In September 2007, two graduate students14 studying at the African Insti- tute of Mathematical Sciences (AIMS) in Muizenberg, South Africa, took the following measurements of "wingspan," (the ?ngertip-to-?ngertip length of outstretched hands) and height for 36 of their classmates.
|
"Wingspan"(cm) 182.50
|
Height(cm) 171.00
|
"Wingspan"(cm) 165.50
|
Height(cm) 158.00
|
|
167.50
|
161.50
|
193.00
|
189.50
|
|
175.00
|
170.00
|
198.00
|
183.00
|
|
163.00
|
164.00
|
181.50
|
181.00
|
|
186.50
|
180.00
|
154.00
|
157.00
|
|
168.50
|
162.50
|
168.00
|
165.00
|
|
166.50
|
158.00
|
174.00
|
166.50
|
|
156.00
|
157.00
|
180.00
|
172.00
|
|
153.00
|
156.00
|
173.00
|
171.50
|
|
170.50
|
162.00
|
188.00
|
179.00
|
|
164.50
|
157.50
|
188.00
|
176.00
|
|
170.50
|
165.50
|
180.00
|
178.00
|
|
173.00
|
164.00
|
160.00
|
163.00
|
|
189.00
|
182.00
|
200.00
|
184.00
|
|
179.50
|
174.00
|
177.00
|
180.00
|
|
174.50
|
165.00
|
179.00
|
169.00
|
|
186.00
|
175.00
|
197.00
|
183.00
|
|
192.00
|
188.00
|
168.50
|
165.00
|
(i) Obtain a two-parameter model relating height as y to "wingspan" as x. Are the two parameters signi?cant? Inspect the residuals and comment on what they imply about the data, the regression model, and how "predictable" height is from a measurement of "wingspan."
(ii) If two new students, one short (156.5 cm), one tall (187 cm), arrive in class later in the school year, estimate the respective expected "wingspans" for these new students, along with 95% con?dence intervals.