1. business analytics II ▌assignment four - solutions mba for yourself 
Managerial Economics &
Decision Sciences Department
Developed for
business analytics II
week 4
▌assignment four - solutions
week 4
mba for yourself 
mba for your employer 
week 3
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II

2. ► statistics & econometrics
assignment four – solutions
dummy variables
Developed for
business analytics II
learning objectives
► statistics & econometrics
 define a dummy variable
 interpret a regression with dummy variables
 understand and interpret slope dummies ►
 run dummy regressions
readings
► (MSN)
 Chapter 5
► (CS)
 MBA (I)
 MBA (II)
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II

3. Est. E[postMBA]  24.659  1.83628·preMBA  1.732·school
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 1: coefficients interpretation. The estimated regression and STATA results are shown below:
Est. E[postMBA]   ·preMBA  1.732·school
b b b2
Figure 1. Results for regression of postMBA on preMBA and school
postMBA | Coef. Std. Err t P > |t|
preMBA |
school |
_cons |
continuous variable
dummy variable
► Coefficients interpretation (all estimates of the true parameters 0, 1 and 2)
 b  the expected postMBA income level if your income prior MBA was zero (preMBA  0) and if you completed MBA at school A (school  0)
 b0  b2  expected postMBA income level if your income prior to MBA income was zero (preMBA  0) and if you completed MBA at school B (school  1)
 b  the expected difference in postMBA income level if you complete MBA at school B (school  1) rather than at school A (school  0)
 b  the change of expected postMBA income level if your income prior MBA changes by $1 regardless of which school you attend
preMBA  0
school  0
preMBA  0
school  1
preMBA any
school: 0  1
preMBA  1
school: any
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 1

4. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 1: assumptions. The estimated regression and STATA results are shown below:
Est. E[postMBA]   ·preMBA  1.732·school
b b b2
Remark. The underlying modelling (model specification) assumption is that there is no interaction between school and preMBA:
For a change in $1 of preMBA income the postMBA will change by the same amount whether you attended school A (school  0) or school B (school  1)
Notice how this assumption has two implications:
Figure 2. Graphical representation of the estimated regression
slope b1 
differential effect of preMBA
for school  1
b2  1.732
differential effect of school
 the differential effect of school on postMBA is the same (given by b2) for at each level of preMBA (graphically: the distance between the two lines is the same for all preMBA levels)
 the differential effect of preMBA on postMBA is the same for both schools (graphically: the two lines have the same slope)
postMBA
b0  b2 
slope b1 
differential effect of preMBA
for school  0
b0 
preMBA
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 2

5. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 2: coefficients interpretation. The estimated regression and STATA results are shown below:
Est. E[postMBA]   ·preMBA  7.314·school  schoolpreMBA
b b b b3
Figure 3. Results for regression of postMBA on preMBA, school and schoolpreMBA
postMBA | Coef. Std. Err t P > |t|
preMBA |
school |
schoolpreMBA |
_cons |
continuous variable
dummy variable
slope dummy variable
Remark. Since this is the “complete” slope dummy regression:
 there are four coefficient coming straight from the regression, namely b0, b1, b2 and b3
 there are two combinations of coefficients b0  b2 and b1  b3, that are meaningful.
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 3

6. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 2: coefficients interpretation. The estimated regression and STATA results are shown below:
Est. E[postMBA]   ·preMBA  7.314·school  schoolpreMBA
b b b b3
 constant b0 – the expected postMBA level in the first year after graduation, if your income prior to MBA was zero (preMBA = 0), if you completed MBA at school A (school = 0)
 coefficient b0  b2 – the expected postMBA level in the first year after graduation, , if your income prior to MBA was zero (preMBA = 0), if you completed MBA at school B (school = 1)
 coefficient b – the expected difference in postMBA level in the first year after graduation, if your income prior to MBA was zero (preMBA = 0), if you completed MBA at school B (school = 1) vs. at school A (school = 0)
 coefficient b – the expected change in postMBA in the first year after graduation if you completed MBA at school A (school = 0)
 coefficient b1  b3 – the expected change in postMBA in the first year after graduation, if you completed MBA at school B (school = 1)
 coefficient b – the expected differential effect in the change in postMBA in the first year after graduation if you completed the MBA at school B (school = 1) vs. at school A (school = 0)
levels
difference in levels
slopes
difference in slopes
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 4

7. differential effect of school
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 2: graphical representation. The estimated regression and STATA results are shown below:
Est. E[postMBA]   ·preMBA  7.314·school  schoolpreMBA
b b b b3
Remark. How do you get the graph?
 The blue line is obtained by plugging school  0 in the estimated regression. The red line is obtained by plugging school  1 in the estimated regression.
 To get the difference between the two lines just subtract the two resulting equations.
Figure 4. Graphical representation of the estimated regression
slope b1  b3  1.936
school  1
postMBA
b0 
slope b1  1.704
school  0
b2  1.732
b0  b2 
b2  b3preMBA
differential effect of school
preMBA
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 5

8. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 2: school choice. The estimated regression and STATA results are shown below:
Est. E[postMBA]   ·preMBA  7.314·school  schoolpreMBA
b b b b3
► If preMBA income is $15 (thousands) and complete MBA:
 at school A (school  0): estimated postMBA   ·15  7.314·0  ·0·15 
 at school B (school  1): estimated postMBA   ·15  7.314·1  ·1·15 
► If preMBA income is $65 (thousands) and complete MBA:
 at school A (school  0): estimated postMBA   ·65  7.314·0  ·0·65 
 at school B (school  1): estimated postMBA   ·65  7.314·1  ·1·65 
► Based on these figures you’d choose school A if your preMBA is $15 but choose school B if your preMBA is $65.
Remark. Two issues here:
 Your choice seems to be changing depending on your preMBA income. How do we explain this feature?
 Based on Regression 1 you would choose school B for any preMBA income… What explains the difference?
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 6

9. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
School choice – a comparison:
simple dummy estimated regression
Est. E[postMBA]   ·preMBA  1.732·school
slope dummy estimated regression
Est. E[postMBA]   ·preMBA  7.314·school  schoolpreMBA
Figure 5. Graphical comparison of simple dummy and slope dummy estimated regressions
Est.E[postMBA ]   1.936·preMBA
school  1
Est.E[postMBA ]   1.836·preMBA
school  1
postMBA
postMBA
30.000
26.391
Est.E[postMBA ]   1.836·preMBA
school  0
22.686
Est.E[postMBA ]   1.704·preMBA
school  0
24.659
preMBA
preMBA
► In Regression 1 we are “forcing” the two lines to have the same slope and we are trying to explain the difference in postMBA income only as a shift in level due to the school choice (this difference is equal to the coefficient of the dummy).
► In Regression 2 we are “allowing” the two lines to have different slopes and the difference in postMBA income is explain as a compound effect: the dummy variable will pick up the difference in level, due to the school choice, while the slope dummy will pick up the difference in slope, due to the interaction of school and preMBA income.
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
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10. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 2: intervals. Applying the klincom and kpredint to obtain confidence and prediction intervals, confidence level 90%, for postMBA income when MBA was completed at school A (school  0) and preMBA income was $40 we get the following output:
Figure 6. Results for regression of postMBA on preMBA, school and schoolpreMBA
predicted | std.er of est.mean. CILow CIHigh PILow PIHigh |
klincom
kpredint
► Can we infer what were the exact klincom and kpredint commands?
 It is clear that the CI interval is related to klincom and the PI interval is related to kpredint
 The klincom is:
klincom _b[_cons]  _b[preMBA]·40  _b[school]·0  _b[schoolpreMBA]·0, level (90)
 The kpredint is:
kpredint _b[_cons]  _b[preMBA]·40  _b[school]·0  _b[schoolpreMBA]·0, level (90)
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 8

11. Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Regression 2: intervals. Applying the klincom and kpredint to obtain confidence and prediction intervals, confidence level 90%, for postMBA income when MBA was completed at school A (school  0) and preMBA income was $40 we get the following output:
Figure 7. Results for regression of postMBA on preMBA, school and schoolpreMBA
predicted | std.er of est.mean. CILow CIHigh PILow PIHigh |
klincom
kpredint
► The question asks about the distribution of postMBA income for individuals not for the average of the 60 students. Thus we definitely use the kpredint interval.
Remark. How would you phrase the question such that, in answering it, you’d choose the confidence interval rather than the prediction interval? Answer: For how many cohorts of 60 students in the past 20 years do you think the average postMBA income (the average being taken over the 60 students in the cohort) is below $96?
► Finally, the interpretation of the kpredint interval: 90% of the observations on postMBA will be within the kpredint interval, 5% of the observation on postMBA income will be to the left of the kpredint interval (below the lower bound) and the remaining 5% of the observations on postMBA income will be to the right of the kpredint interval (above the upper bound):
 90% of 60, that is 54, will have postMBA income within $80 to $116
 5% of 60, that is 3, will have postMBA income below $80
 5% of 60, that is 3, will have postMBA income above $116.
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
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12. … Valuing a MBA: For Yourself
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Yourself
Figure 8. Results for regression of postMBA on preMBA, school and schoolpreMBA
predicted | std.er of est.mean. CILow CIHigh PILow PIHigh |
about
averages of samples
about
individuals
klincom
kpredint
96.868
99.474
79.71
116.63
90% of observations
90% of observations … 1 2 … 60 1 2 … 60 1 2 … 60 1 2 … 60 1 2 3 4 … 57 58 59 60
1 cohort
18 cohorts
1 cohort
3 individuals
54 individuals
3 individuals
these are cohorts
these are individuals
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 10

13. Valuing a MBA: For Your Employer
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Your Employer
Regression 3: regression estimation. The estimated regression and STATA results are shown below:
Est. E[billing]   ·experience  68.43·MBA  experienceMBA
b b b b3
Figure 9. Regression results
billing | Coef. Std. Err t P > |t|
experience |
MBA |
experienceMBA |
_cons |
► Estimation based on regression: for two years of experience (experience = 24 months) we get
 with MBA: Est. E[billing]   ·24  68.43·1  ·24·1 
 with no MBA: Est. E[billing]   ·24  68.43·0  ·24·0 
► The extra value, i.e. change in billing for a change in experience, is really the slope of the regression line once for MBA 1 and then for MBA  0. If the slopes are different then indeed the extra value is different between MBAs and non-MBAs. The slope for the case MBA  1 is 1  3 while for the case MBA  0 is 1 thus the difference in slopes is exactly 3. The test is really for the null that 3  0 vs. the alternative 3  0. The pvalue  in the regression table already suggests that the null cannot be rejected at 1%.
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 11

14. Valuing a MBA: For Your Employer
Managerial Economics &
Decision Sciences Department
assignment four - solutions
dummy variables
Developed for
business analytics II
mba for yourself ◄
mba for your employer ◄
Valuing a MBA: For Your Employer
Regression 3: regression estimation. The estimated regression and STATA results are shown below:
Est. E[billing]   ·experience  68.43·MBA  experienceMBA
b b b b3
► For ten years of experience (experience  120) the estimated billing is
 with MBA: Est. E[billing]   ·120  68.43·1  ·120·1 
 with no MBA: Est. E[billing]   ·120  68.43·0  ·120·0 
Thus the difference is in the favor of a MBA degree holder.
► The prediction is not that reliable as it is really out-of-sample: we are told that all the observations used to estimate the regression comes from consultants with experience of up to 5 years (experience  60). To assert that the result is reliable you must assume, or argue, that the same relation between experience and billing continues to hold after the first 5 years going forward.
© 2016 kellogg school of management | managerial economics and decision sciences department | business analytics II
assignment four
| page 12