06 Aug MATH 1220
1. Modeling the data linearly:
a. Generated a linear model by choosing two points for this data. Linear Model for WalMart
Dry Goods Sales 2002-2003
25000
21200 20000
15200 15000
Sales in $ 10000
5000
0
20 30 40 50 60 70 80 Week b. Generate a least square linear regression model Least Square Linear Regression Model
35000
30000
25000
20000
Sales in $ Sales in $
Linear (Sales in $) 15000
10000
5000
0
20 30 40 50 Week Regression StatisticsY=ax+b 60 70 80 R
0.806575
2
R
0.650563
Adjusted R2
Standard Error
Observations 0.643574
2030.33
52 c. How good is this regression model?
d. What is the marginal revenue for this department using the linear model
with two data points and the regression model? Note that marginal revenue is
the same as the first derivative of the revenue (sale) function.
(Im not sure if this is right)
The marginal revenue function is the first derivative of the total revenue function. so
S=8741.97+180.99w
TR=(8741.97+180.99w)w
MR=8741.97+361.999w
e. Compare the two models. Which do you feel is better?
After comparing the two models, I find that the least square regression model is
better. Although this is a simple linear least squares regression model because there
is only one variable, it is still more effective and complete as compared to the linear
model. The estimates of the unknown parameters obtained from linear least squares
regressions are the optimal estimates from a broad class of possible parameter
estimates under the usual assumptions used for process modeling. Practically
speaking, linear least squares regression makes very efficient use of the data. Good
results can be obtained with relatively small data sets. Aside, the linear model only
takes into account two points and not the whole set of data. 2. Modeling the data quadratically:
a. Generate a quadratic model for this data.
QuadReg. Formula (Y=AX2+BX+C)
A= 3.357
B=-164.762
C=16889.187
R2=.691
b. What is the marginal revenue for this department using this model?
c. Calculate the model generated relative max/min value. Show backup analytical
work. d. Compare actual and model generated relative max/min value. 3. Comparing models
a. Which model do you feel best predicts future trends? Explain your rationale.
b. Based on the model selected, what type of seasonal adjustments, if any, would be
required to meet customer needs?
4. Identify holiday periods or special events that cause spikes in the original
data.
WalMart weeks start the beginning of February. So, for example, Walmart week 30 in
the 2002 is actually week 34 (30 + 4) in the calendar year 2002 which equates to the
end of August 2002. To make the weeks continuous, week 53 is actually WalMart
week 1 in 2003 and this equates to week 5 (53 – 52 +4) or the first week in February
2003. Week 72 is week 24 (72 – 52 + 4) in the year 2003 or mid June 2003.
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