Solution to Homework 1
The following data were collected for a class of 20 students on reading readiness stanines
(X) at the end of kindergarten and reading achievement stanines (Y) at the end of first
grade.
You want to examine how well the readiness scores predict reading achievement.
X:
2
2
1
1
3
4
5
5
7
6
4
3
6
6
8
7
5
9
5
4
Y:
3
1
1
3
5
4
7
6
7
8
5
2
7
6
9
8
4
6
9
7
DO THE FOLLOWING BY HAND!!!
1. Calculate the least square estimates of the intercept and slope of the regression line of
Y on X.
∑
∑
=
=


=
n
1
i
2
2
i
n
1
i
i
i
1
X
n
X
Y
X
n
Y
X
b
=
2
584
(20)(4.65)(5.4)
0.865
527
(20)(4.65)

=

b
o
=
X
b
Y
1

= 1.378
2. Specify the regression equation using your calculated estimates.
1
ˆ
1.378
0.865
o
Y
b
b X
X
=
+
=
+
3. Calculate the predicted values of Y associated with the sample values of X (that is,
calculate
ˆ
i
Y
).
Make a column of these values.
See attached MTB worksheet at
Solutions
4. Calculate the
residuals
(e
i
) corresponding to the predicted and observed values of Y.
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 '08
 SENTURK,DAMLA
 Statistics, Regression Analysis, Prediction interval, bo + b1

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