Question

A geyser is a hot spring that periodically erupts a mixture of hot water and steam. Old Faithful in Yellowstone National Park is the world's most famous geyser. It is suspected that there is a correlation between the duration of the eruptions and the wait time between eruptions. Using the data file Old Faithful.xlsx (Links to an external site.)Links to an external site., find the linear regression line which uses the duration of an eruption to predict the wait time until the next eruption, and construct a 95% confidence interval for the slope of this line. What is the y-intercept of the equation?

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

Open file in excel.

Click on Data->Data Analysis and select Regression.

Enter wait time data range in y-variable.

Enter Duration data range in x-variable.

Click ok.

From above output:

#1 The equation of the linear regression line is:

A 95% confidence interval for the slope of the regression line is:

${(10.110,11.349)}$

In excel, ise formula =FORECAST(6,wait time data range, duration data range) and press enter. The wait time between eruptions following a 6 minute eruption is $\hat{Y}_{x=6}= 97.9} .$

Since (for F test) $p-value=0.000$ , we can conclude that there is a statistically significant linear relationship between the duration of the eruptions and the wait time between eruptions.

The correct null and alternative hypotheses for this analysis:

${ H_0:\beta_1=0 \ H_a:\beta_1\ne 0}$

Kindly check the output below