Question

6. Morning House is a mail-order firm which carries a wide range of rather expensive art objects for homes and offices. It operates by advertising a particular item either in selected magazines or in a direct-mail program. Suppose the sales response varies widely by item and the firm’s management has been unable to predict in advance which items will sell well and which will not. Consequently, the firm frequently experiences either stock-outs or excessive inventories. For many of the products Morning House sells, it is possible to order a limited amount for inventory and to place a subsequent order for delivery within two weeks. Thus, if the firm could make a early prediction of the ultimate sales of a product, its inventory problems would be greatly reduced. Since it takes approximately six weeks to receive 90% of the response to a given campaign, an accurate prediction of total sales made as late as the end of the first week of receiving orders would be useful. The first week’s sales and total sales of the last 12 campaigns of the firm are shown below. Can the first week’s sales be used to predict total sales? * Need help on minitab if this is a regression?

                        First week’s   Total

Campaign      Sales               Sales

1        32                    167

2                      20                    91

3                      114                  560

4                      66                    335

5                      18                    70

6                      125                  650

7                      83                    401

8                      65                    320

9                      94                    470

10                    5                      15

11                    39                    210

12                    50                    265

Answer 1

To predict the total sales using the first week sales, we first need to determine what type of regression might be useful. First we plot the given data on a scatterplot.

We enter the data under seperate columns in minitab.

Go to Graph->Scatterplot->Simple->OK->Y var = Total sales, X var = First week sales-> OK

As we can see from the scatterplot that a simple linear regression can be used to predict the total sales from the first week sales quite accurately.

To fit the regression line

Stat->Regression->Fitted Line Plot->Y(Response)= Total sales, X(Predictor) = First week sales->Type of Regression Model->Linear->OK