Question

The NEPA Bottling Company, which provides glass bottles to soft drink manufacturers, provided the information regarding the number of cases per shipment, size of cartons, and the corresponding transportation cost:

Number of Cases/Shipment

(hundreds)

           15
           22
           35
           43
           58
           65
           73
           82
           85
           98

Size of Carton

(cubic inches)

     12
     16
     20
     24
     28
     32
     36
     40
     44
     48

Transportation Costs

(dollars)

        200
        260
        310
        360
        420
        480
        540
        630
        710
        730

The marketing manager is interested in studying the relationship between the number of cases per shipment and the transportation costs. First, enter the data in SPSS. Now, answer the following questions (30 points).

a) Plot the transportation cost as a function of the number of cases per shipment and interpret the scatter gram (1 to 2 sentences).

b) Run a simple regression between the above two variables. Interpret α and β coefficients.

d) What is the transportation cost for shipping 18 cases?

e) Is the size of the carton associated with the transportation cost per shipment?

Calculate the correlation coefficient and interpret it. Show the SPSS output.

Determine the coefficient of determination and interpret it.

Answer 1

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The Interpretation of the correlation coefficient,r:

The correlation coefficient between the two quantitative variables size of the carton(X) and the transportation cost per shipment(Y) is a very strong positive linear relationship, since the correlation coefficient is r = 0.996.

The interpretation of the coefficient of determination, R² = 0.9927:

The value of the coefficient of determination is R² = 0.9927 indicates that the 99.27% of the variation in the dependent variable transportation cost per shipment (Y) can be explained by the independent variable size of the carton(X).