[SOLVED] Stat 3010: assignment 4

1. In 1609 Galileo proved mathematically that the trajectory of a body falling with a horizontal velocity component is a
parabola. His search for an experimental setting in which horizontal motion was not affected appreciably (to study
inertia) let him to construct a certain apparatus. The data come from one of his experiments.
Location <- c(“A”, “A”, “A”, “B”, “B”, “B”, “C”)
Height <- c(100,200,300,450,600,800,1000)
Distance <- c(253,337,395,451,495,534,573)
(a) Create a data frame called Galileo with the three variables and display the contents of the dataframe.
(b) Compute the mean, median, variance, and IQR of the variable Distance in the dataframe Galileo.
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(c) Create a variable for estimated distance D.Hat = 200 + .708 Height − .000344 Height² and add it to the data
frame Galileo. Create a new variable LO that takes a value of TRUE when the estimated distance is lower than
the measured distance (D.Hat < Distance) and a value of FALSE otherwise and add it to the data frame Galileo.
Use the variable LO to extract a subset of the Galileo dataframe removing the observations for which the
estimated distance is lower than the measured distance. Show the contents of this dataframe.
(d) Plot Distance (y-axis) versus Height (x-axis) and overlay this plot with the curve of
D.Hat = 200 + .708 Height − .000344 Height² .
2. The indoor thermal climate is an important characteristic affecting the health and productivity of workers in
buildings. The paper “Adaptive Comfort Temperature Model of Air-Conditioned Buildings in Hong Kong” (Building
and Environment, 2003: 837–852) reported data on a number of building characteristics measured during the
summer and also during the winter. The data which contain two columns on relative humidity and season are
given in the file hw4q2.csv.
(a) Read in the data and give a comparison boxplot of summer and winter relative humidity. Comment on your
observations.
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(b) Draw two normal quantile plots – one for summer humidity and another for winter humidity. Comment on
your observations.
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(c) Calculate the variances and IQRs for summer humidity and for winter humidity. Comment on your
observations.