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

MATH 12201. Modeling the data linearly:a. Generated a linear model by choosing two points for this data. Linear Model for WalMartDry Goods Sales 2002-20032500021200 2000015200 15000Sales in \$ 100005000020 30 40 50 60 70 80 Week b. Generate a least square linear regression model Least Square Linear Regression Model35000300002500020000Sales in \$ Sales in \$Linear (Sales in \$) 15000100005000020 30 40 50 Week Regression StatisticsY=ax+b 60 70 80 R0.8065752R0.650563Adjusted R2Standard ErrorObservations 0.6435742030.3352 c. How good is this regression model?d. What is the marginal revenue for this department using the linear modelwith two data points and the regression model? Note that marginal revenue isthe 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. soS=8741.97+180.99wTR=(8741.97+180.99w)wMR=8741.97+361.999we. Compare the two models. Which do you feel is better?After comparing the two models, I find that the least square regression model isbetter. Although this is a simple linear least squares regression model because thereis only one variable, it is still more effective and complete as compared to the linearmodel. The estimates of the unknown parameters obtained from linear least squaresregressions are the optimal estimates from a broad class of possible parameterestimates under the usual assumptions used for process modeling. Practicallyspeaking, linear least squares regression makes very efficient use of the data. Goodresults can be obtained with relatively small data sets. Aside, the linear model onlytakes 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= 3.357B=-164.762C=16889.187R2=.691b. What is the marginal revenue for this department using this model?c. Calculate the model generated relative max/min value. Show backup analyticalwork. d. Compare actual and model generated relative max/min value. 3. Comparing modelsa. 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 berequired to meet customer needs?4. Identify holiday periods or special events that cause spikes in the originaldata.WalMart weeks start the beginning of February. So, for example, Walmart week 30 inthe 2002 is actually week 34 (30 + 4) in the calendar year 2002 which equates to theend of August 2002. To make the weeks continuous, week 53 is actually WalMartweek 1 in 2003 and this equates to week 5 (53 – 52 +4) or the first week in February2003. Week 72 is week 24 (72 – 52 + 4) in the year 2003 or mid June 2003.

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