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I Will Look At This Relationship For Each Of The Categories. Taking The First ...

I will look at this relationship for each of the categories.
Taking the first difference of the relationship Total Points = No. of visits x Points earned per visit, we obtain:
d(Total Points) = d(# visits) + d(points earned per visit)
This is the equation that will be used to run a series of regressions for each of the categories. The data used for this is monthly visits, points earned per visit and total points from June 2006 to July 2007 for a sample of 10 customers within each category. (In order to obtain this data, of a sample of 60 customers within each category, 10 were chosen which had information on daily visits, spending per visit each day and points earned during each visit from 1 June 2006 to 7 July 2007. The results for each were summed into months for each variable within each category).
Running an Ordinary Least Squares regression on the data for the Best Category, the results obtained can be written as:
D(BEST_PTS) = 23.10993799*D(BEST_VISITS) + 237.6938197*D(BEST_PTSPERVIS)
This can be interpreted as on average, each additional visit to the supermarket by a Best customer implies an additional 23 points earned from the prior visit and an incremental 237 total points resulting from the spending per visit (or points earned each visit during the month).
The actual regression results are as follows:
Dependent Variable: D(BEST_PTS)

Method: Least Squares

Sample(adjusted): 2006:07 2007:07

Included observations: 13 after adjusting endpoints

Variable
Coefficient
Std. Error
t-Statistic
Prob.

D(BEST_VISITS)
23.10994
4.642456
4.977955
0.0004

D(BEST_PTSPERVIS)
237.6938
14.17514
16.76836
0.0000

R-squared
0.962285
 Mean dependent var
-245.0000

Adjusted R-squared
0.958857
 S.D. dependent var
5963.338

S.E. of regression
1209.591
 Akaike info criterion
17.17459

Sum squared resid
16094213
 Schwarz criterion
17.26151

Log likelihood
-109.6348
 F-statistic
280.6642

Durbin-Watson stat
1.952608
 Prob(F-statistic)
0.000000


Note that both coefficients of the independent variables (d(visits and d(points per visit)) are statistically significant at all levels.
With regards to the Uncertain category, the regression results can be written as
D(UNCERT_PTS) = 25.33455711*D(UNCERT_VISITS) + 12.12611463 * D(UNCERT_PTSPERVIS)
This can be interpreted as on average, each additional visit to the supermarket by an Uncertain customer implies an additional 25 points earned from the prior visit, yet only 12 incremental total points from each point per visit on average. (This result again confirms the definition of this category: low spenders with infrequent visits)
The actual regression results are shown below:
Dependent Variable: D(UNCERT_PTS)

Method: Least Squares

Sample(adjusted): 2006:07 2007:07

Included observations: 13 after adjusting endpoints

Variable
Coefficient
Std.

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