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 ...