MAS183 Statistical Data Analysis

Due 11:00 pm Thursday 25 August 2022

1. [22 marks]
The file NZRivers.csv contains data about rivers on the South Island of New Zealand. The
variables are –
River the name of each river
Length the length of the river in km
FlowsInto whether the river flows into the Pacific Ocean or the Tasman Sea.
(a) Paying careful attention to graphical principles of clarity, simplicity and accuracy, provide
graphs that allow the distributions of river lengths to be compared between rivers that flow
into the Pacific Ocean and those that flow into the Tasman Sea. Construct your graphical
comparison using –
(i) boxplots, and [5]
(ii) histograms. [5]
(b) Provide the mean, median and sample standard deviation for each distribution. [3]
(c) Using your graphs and statistics from parts (a) and (b), briefly compare the two distributions
of river lengths in terms of location, spread and shape. [3]
(d) Do any of the observations appear to be ‘outliers’ relative to the distribution in which they
occur? Justify your answer. [2]
(e) On New Zealand’s South Island, the mountain range running the length of the island is
generally closer to the Tasman coast than the Pacific coast. How could this be deduced
from the data you have analysed? [1]
(f) For each of the variables Length and FlowsInto, classify the variable as –
(i) numerical or categorical,
(ii) discrete or continuous,
(iii) nominal or ordinal.
If any of these distinctions is not relevant to the variable, say “not applicable.” [3]

2. [18 marks]
Anthropologists sometimes want to estimate the standing height (stature) of humans based on
measurements of fragmentary remains. Statistical work on one approach to this problem was
done by Musgrave and Harneja. 1 Their data may be found in the data file Stature.csv. The
variables are –
MetaCarp length (in mm) of the metacarpal I bone. (This is the bone that connects the
thumb to the wrist.)
Stature standing height (in cm)
(a) From an anthropologist’s perspective, which variable is the predictor, and why? [2]
(b) Provide a scatterplot of the data (WITHOUT any trend line). [5]
(c) Based only on the graph in part (b), briefly describe the relationship between MetaCarp and
Stature in terms of direction, shape and strength. [3]
(d) Without referring to parts (e) or (f), or to any numerical results from software, explain why
the line
Stature = -10.68 + 4.067 × MetaCarp
cannot be the least-squares line of best fit for the data. [2]
(e) What is the equation of the least-squares line of best fit? [2]
(f) Calculate the estimated stature of a person whose metacarpal I bone length was 43 mm. [1]
(g) Obtain the R 2 value for the regression and interpret it in the context of the data. [3]