Statistics – Research Methods for Managerial Decisions

a) The regression model was used by Laura to determine predictive values of advertising expenditures on Coffee Time's price index. Bivariate Regression includes two variables, one explanatory and one response; this regression model determines the predicted relationship between two variables. For example when two variables such as an advertising expenditures and coffee time are found to correlate, the presence of one will predict the presence of another and the regression statistic determines the significance of this effect. Assumptions are that the underlying relationship is linear. Dots in the scatterplot tend to be dispersed equally about all parts of the prediction line referred to the assumption of homoscedasticity. Regression generates a least squares regression line using the following least squares regression equation that produces the best fit linking X to Y: y = a + bX, where a and b are constants, y is the predicted value of Y and X is a specific value of the independent variable. Once a line of best fit is calculated, a score for y can be predicted, based on any score for x. By using regression, the score obtained on x can be matched to a point on the regression line. This point can then matched to y to obtain the predicted score on y (Witte, 1980). Multiple regression allows for one response variable and several explanatory variables and their predicted relationship. For example the presence of advertising expenditures and cost of coffee and seasonal factors can be used to predict coffee time's price index. Assumptions are the same as for bivariate regression (Moore & McCabe, 1989).

Lagged values are often used when there is a time series analysis. This means that often, the behavior of a dependent variable can be at least partially explained by its own past behavior. In the case of Coffee Time's price index, this means that the pr