Answer:
a) The regression equation is:
y = 48.2696 + 0.2999 x
where y = interval after an eruption (min), and
x = Height (ft)
b) The predicted time for interval after an eruption that is 99 feet high is
y = 77.9597
y = 78 (approx to whole number - min)
Step-by-step explanation:
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.
