Coffee Time

Part 1

Laura Jones’s first regression model used the normal independent variables. It is a relatively good model because the Multiple R calculated value is relatively high at .738 indicating a “strong” relationship between variables. A coefficient of correlation or Multiple R close to zero shows that the relationship is weak. The R-square value of .546 indicates that there is a 54.6% of the variation is accounted for, and is found by squaring the coefficient of correlation. In the second regression model presented by Jones computes the lagged independent variables relationship. The Multiple R value is .755, indicating a “strong” relationship between variables. The R-square value of .570 indicates that there is a 57% of the variation is accounted for. Thus, the Lagged values model is a slightly better model, due to the higher values.

The R-square values in Jones’s models are not the most optimal. The optimal model is shown below and combines independent variables omitting the variable on Estimate on Quick Brew’s weekly advertising expenditure (X3). The computed R-squared value of .756 indicates that there is a 75.6% of the variation in revenue is accounted for by the variation among the independent variables omitting X3. The general multiple regression with k independent variable is given by:

…

=Predicted weekly revenue

a= the Y-intercept

to are the independent variables

Normal Values Model

Multiple R= .738

R-square = .546

Lagged Values Model

Multiple R = .755

R-square = .570

Optimized Model

Multiple R=.869

R-square = .756

To better understand the independent variables used in the optimized model, a correlation matrix is helpful. The correlation matrix is used to show all possible simple correlation coefficients among the variables and is useful for locating correlated independent variables. It can also show how strongly each independent variable is correlated with the dependent variable. “There is a high degree of correlation between Estimate on Quick Brew’s weekly advertising expenditure (Lagged) and CoffeeTime’s weekly advertising expenditure (Lagged). When there is a high degree of correlation between two variables, it is a good idea to remove one of them. The variable that is to be removed is the one that is correlated with a greater number of independent variables used in the model” (Simulation, 2007). This is evidenced in Correlation Matrix 1, X3 has the highest value at .657. This is also the reason that X3 was omitted from the optimal model.

Correlation Matrix1

X1 X2 X3 X4 X5 X6

X1 1.000

X2 .288 1.000

X3 .657 .080 1.000

X4 .404 .422 .050 1.000

X5 .270 .293 -.078 .829 1.000

X6 .283 .357 .088 .881 .803 1.000

24 sample size

Correlation Matrix 2

X1 X2 X4 X5 X6

X1 1.000

X2 .288 1.000

X4 .404 .422 1.000

X5 .270 .293 .829 1.000

X6 .283 .357 .881 .803 1.000

24 sample size

X1= CoffeTime’s weekly advertising expenditure

X2= CoffeeTime’s price index

X3= Estimate on Quick Brew’s weekly advertising expenditure

X4= CoffeeTime’s weekly advertising expenditure (Lagged)

X5= CoffeeTime’s price index (Lagged)

X6= Estimate on Quick Brew’s weekly advertising expenditure (Lagged)

Part 2

The dilemma of where to focus Coffee Time’s advertising dollar must take the buying power of tourists into consideration. The disposable income of tourists matched with an aspect of culture that the tourists are familiar and comfortable with makes this demographic an important consideration in understanding the Mumbai cafÐ"© market. Laura makes the claim that 10% of tourists will include a visit to a cafÐ"© while in Mumbai. The claim of 10% is based on a survey conducted of 1,233 visitors to Mumbai in the previous year. The survey revealed that 110 visitors of Mumbai visited a small cafÐ"© while in Mumbai. The strongest test to determine the validity of the claim is a chi-square (or П‡2) goodness-of-fit test for unequal expected frequencies. The goodness-of-fit test is selected because “a goodness-of-fit test is used to compare an observed distribution to an expected distribution” (Lind, Marcel, and Wathen, 2005, p. 523). Further, the test can be applied to expected frequencies that are not equal (Lind, et al., p.529). The purpose of this test is to determine whether