The data show the time intervals after an eruption (to the next eruption) of a certain geyser.
Find the regression equation, letting the first variable be the independent (x) variable.
Find the best predicted time of the interval after an eruption given that the current eruption has a height of 99 feet.
Use a significance level of 0.05.

Height (ft) 71 57 73 61 91 57 96 87
Interval after (min) 71 68 67 65 81 64 72 76

1. What is the regression equation?
2. What is the best predicted time for the interval after an eruption that is 99 feet high?

a) The first step is to identify the independent and the dependent variable from the data. As we are told, Height (ft) is the independent variable - x., and interval after an eruption (min) - y.

By regression equation:

y = a + bx +e

where a is the intercept and b is the slope or coefficient of x. e is the error term. Then, the model is (when estimated):

y = a + bx.

if you are familiar with R programming, just enter the following code:

#############################

x = c(71,57,73,61,91,57,96,87)

y = c(71,68,67,65,81,64,72,76)

model = lm(y~x)

model # this gives the estimates.

#############################

And the regression model is:

y = 48.2696 + 0.2999 x

The y is the estimated time for the interval after eruption (min).

b) Having obtained the regression model above; just compute the estimated time for the interval after eruption by substituting the height value given. That is any given height! In this case, we are given 99ft

Hence;

y = 48.2696 + 0.2999(99)

y = 77.9597.