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Since the production, transportation and tax costs are constituent composition of selling price of a unit product this paper’s main objective is to establish the relationship between these variables. The hypothesis is that production, tax and transportation costs increase the selling price of a unit product. Regression model to be used will be of the form; Price= f (cost of transport+cost of production + Tax rate)

P=f (Tp+Ts+Tx)

Where P=Price

Ts=Cost of transport

Tp=Cost of production

Tx=Tax rate

In addition to these, F-test or ANOVA (analysis of variance) will be done in order to determine the reliability of the model. This will be of great help in drawing a valid conclusion about the hypothesis to be tested.

Population Sample

This research made use of secondary source of data. The data used was from United States Census Bureau. The sample data was collected for 48 cities, states across United States.  This data was analyzed and the following results were obtained. The expected relationship is that; Transport costs will have an increasing effect to the price of the product. Production costs will have an increasing effect to the price of a product and tax rates will as well have an increasing effect tom the price of the product. The price of the product is the dependent variable while transport, production and tax rate are independent variables of the regression model.

Discussion

Descriptive statistics

Table 1

Transport costs

 

Production costs

 

Tax average

 

           

Mean

0.535625

Mean

0.463125

Mean

0.069179167

Median

0.45

Median

0.45

Median

0.06935

Mode

0.45

Mode

0.45

Mode

0.0813

Standard Deviation

0.156245

Standard Deviation

0.099212994

Standard Deviation

0.016119909

Sample Variance

0.024412

Sample Variance

0.009843218

Sample Variance

0.000259851

Range

0.44

Range

0.46

Range

0.0912

Count

48

Count

48

Count

48

 Table one shows the descriptive statistics of the three independent variables; production, transport and tax average. The mean, mode and median are measures of location while the variance and standard deviation, rage and median are measures of spread. The mean value of transport cost is 0.5356 while the mode and median are equal with a value of 0.45. This variable has the highest variance and standard deviation of 0.0244 and 0.1562 consecutively. The range, difference between the highest and the lowest observation, is 0.44.

The mean value of production costs is 0.4631. The mean and mode is 0.45. The standard deviation is 0.0992 while the variance is 0.00984.

Unlike the other two variable costs the tax average has different mode and median. The median is 0.06935 while the mode is 0.0813. The mean of variable costs is 0.06917 and while the variance and standard deviation is 0.0002598 and 0.01611 simultaneously.

Price

 

   

Mean

1.068125

Median

0.96

Mode

0.96

Standard Deviation

0.208680314

Sample Variance

1.06847473

Range

0.69

Sum

51.27

Count

48

 The unit price mean is 1.068 while the median and mode are equal with a value of 0.96. The standard deviation is 0.2086 while the variance is 1.068. The range is 0.69.

F-Test

An F-test is used to test whether the regression model fitted fits the data very well. The analysis of this model can be seen in the table4: Anova table. The null hypothesis being tested in this case is that there is no relationship between the independent variables (transport production and tax costs) and the dependent variable (price). As it can be seen from the table the significance F value is 2.67834E-79 which is much less than the F value of 59007.50174. In this case we reject the null hypothesis is rejected. We conclude that there is a relationship between the dependent and the independent variables.

R-squared

 R-squared is the coefficient of multiple determinations. It is used to measure how well the equation fits the data. It ranges from 0 to 1 and the bigger the value the better the regression model created. It is calculated by analysis of various partial regression coefficients of the independent variables in the model. The R-squared in the model is 0.999751506. This indicates the given model fits to the data nearly to perfect as the value is near to 1.

Marginal effects

Marginal effects are used to interpret the effect of the independent variables on the dependent variables. These can be obtained by partially differentiating the regression equation P= 0.0708+1.06889 Ts+ 1.0651Tp+1.0531Tx. In this case all the marginal effects of production, transport and tax costs will be constant.

Prediction

This model (P= 0.0708+1.06889 Ts+ 1.0651Tp+1.0531Tx) can be used to predict the price of products to a reliability of 99.9751506 % as indicated by the coefficient of multiple determination.

Conclusion

The transport, production and tax costs are determinants of price of a product as indicated by the analysis done. However, the variables in the model are not the only determinants of the price of a product. There should be other variables which should be included such as salaries, wages and other overhead costs. The areas of further research should consider analyzing the effects of these costs and inflation.

Code: Sample20

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