Relationship between Sales and the Independent Variables - Statistics Project Example

Statistic project There is usually a very close relationship between sales and the independent variables fulltimers, par timers, the number of hours works, and the space size in square meters. According to Mullins (2006), sales are directly related to the full-timers, part-timers, number of hours worked, and the size space of store in square meters. The relation that can take these variables is the simple regression. In simple regression we will attempt to predict the dependent variable or response variable y (sales) on the basis of assumed linear relationship with predictor or independent variable (full timers, par timers, the number of hours works, and the space size in square meters. In additional to constructing the model we will access the relationship between the dependent variable y and the independent variables x’s. In the project the independent variable is a continuous random variable and the x variables are fixed constant (either discrete or continuous) and that are controlled by the experimenter. Data set The data in this study include a collection of 400 subjects. Data was obtained from the companies. The performance of 400 companies was evaluated in the research and the data of the variables recorded. Correlation analysis A correlation coefficient is a statistic that is used for testing whether there is any relationship between the variables being tested. It varies between -1 to +1. A correlation of +1 implies that there is a full positive relationship between two variables, hence an increase in one of the variable results to an increase in the value of the other. A correlation of 0 implies that there is totally no relationship between the variables being tested. Hence, the presence of one of the variables does not imply the presence of the other. A correlation of -1 implies that there is a full negative relationship between two variables; hence an increase in one of the variables results in a decrease in the value of the other. Any correlation near -1 implies a strong negative relationship and any near 0 from the negative implies a weak negative relationship. Any correlation near 1 implies a strong positive relationship and any near 0 from the positive implies a weak positive relationship (Jeffery M. Wooldridge (2000). A correlation coefficient is a statistic that is used for testing whether there is any relationship between the variables being tested. It varies between -1 to +1. A correlation of +1 implies that there is a full positive relationship between two variables, hence an increase in one of the variable results to an increase in the value of the other. A correlation of 0 implies that there is totally no relationship between the variables being tested. Hence, the presence of one of the variables does not imply the presence of the other. A correlation of -1 implies that there is a full negative relationship between two variables; hence an increase in one of the variables results in a decrease in the value of the other. Any correlation near -1 implies a strong negative relationship and any near 0 from the negative implies a weak negative relationship. Any correlation near 1 implies a strong positive relationship and any near 0 from the positive implies a weak positive relationship. The regression model From normality test the p-value of the AD test statistic is 0.540 which is greater than the 0.05 level of confidence. This implies that we the data on retention rate is normally distributed. A test of normality was carried out so as to determine if the data for graduation were normally distributed so as to determine the type of analysis to be carried out. If the data was not normally distributed, then special methods could be necessary for its analysis Kutner, M. H., C. J. Nachtsheim, J. Neter, andW. Li (2005). In order to test for normality, the frequency distribution for percentage cost and time overrun for was plotted for six classifications of projects. A regression analysis was used to investigate whether there is a relationship between the variables. The regression analysis between the dependent variable graduation rate and independent variable retention rate is examined. The model  is a simple linear regression model. The parameter are called the regression coefficient. Such model describes the hyper plane in the 2-dimensional space of the regression variable. The parameters  represent the expected change in the response variable y per a change in, while all the repressor remains constants. The regression equation is The model assumption 1  Or equivalently  2.  or equivalently  Question one Pair wise correlation between sales and nfull Correlations: sales, nfull From the analysis, the Pearson correlation of sales and nfull = 0.237 with a P-Value = 0.000 which is less than 0.05 level of confidence. This implies that there is significant relationship between the sales and the nfull. The scatter plot From the scatter plot, it can be observed that there is a linear relationship between the sales and the nfull. From the scatter plot, it’s very important to note that an increase in the nfull will lead to an increase in the sales. Correlations: sales, npart From the pairwise correlation analysis, the Pearson correlation of sales and npart = 0.050 with a P-Value = 0.318which is greater than 0.05 level of confidence. this implies that there is no correlation between the sales and npart Scatter plot From above scatter plot is can be observed that the relationship between the sales and the npart is almost not significant Correlations: sales, hoursw From the pairwise correlation, the Pearson correlation of sales and hoursw = 0.263 with a P-Value = 0.000 which is less than the 0.05 level of confidence. This implies that there is significant correlation between the sales and hoursw. The scatter plot From the scatter plot, it can be seen that there is a linear relationship between the sales and the hoursw. Correlations: sales, ssize From the pairwise correlation analysis, the Pearson correlation of sales and ssize = -0.294 with a P-Value = 0.000 which is less than the 0.05 level of confidence. this implies that there is a significant relationship between the sales and the ssize Th scatter plot From the scatter plot, it can be observed that the increase in sales lead to decrease in the s size. Part 2 SUMMARY OUTPUT Regression Statistics Multiple R 0.604817 R Square 0.365804 Adjusted R Square 0.362609 Standard Error 2985.371 Observations 400 ANOVA   df SS MS F Significance F Regression 2 2.04E+09 1.02E+09 114.4947 5.51281E-40 Residual 397 3.54E+09 8912441 Total 399 5.58E+09         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5133.59 321.6934 15.95802 1.21E-44 4501.154717 5766.026 4501.155 5766.026 hoursw 37.52842 2.83722 13.22718 2.4E-33 31.95056262 43.10627 31.95056 43.10627 ssize -22.1446 1.625067 -13.6269 5.87E-35 -25.33938461 -18.9498 -25.3394 -18.9498 From above regression analysis, it can be observed that the regression equation is obtained as expresses. From the regression analysis of variance, it can be observed that the value of the F (2, 397, 0.05) = 114.49 with a p- value of 0.000 which is less than the 0.05 level of confidence. this implies that there is significant relationship between the sales and the independent variables hoursw and size. The regression model can only account for 36.6% of all the errors in the model. This is because the value of coefficient of determination is 0.366. Part 3 From the regression coefficient analysis, it can be observed that the coefficients number of hours worked is significant since the value of p- value is 0.000 which is less than 0.05 level of confidence. This implies that there is significant effect of the number of hours worked and the sales realized. It can also be observed that the coefficients sales floor space of the store is significant since the value of p- value is 0.000 which is less than 0.05 level of confidence. This implies that there is significant effect of sales floor space of the store and the sales realized. Part 4 SUMMARY OUTPUT Regression Statistics Multiple R 0.634177 R Square 0.40218 Adjusted R Square 0.396126 Standard Error 2905.818 Observations 400 ANOVA   df SS MS F Significance F Regression 4 2.24E+09 5.61E+08 66.43357 6E-43 Residual 395 3.34E+09 8443778 Total 399 5.58E+09         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3751.311 427.696 8.770975 5.36E-17 2910.466 4592.156 2910.466 4592.156 nfull 557.3077 172.2475 3.235505 0.001317 218.6712 895.9442 218.6712 895.9442 npart 684.9984 225.4428 3.038457 0.002536 241.7805 1128.216 241.7805 1128.216 hoursw 32.76485 3.061793 10.7012 1.22E-23 26.74541 38.7843 26.74541 38.7843 ssize -23.9079 1.648595 -14.502 1.65E-38 -27.149 -20.6668 -27.149 -20.6668 From the regression analysis, the inclusion of the part timer and the full timers increases the coefficient of determination from 0.366 to 0.402. This implies that there is a significant raise in the efficiency of the regression model when the other independent variables are included into the regression model. References Mullins Li (2006). Applied Linear Statistical Models (5th ed.). New York: McGraw-Hill/Irwin. Kutner, M. H., C. J. Nachtsheim, J. Neter, andW. Li (2005). Applied Linear Statistical Models (5th ed.). New York: McGraw-Hill/Irwin. Jeffery M. Wooldridge (2000). Applied Linear Statistical Models (5th ed.). New York: McGraw Hill/Irwin. Read More