Regression Analysis of the Sales Made by Organization: 3M Company - Case Study Example

ECONOMETRICS MODELLING EXECUTIVE SUMMARY In the previous report we ran regression analysis to help in the prediction of the sales made by organization. The organization mentioned was 3M Company that operates as a diversified technology company worldwide. Among the variables we looked at that could possibly affect the sales made 3M Company. The study found out that the sales depend on the variables mentioned such as the USA nominal GDP, USA unemployment rate and the PMI index. This report provides diagnostic tests for the regression model made in the previous work. Regression diagnostics are methods for determining whether a regression model fit to data adequately represents the data. The diagnostic test shows that the overall regression model is significant at 5% significance level; hence the model is fit/appropriate. However, the diagnostic test for the accuracy of projections showed that only one variable was significant in the model at 5% significance. The value of R-squared (R2) further confirms the fitness/appropriateness of the model. The value is given as 0.9591 implying that approximately 95.91% of variation in the dependent variable (sales) is explained by the three explanatory variables (USA nominal GDP, USA unemployment rate and the PMI index) in the model. INTRODUCTION Just like all the other statistical procedures multiple linear regression analysis relies on a few basic assumptions regarding the population from where the data sets have been derived. The results of the regression (OLS) analysis are only reliable when such assumptions are met and satisfied. It is therefore prudent that regression diagnostic tests are conducted to verify the validity of the model. These assumptions include: i) The relationship between the explanatory (independent) variables and the outcome (dependent) variable is linear. That is to mean that, each increase or decrease by one unit in an explanatory (independent) variable is associated with a fixed increase or decrease in the outcome (dependent) variable. ii) The regression equation states and describes the mean value of the outcome (dependent) variable for a given set of independent variables. iii) The individual data points of the response (dependent) variable for each of the explanatory (independent) variables are normally distributed about the regression line. iv) The variance of the data points about the line of means is the same (homoscedasticity) for each explanatory variable. v) The explanatory variables are independent of each other, that is, having knowledge of the value of one or more of the independent variables does not in any way tell us anything about the others. This is however not often in the real life situations since many variables are normally correlated. Such correlations can many a times lead to mistaken conclusions METHODOLOGY Regression diagnostic is one of available set of procedures for regression analysis that aims at assessing the validity of a model in different number of ways (Everitt, 2002). The assessment may involve exploration of the models underlying statistical assumptions, examining the structure of the model by considering the different formulations that have more, fewer or different explanatory variables, or a study of subgroups of observations, looking for those that are either poorly represented by the model (outliers) or that have a relatively large effect on the regression models predictions. According to Dodge (2003), a regression diagnostic may take graphical form, informal quantitative results or may be formal statistical hypothesis test; each of which provides guidance for further stages of a regression analysis (Dodge, 2003). DIAGNOSTIC TESTS i) ASSESSING ASSUMPTIONS a) DISTRIBUTION OF MODEL ERRORS The value of skewness is given as -0.3895 Read More