43
T
EACHING
S
UGGESTIONS
Teaching Suggestion 4.1:
Which Is the Independent Variable?
We fnd that students are oFten conFused about which variable is
independent and which is dependent in a regression model. ±or
example, in Triple A’s problem, clariFy which variable is
X
and
which is
Y
. Emphasize that the dependent variable (
Y
) is what we
are trying to predict based on the value oF the independent (
X
)
variable. Use examples such as the time required to drive to a store
and the distance traveled, the totals number oF units sold and the
selling price oF a product, and the cost oF a computer and the
processor speed.
Teaching Suggestion 4.2:
Statistical Correlation Does Not
Always Mean Causality.
Students should understand that a high
R
2
doesn’t always mean
one variable will be a good predictor oF the other. Explain that
skirt lengths and stock market prices may be correlated, but rais
ing one doesn’t necessarily mean the other will go up or down. An
interesting study indicated that, over a 10year period, the salaries
oF college proFessors were highly correlated to the dollar sales vol
ume oF alcoholic beverages (both were actually correlated with
in²ation).
Teaching Suggestion 4.3:
Give students a set oF data and have
them plot the data and manually draw a line through the data. A
discussion oF which line is “best” can help them appreciate the
least squares criterion.
Teaching Suggestion 4.4:
Select some randomly generated values
For
X
and
Y
(you can use random numbers From the random
number table in Chapter 15 or use the RAND Function in Excel).
Develop a regression line using Excel and discuss the coeFfcient
oF determination and the ±test. Students will see that a regression
line can always be developed, but it may not necessarily be useFul.
Teaching Suggestion 4.5:
A discussion oF the long Formulas and
shortcut Formulas that are provided in the appendix is helpFul.
The long Formulas provide students with a better understanding
oF the meaning oF the SSE and SST. Since many people use
computers For regression problems, it helps to see the original
Formulas. The shortcut Formulas are helpFul iF students are
perForming the computations on a calculator.
A
LTERNATIVE
E
XAMPLES
Alternative Example 4.1:
The sales manager oF a large apart
ment rental complex Feels the demand For apartments may be related
to the number oF newspaper ads placed during the previous month.
She has collected the data shown in the accompanying table.
Ads purchased, (X)
Apartments leased, (Y)
15
6
94
40
16
20
6
25
13
25
9
15
10
35
16
We can fnd a mathematical equation by using the least squares
regression approach.
Leases, Y
Ads, X
(
X
2
¯¯
X
)
2
(
X
2
¯¯
X
)(
Y
2
¯¯
Y
)
61
5
6
4
3
2
4
9
196
84
16
40
289
102
62
0
9
1
2
13
25
4
6
92
5
4
2
2
10
15
64
0
16
35
144
72
o
Y
5
80
o
X
5
184
o
(
X
2
¯¯
X
)
2
5
774
o
(
X
2
¯¯
X
)(
Y
2
¯¯
Y
)
5
306
b
1
5
306/774
5
0.395
b
0
5
10
2
0.395(23)
5
0.915
The estimated regression equation is
ˆ
Y
5
0.915
1
0.395
X
or
Apartments leased
5
0.915
1
0.395 ads placed
IF the number oF ads is 30, we can estimate the number oF apart
ments leased with the regression equation
0.915
1
0.395(30)
5
12.76 or 13 apartments
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 Spring '11
 MichaelHanna
 Linear Regression, Regression Analysis, Northern Airline

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