DeMarco Company is developing a cost formula for its packing activity. Discussio

Question

DeMarco Company is developing a cost formula for its packing activity. Discussion with the workers in the Packing Department has revealed that packing costs are associated with the number of customer orders, the size of the orders, and the relative fragility of the items (more fragile items must be specially wrapped in bubble wrap and Styrofoam). Data for the past 20 months have been gathered: Packing Number Weight Number of Month Cost of Orders of Orders Fragile Items 1 $45,000 11,200 24,640 58,000 14,000 31,220 39,000 10,500 18,000 9,000 19,350 90,000 21,000 46,200 6 126,000 31,000 64,000 90,600 20,000 60,000 63,000 15,000 40,000 79,000 16,000 59,000 10 155,000 40,000 88,000 11 450,000 113,500 249,700 12 640,000 150,000 390,000 13 41,000 10,000 23,000 54,000 14,000 29,400 1,120 1,400 1,000 850 4,000 5,500 1,800 750 1,500 2,500 11,800 14,000 900 890 4 35,600

Explanation / Answer

DeMarco Company is developing a cost formula for its packing activity. Discussion with the workers in the Packing Department has revealed that packing costs are associated with the number of customer orders, the size of the orders, and the relative fragility of the items (more fragile items must be specially wrapped in bubble wrap and Styrofoam). Data for the past 20 months have been gathered:

1. Using the method of least squares, run a regression using the number of orders as the independent variable. Round "Adjusted R Square" answer to six decimals and "Standard Error" answer to three decimal places.

We have to use dependent variable is packing cost and independent variable is number of orders.

We can do regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Fit regression model --> Responses : packing cost -->Continuous predictors : number of orders--> Results : All that apply --> ok --> ok

Adj Rsq = 0.997000

Standard error = 8195.830

Observations = 20

2. Run a multiple regression using three independent variables: the number of orders, the weight of orders, and the number of fragile items. Round "Adjusted R Square" answer to six decimals and "Standard Error" answer to three decimal places.

Adj Rsq = 99.99% = 0.999900

Standard error of the estimate = 1607.630

Observations = 20

Here second model is better beacause model contains more predictor than first model.

Every time you add a predictor to a model, the R-squared increases, even if due to chance alone. It never decreases. Consequently, a model with more terms may appear to have a better fit simply because it has more terms.

3. Predict the total packing cost for 25,000 orders, weighing 40,000 pounds, with 4,000 fragile items.

Now we have to predict packing cost when number of orders = 25000

weight of orders = 40000

number of fregile items = 4000

We will find packing cost using regression equation

packing cost = 475 + 2.100 number of orders + 0.7443 weight of orders
+ 2.313 number of fragile items

packing cost = 475 + 2.100*25000 + 0.7443*40000 + 2.313*4000 = 91,999

4. How much would the cost estimated for Requirement 3 change if the 25,000 orders weighed 40,000 pounds, but only 2,000 were fragile items?

packing cost = 475 + 2.100*25000 + 0.7443*40000 + 2.313*2000 = 87373

Now we have to do multiple regression with three independent variables.

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