Critical Analysis of the Various Determinants of Annual Gross Revenue - Example

Name: Professor: Subject: Economics Date: Overview This report intends to offer a critical analysis of the various determinants of annual gross revenue. The determinants that will be assessed in this paper include people, income, competitors, price, and distribution. The analysis will entail regression of annual gross income on the aforementioned determinants of annual gross revenue. i) Summary statistics Based on the descriptive statistics above, the average population analyzed in the case study is 59703. However, the data values deviate from the given mean by 9834. These residents earn an average income of $72665 with other data values deviating from the given mean by 7203. On the question of competitors, there is an average of 3 competitors. The descriptive statistics above further indicates that the mean price of brand new model of a mid-size family sedan is $29,207.20 while other observations deviate from the given mean by 3584.57. It is important to note that the distribution of income and competitors is skewed to the right with a long tail stretching rightwards. This implies that most values are intense on the left side of the mean whereas extreme values are to the right. While the minimum income earned by the population is $54,248, the maximum income is $92095. In the same line, there is a minimum of 1 and maximum of 5 competitors in the provided data. Given the skewed distribution, the best measure of central tendency is the median. Mean is usually dragged in the direction of skewness under skewed distribution hence median ought to be used because it is unaffected by extreme values. From the statistics above, the median income and number of competitors is $74,035 and 3 respectively. On the other hand, the distribution of people and price are negatively skewed. This suggests that most values are intense on the right side of the mean while extreme values are to the left. Median, as well, will be used as a measure of central tendency. In this case, median number of population and price is 60320 and $28,650 respectively. The maximum and minimum number of population facing the showrooms is 31720 and 79990 correspondingly. Similarly, the respective minimum and maximum price of the vehicles is $21,550 and $35,500. ii) Representation of regression model to be used In functional form, the applicable representation is as shown below. The regression equation that will be applied is represented below: Where; The justification for application of ordinary least squares to estimate a regression model is the possibility of using the resultant line of best fit to predict future annual gross earnings without worrying about unbiasedness and efficiency of statistical properties of the stated regression model. iii) The estimated model The regression output is attached as appendix 1. The values for intercept and regression coefficients are as follows: Based on the tabulated coefficients, the estimated model is: People: Keeping other independent variables constant, each increase in number of people leads to an increase in annual gross revenue by 33.24. The opposite is also true Income: Keeping other independent variables constant, each increase in earnings leads to an increase in annual gross revenue by 291. The opposite is also true. Competitors: Keeping other independent variables constant, each increase in number of competitors leads to a decrease in annual gross revenue by 471,414.91. The opposite is true. Price: Keeping other independent variables constant, each increase in number of price of sedan leads to an increase in annual gross revenue by 309.77. The opposite is true. Distribution: Keeping other independent variables constant, there is an increase of annual gross revenue by when the showroom is located within 10km from CBD. Otherwise, the change in revenue is zero when a showroom is located outside the CBD. iv) The independent variables that significantly explain the dependent variable is determined by comparing p-values with 0.05 level of significance. The t-statistic and p-values attached in appendix 1 are tabulated below in summary,   t Stat P-value People 0.962 0.34113 Income 5.034 8.6E-06 Competitors (COMPTORS) -1.33 0.18989 Price 2.874 0.00622 Dist 2.892 0.00593 From the table above the coefficients for income, price and distribution are statistically significantly different from zero. These independent variables, therefore, significantly influence the dependent variables. The p-values for people and competitors exceed a level of significance of 0.05. This means that the coefficient values of people and competitors are not statistically different from zero hence do not have any statistical influence on dependent variable. v) Estimated regression model considering eight decimal places The coefficients are tabulated below Predicted annual gross revenue for a showroom located 8 km from CBD and for the mean values of independent variables is obtained by assuming that DIST is 1. Predicted annual gross revenue: The observation made is that annual gross revenue increases to $35,807,869.82. vi) Coefficient of determination adjusted for degrees of freedom In comparison with the value of R-square, as calculated above gives an accurate measure of goodness of fit. It implies that 36.505% of the variation in annual gross income is explained by the independent variables including people, income, competitors, distribution, and price. vii) Justifying inferences The first step is to examine whether the independent variables are statistically significant based on regression output. The coefficients for income, price and distribution are statistically significantly different from zero. These independent variables, therefore, significantly influence the dependent variables. On the other hand, the p-values for people and competitors exceed a level of significance of 0.05. This means that the coefficient values of people and competitors are not statistically different from zero hence do not have any impact on the dependent variable. F-statistic test is also applied in determining whether people and competitors should be included in the model. The initial model is reduced by removing independent variables that are predicted to have no effect on dependent. The following formula is subsequently applied. Hypotheses Test statistic is F-test Where Given that level of significance, people and competitors do not add significantly to the model hence can be removed. By studying the effect of each independent variable on annual gross revenue, the following conclusions can be drawn: People: Keeping other independent variables constant, each increase in number of people leads to an increase in annual gross revenue by 33.24. The opposite is also true Income: Keeping other independent variables constant, each increase in earnings leads to an increase in annual gross revenue by 291. The opposite is also true. Competitors: Keeping other independent variables constant, each increase in number of competitors leads to a decrease in annual gross revenue by 471,414.91. The opposite is true. Price: Keeping other independent variables constant, each increase in number of price of sedan leads to an increase in annual gross revenue by 309.77. The opposite is true. Distribution: Keeping other independent variables constant, there is an increase of annual gross revenue by when the showroom is located within 10km from CBD. Otherwise, the change in revenue is zero when a showroom is located outside the CBD. Works Cited Bluman, Allan. Elementary Statistics: A Step by Step Approach. Boston: McGraw-Hill, 2014. viii) Appendices Appendix 1: Summary regression output Read More