Background | You work for Timp Health, a large, for-prot managed health care company. The division within the company that you work for specializes in pharmacy benet management (PBM). According to the American Pharmacists Association, \"PBMs are primarily responsible for developing and maintaining the formulary, contracting with pharmacies, negotiating discounts and rebates with drug manufacturers, and processing and paying prescription drug claims. For the most part, they work with self-insured companies and government programs striving to maintain or reduce the pharmacy expenditures of the plan while concurrently trying to improve health care outcomes.\"l For this case, you will focus specically on drug costs related to Medicare Part D. Medicare Part D (also called the Medicare prescription drug benet) subsidizes the cost of prescription drugs and drug insurance premiums for Medicare beneciaries in the United States. The following diagram illustrates the role of PBM in the prescription rlllment process. The PBM helps by working with members who have Medicare coverage and need pharmaceutical drugs, the pharmacy that lls drug prescriptions and the government that helps pay for the drugs.2 \fInformation flows: 1. Members pay a premium, usually monthly, to the PBM as part of Medicare. 2. When members need drugs, they go to their doctor, receive a prescription and take their prescription to the pharmacy to have it filled. 3. The pharmacy receives the prescription information from the member and, using the member's medical ID card, contacts the PBM to find out if the drug prescribed is covered by the member's insurance. 4. The PBM tells the pharmacy if the drug is covered by the insurance plan and how much the member must pay as a co-pay. 5. The member pays the co-pay amount to the pharmacy and receives their prescription. 6. The PBM submits claims to the government for reimbursement through a formatted claims file. The government pays the PBM. 7. Sometime later during the period, the PBM reviews all of the pharmacy's drug disbursements and sends the pharmacy a check for the amount that the PBM and the pharmacy previously agreed to contractually as payment for each drug. It is important to note several things about this information flow. The PBM adds value in a few ways. First, since the PBM works with many different members, the PBM is able to negotiate with the pharmacy to receive discounted drug prices. That is, the PBM negotiates with all pharmacies and because of the projected volume of purchasing, the pharmacies are willing to give the PBM, and thus the member, a discount. Second, the PBM manages the information around (and helps determine) what is covered by insurance . As already mentioned, the PBM is a for-profit entity. To make money, the PBM must have revenues that exceed the gross costs of the drugs prescribed to members, plus other business costs (e.g., salaries, administration costs). In this arrangement, on a short-term basis, the PBM has a limited ability to control the revenues and gross costs of the drugs, but it can control other business costs. Thus, it becomes very important for the PBM to understand revenues and gross drug costs so it can make informed business decisions about the other business costs. The data for this case (in the form of text files) comes from a real company and includes a total of seven months of gross drug costs, along with other data fields, at both member and record detail levels. Data from the first six months are in Part I and are used for Parts I, II and III. Please note that the numbers were changed slightly to anonymize the data set, but this anonymization did not impact any of the correlations between the variables.\fData descriptions RecordID - Primary key from the database that is a unique number for each row of data MemberID - A unique ID for each different member Month - The month to which the data pertains, listed in numeric format as 1 for January, 2 for February, etc. GrossDrugCost - The total amount of drug costs incurred by a member during the corresponding month NLISDummy - A dummy variable that takes the value of 1 if the member is listed as non-low income by the government and 0 otherwise LISCHOSERDummy - A dummy variable that takes the value of 1 if the member chose a specific plan and 0 if the member automatically was assigned a plan, i.e., members automatically are assigned (thus, LISCHOSERDummy = 0), but some members take the initiative to choose a specific drug plan other than one assigned (thus, LISCHOSERDummy = 1) RiskScore - A score assigned by the government based on previous government data indicating how sick someone is, higher scores indicate members are sicker SpecialtyDummy - A dummy variable that takes the value of 1 if the member utilizes specialty drugs and 0 otherwise AdjudicationDays - The number of non-holiday workdays in a month Age - The age of each member during the month Gender - A dummy variable that takes the value of 1 if the member is female and 0 if the member is male FrailtyDummy - A dummy variable that takes the value of 1 if the government indicates the member is frail and 0 if the government indicates the member is not frail HospiceDummy - A dummy variable that takes the value of 1 if the member is receiving hospice care and 0 if they are not InstitutionDummy - A dummy variable that takes the value of 1 if the member is receiving institutionalized long-term care (e.g., hospital, nursing facility) and 0 if they are not ESRDDummy - A dummy variable that takes the value of 1 if the member is receiving care for end-stage renal disease (i.e., end-stage kidney disease) and 0 if they are notPart ]I For Part I, you assumed that regression was the appropriate analytics tool and that the data did not violate any regression assumptions or otherwise did not prove to be problematic. Now, in Part 11, you will test the data to evaluate whether these assumptions were warranted For this part, use the following model: GrossDrugCost = Bu + B. 3 NLISDummy + B; \" LISCHOSERDmnmy + B3 * RiskScore + B4 * SpecialtyDummy + 35 * AdjudicationDays + Ba \" Age +31 \" Gender+Bg 3 HospiceDummy + By 3 InstitutionDlnnnm},r + Em * ESRDIIthmy + s Reggired: Complete the matrix of simplied regression assumptions or problems below. Submit Excel workbooks or workbooks from other statistical analysis software you use that clearly show how you generated your outputs on which your answers are based. Regression assumption or problem Are there outliers in the data? What does this assumption or problem mean? Why is it an issue if the assumption or problem is violated? How do you test for this assumption or problem? 'What are the results ofyom' test? 'What do you recommend? Are the relationships between the predicted Y's and Y's linear? Is multicollinearity a problem? Are the error terms independent? Are there violations of the homoscedasticity asslnnption? Are the errors normally distributed