Practice Problem
1.
Alex obtains a random sample of seven students from STAT 100 class he taught in
Fall Semester of 2006 and wants to use it to see if there is a relationship between
the number of absences and students’ final grade. The data and the scatterplot are
given below.
Number of
Absences,
x
Final Grade
Percentage,
y
6
70
2
92
15
47
9
72
11
49
5
96
8
78
Consider the model
Y
i
=
β
0
+
β
1
x
i
+
ε
i
, where
ε
i
’s are i.i.d.
N
(
0,
σ
2
).
a)
Find the equation of the leastsquares regression line. Add the regression line to
the scatter plot.
b)
Use the equation of the leastsquares regression line obtained in part (a) to predict
the final grade percentage for a student who missed 20 classes.
c)
Use the equation of the leastsquares regression line obtained in part (a) to predict
the final grade percentage for a student who missed 7 classes.
d)
In which prediction ( part (b) or part (c) ) would we have more confidence? Why?
e)
Use the equation of the leastsquares regression line obtained in part (a) to find
the residuals.
f)*
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 Spring '07
 STEPANOV
 Statistics, Statistical hypothesis testing, leastsquares regression line, Final grade percentage

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