Use y=faithful$eruptions; x=faithful$waiting to set the eruption

durations and waiting time between eruptions of the R data set

faithful in objects y and x, respectively. and complete the following

parts. 1. Make an scatterplot of the (x,y) data. Does it support the

assumption that the data follows the simple linear regression model? (Include the plot with your answer.) 2. Fit the simple linear regression model and construct a 90% CI for:

a) the slope, and b) the mean eruption duration following a 70 min waiting time. 3. Do a 90% CI for the marginal mean of eruption duration in

two ways:

a) ignoring the regression structure (i.e., ignoring the data on

waiting time between eruptions), and b) taking into

consideration the regression structure. Which Cl is shorter? Lab Assignment 7 Cls and Pie 4. Do an 80% PI for the next eruption duration following a 70

min waiting time. 5. Do an 80% PI for the next eruption duration (without any

information on the waiting time). 6. Do a 95% CI for the proportion of eruption durations that last

at least 4 min. [NOTE The R command

phat:sum( y>=4)/Iength( y) sets the sample proportion into

the object phat] For all parts, include the R commands and R output with your

answer (Copy it from the R console and paste it).