Business Forecasting and Data Analysis - Essay Example

Business Forecasting and Data Analysis Chart showing the distribution of the overall mean management score, if all 17 aspects are treated equally.The distribution of overall mean management scores is shown in the form of a bar chart indicating the count (of cases with the same mean score) on the vertical y-axis, and the various levels of overall mean management scores at the horizontal x-axis. Majority of the cases recorded mean management scores at 2.611, which was registered for more than 40 cases. 2. Charts illustrating variations in the overall mean management score according to: a. Whether the firm is a multinational or not Variations of one variable with respect to another may be graphically presented through a scattergram. Since there are only two dummy variables (multinational or not) this yields the scattergram below. b. Type of ownership The graph above shows that there is no systematic variation in overall management score according to the type of ownership. c. Size of firm as measured by the total weekly hours across all employees For the chart above, in order to improve the chart’s usefulness, the firms included in the graph are those with total weekly labour hours below 100,000. The few firms (approximately 10) which had total labour hours at more than 100,000 were not included. The graph shows that there is no systematic change in overall management score based on total labour hours. 3. Statistical tests to examine variations in the overall mean management score according to certain criteria To determine if variations one variable changes in tandem with another variable, correlation may be used. In this case, SPSS was used to determine Pearson correlation; a correlation statistic of higher than 0.50 is considered moderately strong, and the closer the coefficient is to 1.0, the stronger the correlation. a. Whether the firm is a multinational or not Correlations Ave_all mne_not Ave_all Pearson Correlation 1 .414** Sig. (2-tailed) .000 N 1026 1026 mne_not Pearson Correlation .414** 1 Sig. (2-tailed) .000 N 1026 1026 **. Correlation is significant at the 0.01 level (2-tailed). b. Type of ownership Correlations Ave_all typeown Ave_all Pearson Correlation 1 -.272** Sig. (2-tailed) .000 N 1026 1026 typeown Pearson Correlation -.272** 1 Sig. (2-tailed) .000 N 1026 1026 **. Correlation is significant at the 0.01 level (2-tailed). c. Size of firm based on total weekly labour hours Correlations Overall mgt score Total weekly labour hours Overall mgt score Pearson Correlation 1 .107** Sig. (2-tailed) .001 N 1026 1026 Total weekly labour hours Pearson Correlation .107** 1 Sig. (2-tailed) .001 N 1026 1026 **. Correlation is significant at the 0.01 level (2-tailed). For all three instances above, correlation coefficients are weak because none of them exceeded 0.50 nor approached the maximum of 1.0. In all cases, however, results are significant at the 0.01 level. This means that while the correlations of all three variables with management score are significant, the variations attributed to them are not very large. 4. Multivariate regression model to consider whether management scores (and other variables) might explain variations in sales across firms. In conducting the regression analysis, the intention is to predict the value of a dependent variable if the values of predictor variables are known. The problem given seeks to determine whether or not variations in total sales among firms may be determined based on firm ownership, assets, management score, and weekly labour hours. Because there are four predictor variables, multivariate regression will be used. The assumptions on which the regression is based are that the variables are normally distributed, and that there is a linear relationship between the dependent and independent variables. The model summary table below shows that the model has an R value (representing simple correlation) of 0.914, indicating a high degree of correlation. The R Square value is also given, a figure which indicates the degree to which the dependent variable (total sales) may be explained by the independent or predictor variables (total weekly labour hours, overall mean management score, total company fixed assets, and whether or not the firm is founder-owned). The R Square value of 0.835 indicates that 83.5% of dependent variables may be explained by the predictors, which is a high level of prediction. The ANOVA table which follows indicates that the regression model arrived at in the exercise to be able to predict the outcome well, because the statistical significance is below the 0.05 and even the 0.01 level, meaning that there is a less than 1% chance of error in the estimate arrived at by the model. ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 2.390E14 4 5.976E13 957.982 .000a Residual 4.684E13 751 6.238E10 Total 2.859E14 755 a. Predictors: (Constant), Founder-owned, Total Company fixed assets (US dollars), Overall mgt score, Total weekly labour hours b. Dependent Variable: Total Sales (US dollars) The coefficients table that follows indicates the degree to which each predictor variable is predictive of the dependent variable, sales. A glance at the statistical significance level at the end last column of the table shows that the constant, the overall management score, total company fixed assets, and whether the firm is founder owned or not have high predictive value, because they are within the 0.01 significance level. The total weekly labour hours is likewise predictive, not within the 0.01 significance level but at the 0.05 level, thus it has slightly less predictive value than the other three variables and the constant. Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -145780.891 34413.498 -4.236 .000 Total weekly labour hours -.298 .142 -.043 -2.089 .037 Overall mgt score 57259.363 12317.745 .070 4.649 .000 Total Company fixed assets (US dollars) 2.223 .049 .934 45.173 .000 Founder-owned 62139.818 21468.511 .043 2.894 .004 a. Dependent Variable: Total Sales (US dollars) From the coefficients table, the regression equation may be specified as: The coefficient of each variable indicates the magnitude by which that variable relates to the dependent variable, thus the higher the coefficient, the greater that variable’s influence on the dependent variable. The sign of the variable indicates the direction of the relationship; where the sign is negative, an increase in the variable tends to decrease the value of the resultant variable, and vice versa. Residuals Statisticsa Minimum Maximum Mean Std. Deviation N Predicted Value -66472.37 9412567.00 148835.23 562660.665 756 Residual -1944739.875 3691439.250 .000 249090.944 756 Std. Predicted Value -.383 16.464 .000 1.000 756 Std. Residual -7.787 14.780 .000 .997 756 a. Dependent Variable: Total Sales (US dollars) 5. Residuals For regression analysis to be valid, the variance of the error terms (or residuals) must be constant, and residuals must have a mean of zero. In the preceding table (Residuals Statistics), the mean of the residuals (highlighted in yellow) is equal to zero, and the standard deviation, if squared, will yield the variance, which is a constant. Referring to the earlier table for ANOVA, the highlighted yellow value which is the mean square for the residual is equivalent to the variance, or the square of the standards deviation of the residuals, and it is a constant. These show that the assumptions for residuals holds true for the sales regression model formulated. 6. Prediction of sales using regression equation Assuming that weekly labour hours is 15,000, mean management score is 3.5, total company assets is 30,000 dollars, and the firm is not owned by the founder, the Sales may be computed by substituting these values in the regression equation earlier formulated, yielding: S This yields a resultant sales figure of $116,845.50. 7. Prediction of change of sales given a change in overall mean management score Estimating the effect of the change of mean management score of 2.5 to 4.0 on sales requires using the same equation as that used in the preceding answer. The resulting sales corresponding to the two values of overall mean management scores shall be taken. Substituting 2.5 in the equation: S The above equation yields sales of $59,586.50. Next, the value 4.0 shall be substituted into the equation for the variable overall mean management score. S The second equation yields $145,475 in sales. Thus a change of overall mean management score from 2.5 to 4 will tend to increase total sales by $85,888.50, the difference between the results of the two equations above. Extension 1. Modification of sales regression model by distinguishing among management scores for monitoring, target setting, and incentives. It was suggested that the sales regression model may be improved by differentiating the scores for monitoring, target setting and incentives instead of the overall mean management score. The previous model had an R square value of 0.836, while the adjust model below has a higher R square of 0.849, indicating that the model explains 84.9% of the sales amounts, making this model a more accurate model by 1.3 percentage points. ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 2.428E14 6 4.046E13 702.864 .000a Residual 4.311E13 749 5.756E10 Total 2.859E14 755 a. Predictors: (Constant), Incentives, Founder-owned, Total Company fixed assets (US dollars), Monitoring, Total weekly labour hours, Target setting b. Dependent Variable: Total Sales (US dollars) The significance level of the model derived shows it to be a reliable predictor to within the 0.01 significance level. Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -118978.318 33713.684 -3.529 .000 Total weekly labour hours -.245 .137 -.036 -1.788 .074 Total Company fixed assets (US dollars) 2.198 .047 .924 46.395 .000 Founder-owned 84534.235 20913.392 .059 4.042 .000 Monitoring 74981.800 14232.990 .110 5.268 .000 Target setting 53261.500 13381.918 .083 3.980 .000 Incentives -93095.665 15119.404 -.115 -6.157 .000 a. Dependent Variable: Total Sales (US dollars) Based on the coefficients table, the constant and all explanatory variables except total weekly labour hours are statistically significant to within the 0.01 level. Since total weekly labour hours is not significant, it is eliminated in the final sales model below. Residuals Statisticsa Minimum Maximum Mean Std. Deviation N Predicted Value -163047.03 9299125.00 148835.23 567034.252 756 Residual -1850017.750 3439474.750 .000 238967.527 756 Std. Predicted Value -.550 16.137 .000 1.000 756 Std. Residual -7.711 14.336 .000 .996 756 a. Dependent Variable: Total Sales (US dollars) The residuals test shows that mean residual value is zero, and variance (square of the standard deviation, and the mean square in the ANOVA table) is constant. The assumptions for residuals are thus proven true. 2. Modifying the sales regression model from Extension (1) by including type of multinational A further refinement was sought by adding ‘type of multinational,’ referring to the nature of the firm, as an explanatory variable. It will be noted that this new model is not a significant improvement over the model arrived at in Extension (1) since the R square statistic is exactly the same at 0.849. This model is just as reliable in predicting sales values as the model without type of multinational. ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 2.428E14 7 3.469E13 602.492 .000a Residual 4.306E13 748 5.757E10 Total 2.859E14 755 a. Predictors: (Constant), Type of mulitnational, Total Company fixed assets (US dollars), Incentives, Founder-owned, Monitoring, Total weekly labour hours, Target setting b. Dependent Variable: Total Sales (US dollars) The significance statistic is well within the 0.01 significance level, thus the model is significantly predictive of the value of sales. Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -76452.431 56317.969 -1.358 .175 Total weekly labour hours -.252 .137 -.037 -1.835 .067 Total Company fixed assets (US dollars) 2.198 .047 .924 46.397 .000 Founder-owned 90503.172 21852.347 .063 4.142 .000 Monitoring 72908.880 14402.890 .107 5.062 .000 Target setting 51292.074 13544.989 .080 3.787 .000 Incentives -93936.492 15146.810 -.116 -6.202 .000 Type of mulitnational -12263.177 13008.421 -.016 -.943 .346 a. Dependent Variable: Total Sales (US dollars) From the table above, it is seen that two explanatory variables are not significant in predicting sales even at the 0.05 level; these are total weekly labour hours, which was determined even in the previous model, and type of multinational, the new explanatory variable added. The latter was evident in the absence of change in the R square value. The final regression model for this attempt is: The following table shows that the residuals comply with the assumptions on zero residual square and constant variance. Residuals Statisticsa Minimum Maximum Mean Std. Deviation N Predicted Value -168336.44 9309675.00 148835.23 567094.005 756 Residual -1844212.000 3445031.500 .000 238825.694 756 Std. Predicted Value -.559 16.154 .000 1.000 756 Std. Residual -7.686 14.358 .000 .995 756 a. Dependent Variable: Total Sales (US dollars) Bibliography Bloom, N & Reenen, J V 2010 ‘Why Do Management Practices Differ across Firms and Countries?’ Journal of Economic Perspectives, 24(1), 203-224 Pardoe, I 2012 Applied Regression Modeling, 2nd edition. Hoboken, N.J.: John Wiley & Sons SPSS Tutorial and Help XinYan & Xiao Gang Su 2009 Linear Regression Analysis: Theory and Computing. London: World Scientific Publishing Co. Pte Ltd. Read More