Management at the A. J. Davis company wishes the business to retain a competitive edge in the marketplace; ergo, they had statistical data collected regarding a selection of their customers who carry credit with the corporation. Based upon studies conducted on this data, it can be stated with a high degree of confidence that relationships do exist between certain discreet portions of the information gathered.
Household Size vs. Credit Balances
Predictably, the data bears out the fact that customers‟ household size does have a correlation with the size of their allowable credit balances at A. J. Davis: The greater the number of persons in the household, the strong positive trend shows that there is a high degree of likelihood that their credit balance will be higher, relative to a smaller-sized household. The trend is strong enough for Management to be able to utilize the data in an X/Y-axis layout to reveal a clearly positive line, showing correlation between growth in customer family size and respective credit.
Income, Size, and Years
Unfortunately, as Part A of this project already bore out, just because trends can be gleaned from one comparison of data sets does not mean this will always hold true. It was A. J. Davis‟ goal to, as a company, first and foremost study their credit customers, hence the data collection in the first place. Ergo, credit balance was in many ways the central hub of this investigation, with the other aspects (income, years of residency, family size, location, etc.) being rather like spokes in this wheel of prediction we call statistical analysis. Thus, in testing the data present, it is clear that both the income and family size of clients form strongly positive trends in being able to act in future uses as good predictive values that A. J. Davis can thereby use to its advantage. This did not hold true, though, of the third parameter focused ultimately on: years of residency in one location. In Part B it was pointed out that Management produced a botched prediction about that element, but even further studies again prove conclusively that this particular information does not form a coherent trend to any solid degree of predictive usefulness, ergo, it should be overlooked in favor of the data, like those mentioned above, that do enable A. J. Davis to remain on the „cutting edge‟ competitively with regards to its customer base and its future planning, especially as far as where and how it should target its various marketing ventures down the road. Graham 3
Using MINITAB perform the regression and correlation analysis for the data on CREDIT BALANCE (Y) and SIZE (X) by answering the following: 1. Generate a scatterplot for CREDIT BALANCE vs. SIZE, including the graph of the "best fit" line. The data has been arranged in a scatterplot in the above image, and the regression line has been added, showing the strongly positive relationship that size and credit balance share in the customer data collected for A. J. Davis. 2. Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE. 765432160005000400030002000SizeCredit Balance($)Scatterplot of Credit Balance($) vs Size Graham 4
The equation of the "best fit" line is highlighted below (in green) as produced in MINITAB. The regression equation is Credit Balance($) = 2591 + 403 Size 3. Determine the coefficient of correlation.
The data clearly share a strong correlation, given that the coefficient is quite close to 1.0, being 0.752. Ergo, this again reveals the strong relationship shared between size and credit balance. The positive trendline that was mentioned in the first section also attests to this fact. Correlations: Size, Credit Balance($)
Pearson correlation of Size and Credit Balance($) = 0.752
P-Value = 0.000
4. Determine the coefficient of determination.
The coefficient of determination is determined by the value of R2. This value is...