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1.Executive summary
The main purpose of this report is to conduct a statistical analysis of the corner store chain. The report comprises a analysis about variables and regression analysis using given data. The data provides information relating to the gross monthly sales of a hypothetical corner store chain. Each observation in the data represents a corner store at a different location.
Because the owners of the corner store want to open new stores in several areas where they are currently not operating , so this report also aims to finding the determinants of gross sales and predicting the characteristics of the areas they should be considering for establishment.
2. Variables analysis
Before making regression analysis, we should have a detailed understanding about the variables. Each variable is analyzed according to its effect on the gross monthly sales.
2.1 The number of competitors within 10km
Basically, the larger number of competitors around the store, the less gross monthly sales would be.
Graph 1. Relationship between gross monthly sales and number of competitors within 10km
Graph 1 shows that the gross monthly sales decreases if the number of competitors within 10km increase from the overall angle. But there is a thing required notice .When number of competitors is 2, the gross monthly sales range 000 from 0000. It shows that we need to do a deep investigation about the store locations with 2 numbers of competitors within 10km in order to find the reason of higher profitability with same number of competitors.
2.2 The population within 10km
According to Porter’s 5 forces model, buyers may try to force down prices while requiring better quality or service ( Porter 2008:86)
Graph 2. Relationship between gross monthly sales and population within 10km
Basically, Graph 2 shows more population with 10km would improve the gross monthly sales. But when population ranges 50000 from 100000, the sales number could stay at 0000. It may result from than the most effective bargaining power comes from the environment with 50000 from 100000 population.
2.3 The average income of the population within 10km ($)
The average income of population is a signal of purchasing power. Generally more average income of population would bring more gross monthly sales.
Graph 3. The relationship between gross monthly sales and average income of residents within 10km
According to the Graph 3, the gross monthly sales is larger with higher income of residents within 10km. Whether the gross monthly sales is sensitive to the average income of residents needs to be tested by regression analysis.
2.4 The average number of cars owned by households within 10km
Graph 4. The relationship between gross monthly sales and average number of cars owned.
The location with more average number of cars owned by households generally has higher gross monthly sales. This may show that the households would like to drive far to go shopping. And these households need parking around the store.
2.5 The median age of dwelling within 10km
Graph 5. The relationship between gross monthly sales and median age if dwelling within 10km
This graph seems irregular. The store location with different median age of dwelling in area tends to have same gross monthly sales. It looks like that the gross monthly sales is not very sensitive to the median age of dwelling within 10km.
3. Regression analysis
3.1 Dependent variable and independent variables
Regression analysis focuses on the relationship between the dependent variable and one or more independent variables. To simplify the regression, we use abbreviation to represent variables.
Table 1. Dependent variable and independent variable
Gross monthly sales
S : dependent variable
The number of competitors within 10km
Cptr : independent variable
The population within 10km
P : independent variable
The average income of the population within 10km
AI : independent variable
The average number if cars owned by households within 10km
Car: independent variable
The median age of dwelling within 10km
Dwe : independent variable
Based on what we have analyzed, we can make a rough understanding as following table.
“-” means that independent variable have negative effect on dependent variable while “+” means positive effect.
Table2. Hypothesis about effect of independent variables on dependent variable
Effect on S
Cptr
P
AI
Car
Dwe
S
_
+
+
+
_
3.2 Regression of S and Cptr
Significance testing hypothesis:
H0: Cptr does not have negative effect on S.
H1: Cptr has negative effect on S.
This is the single linear regression between S and Cptr. Using EVIEWS, the result is as:
Table 3. Regression of S and Cptr
Dependent Variable: S
Method: Least Squares
Date: 08/30/12 Time: 22:47
Sample: 2000 2049
Included observations: 50
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
143415.6
12510.27
11.46383
0.0000
CPTR
-23555.52
5141.689
-4.581281
0.0000
R-squared
0.304228
Mean dependent var
96304.60
Adjusted R-squared
0.289733
S.D. dependent var
59776.51
S.E. of regression
50378.06
Akaike info criterion
24.53168
Sum squared resid
1.22E+11
Schwarz criterion
24.60816
Log likelihood
-611.2919
Hannan-Quinn criter.
24.56080
F-statistic
20.98813
Durbin-Watson stat
0.522103
Prob(F-statistic)
0.000033
The coefficient of Cptr is negative which means that the number of competitors within 10km has negative effect on the gross monthly sales. The zero probability of t-statistic suggests that we should reject H0 and accept H1( Draper & Smith, 1998)
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