The data show the time intervals after an eruption to the ne

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 131 feet. Use a significance level of 0.05.

Use the critical values of the Pearson correlation coefficient r.

Height (ft): 136, 144, 140, 151, 115, 129, 160, 123

Interval after (min): 80, 76, 78, 94, 69, 75, 93, 72

What is the regression equation?

y = _____________+______________x (Round to two decimal places as needed.)

What is the best predicted value?

y _____________(Round to one decimal place as needed.)

thank you for the help.

Solution

x = Height is independent variable.

y= Interval after (min) is dependent variable.

8

Regression equation is given below

Y = 2.734 + 0.56 * x      where y = Interval after and    x= Height

R² of the regression model is 0.807268. its means model linearly good fit for the given data set.

best predicted value of Interval after (y ) at height (x) = 131 is

y = 2.734 + 0.56*131 = 76.094

and Pearson correlation coefficient (r) between height and Interval after variable is gicen below

r = 0.898 .