CONTENTS - Department of Mathematics and Statistics - University ...

SOLUTIONS
−8698.33
1. (a) b YX = =− 0.054
160613.28
ŷ = 47.67 – 0.054(x – 831.4)
= 92.566 – 0.054x
(b) Estimated standard error =
∑
se
( x − x)
i
2
where
55.25/16
That is, standard error = = 0.004637
160613.28
A 95% confidence interval for the true slope is
–0.054 ± t 16 (0.004637) where t 16 = 2.120
That is, –0.054 ± 0.0098
giving – 0.064 < β YX < –0.044
y ˆ
2 i
− yi
e
=
s
∑
( )
n − 2
(c) The maximum volume of oxygen uptake is smaller for men who take longer to run 2
miles.
2
(d)
Oxygen uptake reduces by 50(0.054) = 2.7 units.
The 95% confidence interval extends from 50(0.064) to 50(0.044) or a reduction from
2.2 to 3.2 units.
(e) When x = 660 seconds, ŷ = 92.566 – 0.054(660) = 56.93
The 95% confidence interval is
1
56.93 ± t s 1+ +
( x − x)
2
k
16 e
2
n ( xi
− x)
∑
That is, 56.93 ± 2.120
or 56.93 ± 4.38
52.55 < ŷ
660
< 61.31
1 (660 − 831.4)
55.25/16 1+ + 18 160613.28
2
372
Section 9