note that the Holt-Winters method assumes that the past pattern or trend will continue into the future. However, keep in mind that this method is just a prediction and may not accurately reflect the actual tuition amounts in the future.

If you have the historical tuition data, you can use statistical software or programming languages like R or Python to perform the Holt-Winters method. There are also online forecasting tools available that can help you with this analysis.