Volume of Sales of Auxiliary Variables - Report Example

A REPORT ON THE VOLUME OF SALES PER SQUARE ,TOTAL NUMBER OF HOURS WORKED,NUMBER OF PART TIME WORKERS,NUMBER OF FULL TIME WORKERS AND SIZE OF FLOOR COVERED BY THE STORE PER SQUARE METRE INTRODUCTION The following is a report on a study that aimed at establishing the relationship between the volume of sales and four auxiliary variables namely; a. Total number of hours worked b. Size of the floor covered by the store per square metre c. Number of Part time workers d. Number of Full time workers STUDY OBJECTIVES The study aimed at investigating the following objectives; To calculate the pair-wise correlation coefficients between sales per square meter and each of the other variables and test their statistical significance. To write down an equation representing a linear regression model in which sales per square metre depend on a constant, the total number of hours worked and floor space of the store (in square metres) To interpret the estimated coefficients from an economic perspective and comment on their statistical significance To determine if the inclusion of the number of full-timers and part-timers significantly improve the model HYPOTHESES Hypothesis 1: Ho:sales are not significantly correlated to hoursw Ha:sales are significantly correlated to hoursw Hypothesis 2: Ho:sales are not significantly correlated to ssize Ha:sales are significantly correlated to ssize Hypothesis 3 Ho:sales are not significantly correlated to nfull Ha:sales are significantly correlated to nfull Hypothesis 4: Ho:sales are not significantly correlated to npart Ha:sales are significantly correlated to npart Results and analysis QUESTION_1 To perform pairwise correlation coefficient between sales per square metre and each of the following nfull(Number of full timers) HYPOTHESIS Ho:sales are not significantly correlated to nfull Ha:sales are significantly correlated to nfull PART_A _AND_B(PERFORM PAIR-WISE CORRELATION AND TEST FOR STATISTICAL SIGNIFICANCE) cor.test(sales,nfull) Pearsons product-moment correlation data: sales and nfull t = 4.8708, df = 398, p-value = 1.607e-06 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.1424465 0.3276179 sample estimates: cor 0.2371854 PART_D(PROVIDE WRITTEN INTERPRETATION FOR CORRELATION COEFFICIENTS AND SCATTER PLOTS) Discussion From the results above a sample correlation coefficient of 0.2371854 is generated by the pearson’s product-moment correlation coefficient. A 95% confidence interval of the correlation coefficient is (0.1424465, 0.3276179) A t-statistic of 4.8708 with 398 degrees of freedom is also produced with a p-value of 1.6073-06(0.003983355) p-value is less than 5% level of significance. Conclusion Since the p-value obtained is less than 5% level of significance this provides a strong evidence to reject the null hypothesis and instead the alternative hypothesis that their exists a positive relationship between sales and number of full time workers. PART_C(SCATTER PLOT AND INTERPRETATION) Discussion From the scatter plot its evident that the volume of sales increase with an increase in the number of full timers the highest amount of sales recorded when number of full timers is 3. QUESTION_1 To perform pairwise correlation coefficient between sales per square metre and each of the following II).npart(Number of part timers) HYPOTHESIS Ho:sales are not significantly correlated to npart Ha:sales are significantly correlated to npart PART_A _AND_B(PERFORM PAIR-WISE CORRELATION AND TEST FOR STATISTICAL SIGNIFICANCE) cor.test(sales,npart) Pearsons product-moment correlation data: sales and npart t = 1.0004, df = 398, p-value = 0.3177 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.0482034 0.1474128 sample estimates: cor 0.05008504 PART_D (PROVIDE WRITTEN INTERPRETATION FOR CORRELATION COEFFICIENTS AND SCATTER PLOTS) Discussion From the results above a sample correlation coefficient of 0.05008504 is generated by the pearson’s product-moment correlation coefficient. A 95% confidence interval of the correlation coefficient is (-0.0482034, 0.1474128) A t-statistic of = 1.0004 with 398 degrees of freedom is also produced with a p-value of 0.3177 which is greater than 5% level of significance. Conclusion Since the p-value obtained is greater than 5% level of significance this provides a strong evidence to reject the alternative hypothesis and instead adopt the null hypothesis that their exists no positive relationship between sales and number of full time workers. PART_C(SCATTER PLOT AND INTERPRETATION) Discussion From the scatter plot its evident that the volume of sales varies randomly with an increase in the number of full timers the highest amount of sales recorded when the number of full timers was less than 2 thereafter a steady decline is observed. QUESTION_1 To perform pairwise correlation coefficient between sales per square metre and each of the following III) ssize(Sales floor space of the store in square metre ) HYPOTHESIS Ho:sales are not significantly correlated to ssize Ha:sales are significantly correlated to ssize PART_A _AND_B(PERFORM PAIR-WISE CORRELATION AND TEST FOR STATISTICAL SIGNIFICANCE) Pearsons product-moment correlation data: sales and ssize t = -6.1317, df = 398, p-value = 2.097e-09 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.3808711 -0.2015451 sample estimates: cor -0.293791 PART_D(PROVIDE WRITTEN INTERPRETATION FOR CORRELATION COEFFICIENTS AND SCATTER PLOTS) Discussion From the results above a sample correlation coefficient of -0.293791 is generated by the pearson’s product-moment correlation coefficient. A 95% confidence interval of the correlation coefficient is (-0.3808711 -0.2015451) A t-statistic of -6.1317 with 398 degrees of freedom is also produced with a p-value of 2.097e-09 (0.0002587904) is less than 5% level of significance. Conclusion Since the p-value obtained is less than 5% level of significance this provides a strong evidence to reject the null hypothesis and instead the alternative hypothesis that their exists a negative relationship between sales and the amount the sales floor space of the store in square metres. PART_C(SCATTER PLOT AND INTERPRETATION) Discussion From the scatter plot its evident that the volume of sales decrease steadily with an increase in the sales floor space,sales are at the lowest when the floor size is 750 square metres. QUESTION_1 To perform pairwise correlation coefficient between sales per square metre and each of the following IV) hoursw(Total number of Hours Worked ) HYPOTHESIS Ho:sales are not significantly correlated to hoursw Ha:sales are significantly correlated to hoursw PART_A _AND_B(PERFORM PAIR-WISE CORRELATION AND TEST FOR STATISTICAL SIGNIFICANCE) cor.test(sales,hoursw) Pearsons product-moment correlation data: sales and hoursw t = 5.4382, df = 398, p-value = 9.412e-08 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.169311 0.351972 sample estimates: cor 0.2629966 PART_D(PROVIDE WRITTEN INTERPRETATION FOR CORRELATION COEFFICIENTS AND SCATTER PLOTS) Discussion From the results above a sample correlation coefficient of 0.2629966 is generated by the pearson’s product-moment correlation coefficient. A 95% confidence interval of the correlation coefficient is (0.169311 ,0.351972) A t-statistic of 5.4382 with 398 degrees of freedom is also produced with a p-value of 9.412e-08(0.003157374) is less than 5% level of significance. Conclusion Since the p-value obtained is less than 5% level of significance this provides a strong evidence to reject the null hypothesis and instead the alternative hypothesis that there exists a positive relationship between sales and the total number of hours worked. PART_C(SCATTER PLOT AND INTERPRETATION) Discussion From the scatter plot its evident that the volume of sales increases gradually with an increase in the number of hours worked the highest amount of sales recorded was at 200th hour. RECOMMENDATIONS From the results above its clear that the volume of sales is influenced by positively by the number of fulltime workers(nfull),number of part time workers(npart) and Total number of workers(hoursw) and the amount of space of store per metre square negatively influences the volume of sales as proved by the fitted regression equation. CONCLUSION From the observations above I would like to make the following recommendations ; a. increase the number of full time workers b. increase the number of part-time workers c. increase the number of hours worked d. Reduce the amount of space of store The above recommendations once implemented will see an increase in volume of sales in the store. Doing the above will help in improving the volume of sales since there is realization of positive correlation with the exception of the amount of space of store. Read More