The image contains a problem related to simple linear regression using sampled data. Let's break down what needs to be calculated based on the provided table and fields:

Table Details

1. Columns:

   • Time since last eruption ($x$, in hours)
   • Eruption height ($y$, in meters)
   • The product ($xy$).

2. You are required to calculate:

   • $n$: Sample size (the number of data points).
   • $\sum x$: Sum of all $x$ values.
   • $\sum y$: Sum of all $y$ values.
   • $\sum x^2$: Sum of the squares of all $x$ values.
   • $\sum xy$: Sum of the products ($xy$).

3. Regression Details:

   • Sample correlation coefficient ($r$).
   • Slope ($\beta_1$).
   • $y$-intercept ($\beta_0$).

Would you like me to calculate these values step-by-step based on the data in the table?