Sample Essay On Using The Following Commands Two Graphs Were Generated.
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(a) Describe the economic issue
The economic issue under investigation is to determine whether there is a relationship between the number of customers and the total bill met by the company.
(b) Describe the data
The dataset is in CSV format. It contains 72 unique observations based on data collected from different cities. The dataset is made up of qualitative variables such as area and size. It is also made up of quantitative variables such as customer, OMandA and Total.Bill.
The first graph (chart 1) was a scatterplot showing the relationship between OMandA and customers. The second graph (chart 2) was a scatterplot showing the relationship between Total.Bill and customers. A regression line was added in order to show the direction of the relationship.
(d) Describe your model
In order to investigate the economic problem posed above a linear regression model will be utilized. The regression model will involve the explanatory variables OMandA and customers while the independent variable to be used will be is Total Bill. The equation for the model to be used is:
Total Bill = c1 Customers + c2 Customers2 + c3OMandA + Constant
(e) State your hypotheses in terms of the model.
Ho: The regression model will show that there is a statistically significant relationship between total bill and number of customers
H1: The regression model will show that there is no statistically significant relationship between total bill and number of customers
(f) Present the regression results
The results of the regression model Total Bill = c1 Customers + c2 Customers2 + c3OMandA + Constant from R are as shown below:
(g) Interpret the regression results and state whether your hypotheses were supported by the data
The results of the regression model show that the explanatory variables can be used to predict the total bill as follows:
Total.Bill = 0.000015 (Customers) – 1.667 x 10-9(Customers2) + 0.004171 OMandA + 99.51
This results support the null hypothesis, which indicates that there is a significant causality between the dependent and explanatory variables.
(h) Draw conclusions
In conclusion, the data analysis indicates that the number of customers directly affects the total bill.
Fox, J., Weisberg, S., & Fox, J. (2011). An R companion to applied regression. Thousand Oaks, Calif: SAGE Publications.
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