Analytical Methods in Economics and Finance - Assignment Example

Analytical Methods in Economics and Finance Name: Tutor: Course: Date: (i) The summary statistics of the variables selected as the determinants of success of a given store are indicated in table 1 below. Included in the summary statistics are the measures of central location such as the mean as well as the measures of dispersion such as the standard deviation. Table 1   Revenue People Income COMPTORS Price Mean 343965.68 5970.26 41522.96 2.8 5.68 Standard Error 5307.89863 139.0845281 582.1376385 0.142857143 0.0510302 Median 345166.5 6032 41339.5 3 5.75 Mode #N/A 5917 #N/A 3 6 Standard Deviation 37532.51115 983.47613 4116.334718 1.010152545 0.36083803 Sample Variance 1408689393 967225.2984 16944211.51 1.020408163 0.13020408 Kurtosis -0.58050278 0.965044145 0.866669536 -0.192246809 -0.7738904 Skewness -0.17644248 -0.5668814 0.380395523 0.296984848 -0.6727417 Range 152895 4827 21627 4 1 Minimum 256640 3172 30999 1 5 Maximum 409535 7999 52626 5 6 Sum 17198284 298513 2076148 140 284 Count 50 50 50 50 50 From the summary statistics of the variables included the table above, the measures of central location; mean and median seem not to differ significantly for all the five variables analyzed. This indicates that the distribution of the sample data is approximately symmetrical. To further analyze the distribution of the sample data above, the use of a histogram would be appropriate since it would illustrate whether the data comes from a skewed or symmetrical distribution. The histogram of the annual gross revenue is as illustrated in figure 1 below. The histogram is bell-shaped, which indicate that the distribution of the sample data is approximately symmetrical. This implies that the sample data was drawn from a population with approximately normal distribution. Figure 1 (ii) The equation of the multiple-regression model which is to be estimated is as shown below; REVENUE = β0+ β1 PEOPLE + β2 INCOME + β3 COMPTORS + β4 PRICE As indicated by the equation above, REVENUE is the dependent variable in the model. The model has four independent variables namely PEOPLE, INCOME, COMPTORS and PRICE. The regression model is considered appropriate in this case because the relationship between the dependent variable and each of the independent variable is assumed to be linear. In addition, the error from the model is assumed to be normally distributed with an expected mean of zero and equal variance. Therefore, the prediction of REVENUE using the multiple-regression model with the indicated independent variables is considered appropriate because for the given regression model, the regression assumption are assumed to have been satisfied. (iii) Using excel, the regression analysis yields the output shown in figure 2 below; Figure 2 The regression model initially established and to be estimated is; REVENUE = β0+ β1 PEOPLE + β2 INCOME + β3 COMPTORS + β4 PRICE Therefore, inserting the estimates of the regression coefficients in the established regression model above, the regression model with the estimated coefficients is as shown below; REVENUE = - 68363.15 + 6.44 PEOPLE + 7.27 INCOME – 6709.43 COMPTORS + 15968.76 PRICE The independent variable (PEOPLE) has a positive coefficient of 6.44. This shows that there is positive linear relationship between REVENUE and PEOPLE, such that for every additional person within 1km of the store, annual gross revenue is expected to increase by 6.44. INCOME also has a positive linear relationship with REVENUE. Based on the regression coefficient of INCOME, a unit change in the mean income of households within 1 km of the store changes the annual gross revenue of the store by 7.27. The regression coefficient of COMPTORS (competitors) indicates that there is a negative linear relationship between COMPTORS and REVENUE. Therefore, every additional competitor within 1 km of the store causes a reduction of annual gross revenue by 6,709.43. Finally, the regression analysis established a positive linear relationship between REVENUE and PRICE. The regression coefficient indicates that a unit change in price subsequently changes the annual gross revenue by approximately 15,968.76. (iv) To test whether an independent variable is significant or not, formulate a null hypothesis and test against an alternative hypothesis at 5% level of significance; Null hypothesis, H0: βi = 0 (independent variable not significant) Alternative hypothesis, H1: βi ≠ 0 (independent variable is significant) Decision rule: Reject the null hypothesis if the p-value is less than the 0.05 level of significance. PEOPLE: p –value = 0.089 > 0.05, hence do not reject H0 INCOME: p –value ≈ 0 < 0.05, hence reject H0 COMPTORS: p –value = 0.086 > 0.05, hence do not reject H0 PRICE: p –value = 0.125 > 0.05, hence do not reject H0 Conclusion: INCOME is the only independent variable which significantly explains the dependent variable (REVENUE). (v) The mean values of the variables (PEOPLE, INCOME, COMPTORS AND PRICE) are as indicated below; Mean of PEOPLE = 5970.26 Mean of INCOME = 41,522.96 Mean of COMPTORS = 2.8 Mean of PRICE = 5.68 Using the mean values of the respective independent variable, the estimated value of REVENUE is determined as follows; REVENUE = - 68363.15 + 6.44 PEOPLE + 7.27 INCOME – 6709.43 COMPTORS + 15968.76 PRICE REVENUE = - 68363.15+(6.44 x5970.26)+(7.27 x 41522.96)–(6709.43 x 2.8)+(15968.76 x 5.68) REVENUE = 343,873.40 Using the mean values of the respective independent variables, the established estimate of the REVENUE is 343,873.40. This estimated value of the dependent variable determined using the mean values of the respective independent variable seem to not differ significantly with the actual sample mean of the dependent variable (REVENUE) 343,965.68. (vi) The coefficient of determination adjusted for degrees of freedom (Adjusted R Square) is 0.551. The adjusted R square implies that a total of 55.1% of variation in the REVENUE is jointly explained by the four independent variables (PEOPLE, INCOME, COMPTORS and PRICE) included in the regression model. This shows that the majority of total variation in REVENUE is explained by the four independent variables. (vii) The current selection of independent variables (PEOPLE, INCOME, COMPTORS and PRICE) is appropriate in estimating the sales revenue of the store. This can be established by testing the null hypothesis and the alternative hypothesis at 5% level of significance as follows; Null hypothesis, H0: β = 0 (model selected is not significant) Alternative hypothesis, H1: β ≠ 0 (model selected is significant) Decision rule: Reject the null hypothesis if the p-value is less than the 0.05 level of significance. ANOVA results F (4, 45) = 16.05, p = .000. As established the p-value < 0.05, hence, reject the null hypothesis; H0. Conclusion: From the hypothesis test above, it can be concluded that the regression model is significant in explaining the dependent variable (REVENUE). This shows that the current selection of independent variables; (PEOPLE, INCOME, COMPTORS and PRICE) is significant in explaining the variation in the sales revenue of the store. Read More