Midterm Exam 2 B09 - MidtermexamEMBAS21.pdf

EMBA Final Exam B01.1305
12 May 2021
 Please write your name on every answer book that you use. Make sure that you number
your solutions correctly.
 Read all questions carefully.

 Show your work so that partial credit can be given. Poorly described solutions will be
penalised.
 All questions are not of the same level of difficulty.

 For all multiple choice questions, one point for the right choice, the remaining
points for justification.
 There are 4questions on this exam. You must complete all 4questions correctly to get full
points (i.e.50 points) on this exam. Good Luck !
Name: ______________________________________________________________
1) [16 points] Answer the following questions. Justify your answers briefly. No credit will be
given if you merely provide a choice without some justification for it.
a)[4points]Your colleague in a financial institution says that she has been tracking the
movements of the monthly returns of Facebook and Amazon stock returns. Using data on these
returns over the last 10 years, she says thatshe has computed the COVARIANCE between these
two returnsseries and found that it is 0.00042.Since this COVARIANCE is so low and close to
zero, she says that there does not seem to be any association between the two return series.
You tell her that (choose one of the following)
(i) her reasoning is faulty because….(give a brief reason)
(ii) her reasoning is correct because…(give a brief reason)
(ii) Her reasoning is faulty because COVARINCE tells about direction of association. But
we cannot interpret from the value of covariance whether there is strong association
between variables or not.
b) [4 points] Is it possible that when you fit a simple regression model, the t-statistic for the
slope coefficient is large (outside the range of (-2,2)), indicating that the X variable has a linear
relationship with the Y variable, but that the R-squared value is quite low, say 8%?
(i) Yes (justify your choice with a short explanation)
(ii) No (justify your choice with a short explanation)
(i) Yes. Because R-squared does not have any relationship with significance of slope. The value
of R-squared may be change drastically because of even single outlier. R-squared just tell about
variation in dependent variable because of independent variable. But it does not tell about
whether or not slope is significant or not.
c) [4 points]Your colleague is running a simple regression of Y on X. He makes a plot of the
standardized residuals vs. the fitted values shown below and you observe that there is a funnel
shape and so very clear evidence that there is non-constant variance in the data.
Fitted Value
S
ta
n
d
a
rd
iz
e
d
R
e
s
id
u
a
l
160155150145140
4
3
2
1
0
-1
-2
Residuals Versus the Fitted Values
(response is y)


However, your colleague insists on going ahead and fitting the regression model without
replacing the Y values by log(Y). Briefly yet clearly, describe the two errors that his resulting
analysis, based on the untransformed Y variable, is likely to make.
i) It will invalidate all the significance tests.
ii) Variability of Y values larger for some X values than for others.
d) [4 points]The regression of log(revenue of a firm) on log(R&D expenditure of firm) yields the
following equation:
Log(Revenue) = 1.3 + 0.65 Log(R&D Expenditure)
In one sentence, interpret the value 0.65 of the slope in terms of the original variables “revenue
of a firm” and “R&D expenditure of firm” (i.e. in terms of the unlogged variables)
For each 10% increase in R&D Expenditure, the revenue increase by [(1.10)
0.65
-1]=6.39%
2) [14 points] The marketing manager of a large supermarket chain would like to determine the
effect of shelf space and whether the product was placed at the front or back of the aisle on the
sales of pet food. A random sample of 12 equal sized stores was taken and the following
variables were noted:
Y= sales=daily sales of the pet food (in thousands of $)

1
X space=shelf space for the per food in square feet

2
X location=0 if the pet food was placed at the back of the aisle
= 1 if the pet food was placed at the front of the aisle
The output from the fitted multiple regression is shown below
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.213177 86.38% 83.35% 77.88%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 1.300 0.157 8.29 0.000
space 0.0740 0.0110 6.72 0.000 1.00
location ...