10.
10b. number of samples = 40, number of independent variables = 2
The critical value at 95% confidence level is plus or minus 2.03
Inc has a positive slope, NRUR has a negative slope but is not
significant. 10c.
The percent of variation to the sales that the model explains is 85.81%
9a. b0 = -307,682.5786
b1 = 14.5683
b2 = 1,396.9776
the intercept is b0 and the coefficient of INC would be b1 and the coefficient of POP would be
b2.
9d. The percent given of the variation of AS given by the model is 92.96%
9e. The point estimate of AS in a city where INC is 23,175 and POP 128.07 is found to be
208,848.6951
This answer is found by substituting these variables with the formula from the model in part A to
get the point of AS.
9b. b1 = 14.5683
b2 = 1,396.9776
When the units increase in the indepedent variable shows the increase of the dependent
variables, ie more sales when income increases, as well as increase sales when population rises.
9c. If the p-value ends up being less then the level of significance we would reject the
hypothesis. A decision is made according to how the P-value is compared with the level of
significance. INC variable isn't relevant, but variable pop is showing to be relevant.
11.
10d.
10e. The MAPE is 17,456.89 showing that the model doesn't appear to be all that accurate due
to high number.
10f.
HeathCo
Sales
350,000
300,000
250,000
200,000
150,000
100,000
50,000
0
SESBSBSBSBSBSR
ASR
RBSESSZE
HSS
SSSSSSESESESETESESES
There
does
appear
to
be
seasonality
with
peak
seasons
starting
in
the
fourth
quarter
and
continuing
into
the
first
quarter
of
the
next
year.
Some
fourth
quarters
are
no
as
high
as
others.
SALES
bg +
by(TIME)
+
b2Q1
+
b3Q4
Sales
=
75,767.16
+
5,364.22*Time
+
26,166.59*Q1
+
25,597.51*Q4)
Evaluate
these
results
by
answering
the
following:
Do
the
signs
make
sense?
Why
or
why
not?
The
model
is
logical
because
the
signs
do
make
sense.
From
the
graph
we
see
an
upward
trend
in
the
data
so
a
positive
slope
for
time
is
logical.
For
Q4
and
Q1
the
positive signs
are
logical
because
this
would
be
the
peak
period
for
the
ski
industry.
Are
the
coefficients
statistically
different
from
zero
at a
95
percent
confidence
level
(one-tailed
test)?
Audit
Trail
--
Coefficient
Table
(Multiple
Regression
Selected)
Coefficient
Std
error
T-test
P-value
Intercept
75,767.16
7,815.17
9,69
0.00
Time
5,364.22
298,71
17.96
0.00
01
26,166.59
8,422.39
3.11
0.00
Q4
25,597.51
8,422.39
3.04
0.00
Based
on
the
high
t-ratios
and
the
low
P-values
we
can
say
that
all
the
coefficients
are
significantly
positive
at a
95%
confidence
level.
What
percentage
of
the
variation
in
SALES
is
explained
by
this
model?
Accuracy
Measures
Value
MAPE
9.36%
Adjusted
R-
Square 89.61%
The
adjusted
R?
tells
us
that
89.61%
of
the
variation
in
sales
is
accounted
for
by
this
model.
Use
this
model
to
make
a
forecast
of
SALES
(SF2)
for
the
four
quarters
of
2017
and
calculate
the
MAPE
12.
4a. MAPE is 13.93%
12c. The MAPE is 100.24 and this number is low and the forecast is accurate.
Appendix 5 Question 4
MAPE is 8.98%
