Data were collected on eruptions of the Old Faithful geyser [14]. A least squares regression using 99 observations on the time between eruptions Y (in minutes) and the duration X (in seconds) of the preceding eruption yielded this estimated equation:

Y = 34.549 + 0.2084X. The value of R² is 0.87, and the estimated coefficient of X has a standard error of 0.0076 and a t value of 27.26.

a. Interpret the estimated coefficient of X.

b. Calculate a 95 percent confidence interval for the coefficient of X.

c. Is the relationship statistically significant at the 5 percent level?

d. What percentage of the variation in the time interval between Old Faithful’s eruptions can be explained by the duration of the preceding eruption?