Stat 501 Homework 1 ANSWERS Fall 07
1.
a
. The slope is −0.269. For each onehour increase in studying average (or, predicted) amount of sleep
decreases by 0.269 hours.
b.
Intercept = 7.56 hours. It does have useful meaning for this problem.
It’s the average hours of sleep for
people who studied 0 hours.
c.
The estimated value of average hours of sleep the previous day is y
ˆ
= 7.022, calculated by substituting
2 hours into the regression equation.
d.
The value of the residual for that person is –1.022, calculated by finding the difference between the
observed value of 6 hours and the predicted value found in part c.
2. a.
X
70
75
80
80
85
90
Y
75
82
80
86
90
91
i
y
ˆ
76
80
84
84
88
92
i
e
−1
2
−4
2
2
−1
b.
SSE
= 30. SSE
=
(
29
30
)
1
(
)
2
(
2
)
4
(
)
2
(
)
1
(
2
2
2
2
2
2
=

+
+
+

+
+

c.
MSE = SSE/(n−2) = 30/(62) = 7.5
d.
s
=
5
.
7
=2.74. This is roughly the average absolute size of a residual (difference between actual and
predicted value of y).
e.
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 Fall '07
 HECKARD,ROBERTF
 Regression Analysis, Errors and residuals in statistics, 2 hours, 0 hours, square feet area, 0.5963 cm

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