Quick Stab Collection Agency (QSCA) Collects Bills In An Eastern Town. The Company Specializes In …

     Statistical analysis of a case and present   your findings and interpretations in a management report. This will be a   single Word document, including required output.                Quick   Stab Collection Agency (QSCA) collects bills in an eastern town. The company   specializes in small accounts and avoids risky collections, such as those in   which the debtor tends to be chronically late in payments or is known to be   hostile.               The   business can be very profitable. OSCA buys the rights to collect debts from   their original owners at a substantial discount. For example, QSCA might pay   $10 for the right to collect a $60 debt. QSCA takes the risk of not   collecting the debt at all, of course, but often a single official-looking   letter yields full or nearly full payment, particularly for small debts.                Profitability at QSCA depends critically on   the number of days to collect the payment and on the size of the bill, as   well as on the discount rate offered.               A   random sample of accounts closed out during the months of January through   June yielded the data set below (and in file OVERDUE). Write a brief memo to   QSCA management advising them on the relationship, if any, between size of   bill and number of days to collect the payment, and BILL is the amount of the   overdue bill in dollars, while TYPE = 1 for residential accounts and 0 for   commercial accounts.               · Describe your assumptions.                      · Show your statistical analysis.                      · Give a correct statistical conclusion.                     DAYS (y) BILL (x1) TYPE (x2)   Variables:       41 215 1   DAYS = the number of days   to collect the payment   60 205 0   BILL = amount of the   overdue bill     86 79 0   TYPE = 1 for residential   accounts and 0 for commercial accounts   81 97 0          37 201 1          52 302 1          60 197 0          47 288 0          26 150 1          71 158 0          83 98 0          55 225 0          69 150 0          48 273 1          25 146 1          90 50 0          94 46 0          83 95 0          84 100 0          79 140 0          47 299 0          33 187 1          47 264 1          69 180 0          19 97 1          36 179 1          30 154 1          39 310 0          63 205 0          17 110 1          85 75 0          21 100 1          49 301 1          83 95 0          13 75 1          16 79 1          53 240 0          40 197 1          47 311 0          48 299 1          70 162 0          43 240 1          59 215 0          31 158 1          30 149 1          70 154 0          34 180 1          38 205 1          42 220 1          29 162 1          83 97 0          50 311 1          49 250 0          25 153 1          16 80 1          43 225 1          51 310 1          71 179 0          74 150 0          67 201 0          22 97 1          53 273 0          5 90 1          57 220 0          10 50 1          80 110 0          47 289 1          15 70 1          11 60 1          60 210 0          42 210 1          36 205 1          50 302 0          68 187 0          22 95 1          11 46 1          44 301 0          47 289 0          19 98 1          67 199 0          73 149 0          91 70 0          82 90 0          63 211 0          74 153 0          24 150 1          92 80 0          65 146 0          99 60 0          47 288 1          51 264 0          39 211 1          27 140 1          44 250 1          35 199 1          6 95 1

Let us   examine if the size of the bill and or whether the customer is residential or   commercial have an effect on the number of days the bill is late. The   statistical analysis of the data involves regression analysis. Here are some   questions that we may like to answer based on the analysis …

(a) Does   the size of the bill relate to the number of days the payment is late? If so,   how? Find a model that can be used to predict how late a bill may be.

(b) Does   whether the customer is a residential or commercial relate to the number of   days the bill is late?

(c)   Conduct a regression hypothesis at α = 0.05 to test the hypothesis that the   number of days the bill is late is not correlated to either the size of the   bill or type of customer

(d)   Prepare a short summary of your findings to present to the Management.