# Math 1220 1. modeling the data linearly: a. generated a linear model

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.