Using R,

Exercise 1 (Using lm) For this exercise we will use the faithful dataset. This is a default dataset in R, so there is no need to load it. You should use ?faithful to learn about the background of this dataset. (a) Suppose we would like to predict the duration of an eruption of the Old Faithful geyser in Yellowstone National Park based on the waiting time before an eruption. Fit a simple linear model in R that accomplishes this task. Store the results in a variable called faithful_model. Output the result of calling summary on faithful_model (b) Output only the estimated regression coefficients. Interpret Bo and B in the contert of the problem. Be aware that only one of those is an estimate (c) Use your model to predict the duration of an eruption based on a waiting time of 80 minutes. Do you feel confident in this prediction? Briefly explain. (d) Use your model to predict the duration of an eruption based on a waiting time of 120 minutes. Do you feel confident in this prediction? Briefly explain. (e) Calculate the RSS for this model. (f) Create a scatterplot of the data and add the fitted regression line. Make sure your plot is well labeled and is somewhat visually appealing (g) Report the value of R2 for the model. Do so directly. Do not simply copy and paste the value from the full output in the console after running summary) in part (a)