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Chapter 14
§14.2, 14.3, 14.4
Simple Linear Regression Model
True Regression Equation
i
i
i
x
y
ε
β
+
+
=
1
0
Estimated Regression Equation
x
b
b
y
1
0
ˆ
+
=
i
x
denotes the value of the independent variable for the i
th
observation, and
i
y
denotes the value of
the response variable for the i
th
observation. n denotes the number of observations.
y
ˆ
is the predicted value of the response when the independent variable has the value x
b
1
=
(
29
(
29
(
29
∑
∑



2
x
x
y
y
x
x
i
i
i
=
∑
∑


2
2
x
n
x
y
x
n
y
x
i
i
i
b
0
=
x
b
y
1

Five observations have yielded the results recorded
in the table to the right.
observation
x
y
1
4
2
2
5
4
3
5
6
4
8
12
5
8
16
a)
Find the estimated regression equation.
b)
Find the predicted value of y when x is 5
c)
Find the predicted value of y when x is 7.
d)
Find the predicted value of y when x is 10.
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View Full DocumentSum of Squares Total:
SST =
(
29
∑

2
y
y
i
=
(
29
2
1
y
s
n

Sum of Squares Due to Regression:
SSR =
(
29
∑

2
ˆ
y
y
i
=
(
29
2
ˆ
1
y
s
n

Sum of Squares Due to Error:
SSE =
(
29
∑

2
ˆ
i
i
y
y
Fact:
SST = SSR + SSE
e)
Calculate SST
f)
Calculate SSR
g)
Calculate SSE
Coefficient of Determination:
r
2
=
SST
SSR
h)
Calculate the coefficient of determination.
Mean Square Error (estimate of
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 Spring '08
 Fry
 Business Law

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