Convenience Shopping

Table of Content

                Executive Summary        1

                Descriptive Statistics        1

        Methodology-Statistical Tests         3

        Practical Applications         6

        Final Conclusion.        7

Executive Summary

One import thing for U.S. -the country on wheels is gas. Since there are more and more gas stations in convenience stores or supermarkets, the relationship between volume gallons sold and the sales dollars in the convenience store is worth for us to research. Considering there are other factors may impact the sales dollars in the convenience store, we also include other variables such as the number of car washes sold, day of week and price of gas in our research.

To identify the relationship between sales in the convenience store and gas sold, we analyze utilizing three methods - visualize data, mathematic method and statistic regression model. First, we draw a scatter plot to observe data visually. Then we test the correlation coefficient of these two variables. Second, we use math method to calculate the sales of the convenience store when 2,000 gallons of gas was sold and when 3,000 gallons of gas was sold. Third, we use statistic regression model to test the relationship between the two sales amount.

Moreover, in order to distinguish dependent variable and independent variable, we reverse the response and the explanatory variables. Then, considering two explanatories may both impact the sales of convenience store, we draw regression lines. Finally, we find out the best model is the multiple regression model. Therefore, both gas sold and car washes sold have impact on sales of the convenience store, and gas sold has a stronger impact on the sales.

Descriptive Statistic/Graph and Tables

We analysis our data from two methods, scatter plot and regression line.

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To analysis the relationship between sales dollars, volume dollars and washes, we draw graphs for three sets of data: sales dollars and volume gallons; sales dollars and washes; and volume gallons and washes. According to the scatter plot of these three set of data, we conclude that sales dollars and volume gallons has positive relationship, meaning that as volume gallons’ sales increase, sales for the convenience store increase, and the regression model also prove that point.  However, for the other two sets: sales and washes; washes and volume gallons, the relationships are not significant. As washes increase, sales dollars keeps in a certain range and does not increase or decrease. The scatter plot for volume gallons and washes are distributed randomly.

Methodology –Statistical Tests

First, we use correlation method to calculate the correlation coefficient between each pair of variables, we set hypothesis test as H0: ρ=0, H1: ρ≠0. If ρ=0, there is no relationship between two variables; if ρ≠0, there is some correlation between variables.

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According to SAS result, we find there are four pair of variables has correlation with each other, when p-value less than 0.0001, we reject H0. Among these four pairs of data, sales of convenience store and volume of gas sold has the strongest correlation coefficient, which is 0.64955.

After identifying the correlation between each pair of variables, we use mathematic method to prove the sales of convenience store are increasing when we raise volume of gallons sold from2000 to 3000.

First we construct a regression model of sales of convenience store and volume of gas sold to calculate the confidence interval of the difference in average sales in the convenience store between days on which the station sells 2000 gallons of gas and those on which the station sells 3000 gallons. We set our confidence level as 95%, since we are calculating 1000 interval, the equation is 1000*,  (slope) is 0.32059, standard error is 0.02239,  is 1.968. Because and are both consistent with simple regression model, both numbers are normally distributed. Therefore, the 95% confidence interval is between 276.53 and 364.35. When we raise our volume of gallons sold from 2000 to 3000, on average, the increased sales of convenience store range will fall in (276.53, 364.35). [pic 11][pic 12][pic 13][pic 14][pic 15]