QM 222 Boston University Engineering Departments Regression Model Excel Task

PART 1 OF 3 – OMITTED VARIABLE BIAS: ADVERTISING AND SALES

POMME, INC. SELLS A VARIETY OF CONSUMER ELECTRONICS, INCLUDING THE A-PHONE AND A-PAD. THEIR MARKETING DEPARTMENT IS ANALYZING THEIR ADVERTING DATA. THEIR DATASET INCLUDES:

• PRODUCT NAME,
• TOTAL SALES (IN DOLLARS)
• DOLLAR AMOUNT SPENT ON ADVERTISING (“ADS”).

EACH OBSERVATION IS MONTHLY DATA ON A SINGLE PRODUCT. IN THE PAST, POMME, INC. DETERMINED THE AMOUNT TO SPEND ON ADVERTISING (ADS) BASED ON THE RESULTS OF FOCUS GROUP RATINGS (“RATINGS”). POMME, INC. BELIEVES RATINGS ARE A GOOD MEASURE OF HOW USEFUL THE PRODUCT IS, SINCE PREVIOUSLY THEY HAD MEASURED THAT THE HIGHER THE RATINGS, THE HIGHER THE TOTAL SALES.

HOWEVER, POMME, INC., HAS STOPPED COLLECTING INFORMATION ON RATINGS BECAUSE IT IS TOO COSTLY. INSTEAD, POMME, INC. WANTS TO CHOOSE THE AMOUNT TO SPEND ON ADVERTISING BASED ON DATA ANALYSIS OF HOW ADS AFFECT TOTAL SALES.

THE MARKETING DEPARTMENT PROPOSES THE FOLLOWING MODEL OF SALES:

WHERE C0 AND C1 ARE PARAMETERS TO BE MEASURED BY REGRESSION.

THEY THEN ESTIMATE THE REGRESSION, WHICH GIVES:

THE ENGINEERING DIVISION DISAGREES, AND SAYS THAT TOTAL SALES ALSO DEPENDS ON HOW USEFUL THE DEVICE IS TO CONSUMERS WHICH IS MEASURED BY FOCUS-GROUP RATINGS. THEY ARGUE THAT A BETTER MODEL FOR TOTAL SALES IS:

WHERE B0, B1 AND B2 ARE COEFFICIENTS TO BE ESTIMATED BY REGRESSION.

UNFORTUNATELY, THE MARKETING DEPARTMENT DOES NOT HAVE THE RATINGS DATA THEY USED PREVIOUSLY THAT WOULD ALLOW THEM TO RUN THAT REGRESSION. BUT POMME, INC. REALLY WANTS TO KNOW THE VALUE OF B1 IN ORDER TO OPTIMALLY CHOOSE ADS.

THE MARKETING DEPARTMENT DOES KNOW THE RELATIONSHIP THEY HAD PREVIOUSLY USED TO DECIDE ADS BASED ON RATINGS:

ADS = -25 + 5 RATINGS

WHICH CAN BE REWRITTEN AS:

RATINGS = 5.0 + .2 ADS

QUESTION 1) BASED ON ALL OF THIS EVIDENCE AND THE FACT THAT RATINGS ARE POSITIVELY ASSOCIATED WITH SALES, DO YOU THINK THAT IF POMME, INC. INCREASES ADS BY $1, THEIR TOTAL SALES WOULD GO UP BY $9.95? IF NOT, DO YOU THINK TOTAL SALES WOULD GO UP BY MORE OR LESS THAN $9.95? USE THE EQUATION C1= B1+ B2A1 AND THE SIGN (+ OR -) OF THE BIAS TERM TO DETERMINE YOUR ANSWER AND SHOW YOUR WORK.

QUESTION 2) ASSUME THAT FROM OTHER STUDIES, YOU KNOW B2=45 (WHERE B2 IS THE EFFECT OF RATINGS ON TOTAL SALES HOLDING CONSTANT ADS).THEN, HOLDING CONSTANT RATINGS, WHAT EFFECT DO ADS HAVE ON TOTAL SALES? IN OTHER WORDS, WHAT IS THE VALUE OF B1? SHOW YOUR WORK/CALCULATIONS

QUESTION 3) BASED ON THE VALUE OF B1 THAT YOU ESTIMATED, WILL INCREASING ADS BY $1 RAISE OR LOWER POMME, INC.’S PROFITS?

PART 2 OF 3 – OMITTED VARIABLE BIAS: COLLEGE GPA

THE DATA SET COLLEGE GPA ATTACHED HERE AND ALSO IN THE PROBLEM SET DIRECTORY CONTAINS DATA (NOT BU) FOR EACH STUDENT’S COLLEGE GPA, WHETHER THE STUDENT IS MALE OR FEMALE AND THE # OF ALCOHOLIC DRINKS THEY CONSUMED PER MONTH (VARIABLE DRINK). CREATE A DUMMY VARIABLE FOR MALE (=1) AND RUN A REGRESSION OF COLLEGE GPA ON MALE. (REGRESSION 1)

QUESTION 4) TYPE OUT YOUR ESTIMATED REGRESSION EQUATION AND PUT THE STANDARD ERRORS BELOW EACH COEFFICIENT IN PARENTHESIS.

QUESTION 5)INTERPRET THE COEFFICIENT ON MALE.

QUESTION 6) WHAT IS THE AVERAGE GPA FOR FEMALES?

QUESTION 7) NOW RUN REGRESSION 2 ( THE FULL MODEL) ON GPA USING BOTH THE MALE DUMMY AND # DRINKS PER MONTH (DRINK). TYPE OUT YOUR ESTIMATED REGRESSION EQUATION AND PUT THE STANDARD ERRORS BELOW EACH COEFFICIENT IN PARENTHESIS.

QUESTION 8) USING REGRESSION 2 (THE FULL MODE), INTERPRET THE COEFFICIENT ON MALE?

QUESTION 9) USING THE RESULTS FROM BOTH REGRESSIONS, IS THERE EVIDENCE OF POSITIVE OR NEGATIVE BIAS FOR THE COEFFICIENT ON MALE IN YOUR FIRST REGRESSION? SUPPORT YOUR ANSWER BY INCLUDING CALCULATION(S).

QUESTION 10) IS THE CORRELATION BETWEEN # DRINKS PER MONTH AND GPA POSITIVE OR NEGATIVE? HOW DO YOU KNOW (SHOW YOUR WORK)?

QUESTION 11) IS THE CORRELATION BETWEEN MALE AND DRINK POSITIVE OR NEGATIVE? SHOW YOUR WORK.

QUESTION 12) AFTER CONTROLLING FOR DRINK IN THE FULL MODEL, ARE YOU 95% CONFIDENT THAT MALES HAVE A LOWER GPA THAN FEMALES, ON AVERAGE? EXPLAIN, IN SIMPLE LANGUAGE, WHY LEAVING OUT THE VARIABLE DRINK FROM REGRESSION 1, RESULTED IN OMITTED VARIABLE BIAS FOR THE COEFFICIENT ON MALE.

PART 3 OF 3 – LINEAR PROBABILITY MODEL: STOCK OWNERSHIP

LINEAR PROBABILITY MODEL

EXECUTIVES AT A MAJOR FINANCIAL COMPANY ARE TRYING TO MODEL WHICH HOUSEHOLDS OWN STOCKS. THEY COLLECTED DATA FOR A NATIONAL SAMPLE OF HOUSEHOLDS FROM AROUND THE COUNTRY. THE DATA THEY COLLECTED INCLUDES:

OWN_STOCK:WHETHER OR NOT THE HOUSEHOLD OWNS ANY STOCKS.

COLLEGE: WHETHER THE MOST EDUCATED PERSON IN THE HOUSEHOLD COMPLETED COLLEGE

HIGHSCHOOL: WHETHER THE MOST EDUCATED PERSON IN THE HOUSEHOLD COMPLETED HIGH SCHOOL BUT NOT COLLEGE

NET_WEALTH:THE TOTAL AMOUNT OF WEALTH IN MILLIONS OF DOLLARS (INCLUDES VALUE OF REAL ASSETS LIKE HOUSES; OF FINANCIAL ASSETS LIKE BANK ACCOUNTS, BONDS EXCLUDING STOCKS; AND SUBTRACTS OUT AMOUNT THE HOUSEHOLD OWES INCLUDING LOANS, MORTGAGES ETC.)

HOUSE: WHETHER OR NOT THE HOUSEHOLD OWNS THEIR OWN HOUSE

THERE ARE 3 POSSIBLE EDUCATION LEVELS IN TOTAL, INDICATING WHETHER THE MOST EDUCATED PERSON IN THE HOUSEHOLD

1. DID NOT COMPLETE HIGH SCHOOL
2. IS A HIGH SCHOOL GRADUATE BUT DID NOT COMPLETE COLLEGE
3. HAS A COLLEGE DEGREE OR MORE.

THEY ASK YOU TO MODEL WHO OWNS STOCKS, SO YOU RUN A SET OF REGRESSIONS WITH “OWN_STOCK” AS THE LEFT HAND SIDE (Y) VARIABLE.

QUESTION 13) YOU FIRST RUN REGRESSION 1 (LINEAR PROB REG 1 AND 2 DOCX). WHAT DOES THE COEFFICIENT 0.1296 TELL US? (1-2 SENTENCES.)

QUESTION 14) WOULD IT BE POSSIBLE FOR REGRESSION #1 TO ACTUALLY PREDICT A PROBABILITY GREATER THAN 1? LESS THAN 0? EXPLAIN (1-2 SENTENCES)

QUESTION 15) YOU THEN RUN REGRESSION 2 (SEE SAME ATTACHMENT AS ABOVE). WHAT IS THE PROBABILITY OF OWNING STOCK FOR SOMEONE WHO HAS NOT GRADUATED FROM HIGH SCHOOL, DOES NOT OWN A HOUSE AND HAS A NET WEALTH OF ONE HUNDRED THOUSAND DOLLARS? (HINT: NET WEALTH IS IS IN MILLIONS, SO 1 = 1 MILLION DOLLARS). IS THIS POSSIBLE?