FORECASTING
Week 6
Statistical Analysis
1
9
/
2
6
/
1
5

AGENDA
2
test of goodness of fit – 13.1
Linear regression – 14.1, 14.2, 14.3, 14.5
Final schedule
2
9
/
2
6
/
1
5

2
TEST FOR GOODNESS
OF FIT
3
9
/
2
6
/
1
5

Suppose we have the following data from
interviewing people in New York City:
Prefer Diet Coke: 30% (
p
1
=0.3)
Prefer Diet Pepsi: 25% (
p
2
=0.25)
Prefer Regular Coke: 30% (
p
3
=0.3)
Prefer Regular Pepsi: 15% (
p
4
=0.15)
You ask 200 people in Baltimore the same
question and get this answer:
Prefer Diet Coke: 50
Prefer Diet Pepsi: 40
Prefer Regular Coke: 60
Prefer Regular Pepsi: 50
4
9
/
2
6
/
1
5

ARE THE RESPONSES IN BALTIMORE
SIGNIFICANTLY DIFFERENT FROM
RESPONSES IN NEW YORK CITY OR
DO THEY FOLLOW THE SAME
DISTRIBUTION?
5
9
/
2
6
/
1
5

2
TEST FOR GOODNESS OF FIT
H
0
: probabilities in Baltimore are also p
1
,
p
2
, p
3,
p
4
H
a
: at least one of the probabilities in
Baltimore differs from p
1
, p
2
, p
3,
p
4
6
9
/
2
6
/
1
5

2
TEST FOR GOODNESS OF FIT
Can
Reject H
0
7
9
/
2
6
/
1
5
81
.
7
17
)
(
)
(
2
05
.
0
2
4
1
2
2
1
2
2
i
i
i
i
k
i
i
i
i
E
E
f
=
E
E
f
=

2
TEST FOR GOODNESS OF FIT
When to use:
To test if the data comes from a
specified distribution.
1.
Test the following null and alternative
hypotheses:
H
0
: the population has a specified
distribution
H
a
: population does not have the specified
distribution
2.
Define k intervals for the test
3.
Record observed frequency (f
i
) for each
interval and calculate expected frequency
(E
i
)
4.
Calculate the chi-square statistic
8
9
/
2
6
/
1
5

EXAMPLE 1
A supervisor predicts that the number of
phone calls at his call center follow a
Poisson distribution with mean 4.7 calls
per minute. His boss asks him to take 100
samples and confirm his belief. Here is
the data: is the supervisor right?
Number
of
Phone
Calls
per
minute
1 or less
2
3
4
5
6
7
8
9 or
more
5
7
12
21
10
10
12 10
13
9
9
/
2
6
/
1
5

EXAMPLE 1
H
0
: Data comes from a Poisson with mean 4.7
H
A
: Data has a different underlying
distribution
α=0.1
10
9
/
2
6
/
1
5

EXAMPLE 1
Number of
Phone Calls
Per Minute
(x)
p(x) given
μ=4.7
Expected
Number
(n=100)
Observed
Number
1 or less
0.0518
5.18
5
2
0.1005
10.05
7
3
0.1574
15.74
12
4
0.1849
18.49
21
5
0.1738
17.38
10
6
0.1362
13.62
10
7
0.0914
9.14
12
8
0.0537
5.37
10
9 or more
0.0503
5.03
13
11
9
/
2
6
/
1
5

EXAMPLE 1
Reject H
0
12
9
/
2
6
/
1
5
36
.
13
77
.
23
)
(
)
(
2
1
.
0
2
9
1
2
2
1
2
2
i
i
i
i
k
i
i
i
i
E
E
f
=
E
E
f
=

FORECASTING
13
9
/
2
6
/
1
5

QUANTITATIVE FORECASTING
A statistical technique for making
projections about the future using
numerical facts and prior experience
to predict future events
EXAMPLES
Sales forecasts
Financial projections
Assessing future risk and returns
14
9
/
2
6
/
1
5

REVIEW: EQUATION OF A LINE
y = mx + b
m = slope of the line
b = intercept of the line = point where x
= 0
15
9
/
2
6
/
1
5

EXAMPLE 2
A new company is trying to figure out how
much $$$ to spend in advertising.

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