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# 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...

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&gt;=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).

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