PROBLEM SET 1
SOLUTION
QUESTION 1
(i)
Omitted
variables
Random or
unpredictable
occurrences
Error
Term
Measurement
error
Specification
error
Some of the omitted variables may be correlated
with education such as income. Discuss other
examples.
ii.
A simple regression equation like this
includes just one independent variable.
Other variables such as those mentioned in
part (i) may be correlated with education
and included in u, thus uncovering the
Ceteris Paribus effect.
QUESTION 2
Student
GPA (Y)
ACT (X)
(X-Xbar)
(Y-Ybar)
(X-Xbar)²
(X-Xbar)*(Y-Ybar)
1
2.80
21
-4.875
-0.4125
23.7656
2.0109
2
3.40
24
-1.875
0.1875
3.5156
-0.3516
3
3.00
26
0.125
-0.2125
0.0156
-0.0266
4
3.50
27
1.125
0.2875
1.2656
0.3234
5
3.60
29
3.125
0.3875
9.7656
1.2109
6
3.00
25
-0.875
-0.2125
0.7656
0.1859
7
2.70
25
-0.875
-0.5125
0.7656
0.4484
8
3.70
30
4.125
0.4875
17.0156
2.0109
∑=56.875
∑=5.8125
Ybar=3.2125 Xbar=25.875
GPA hat = 0.5681 + 0.1022ACT
N=8

Positive relationship ; higher ACT, higher the
estimated GPA.

If ACT is 5 points higher, GPA increases by
0.1022*5=0.511.

No meaningful interpretation of intercept as
ACT is no where close to zero.
GPA (Y)
GPA hat (Y hat)
e hat
e hat²
(Y-Ybar)²
2.80
2.7143
0.0857
0.0073
0.1702
3.40
3.0209
0.3791
0.1437
0.0352
3.00
3.2253
-0.2253
0.0508
0.0452
3.50
3.3275
0.1725
0.0298
0.0827
3.60
3.5319
0.0681
0.0046
0.1502
3.00
3.1231
-0.1231
0.0152
0.0452
2.70
3.1231
-0.4231
0.1790
0.2627
3.70
3.6341
0.0659
0.0043
0.2377
∑=(0.0002)
∑=0.4347
∑=1.0288
(iii) GPA (hat) = 0.5681 + 0.1022 (20) = 2.61
(iv) TSS= 1.0288 ; RSS=0.4347;
R²=1-(RSS/TSS)=1(0.4347/1.0288)=0.577
QUESTION 3
(i) When cigs=0, bwght=119.77
When cigs=20, bwght=119.77-10.28=109.49
10.28 is the ounces by which bwght falls if a
woman smokes 20 cigs in comparison to 0.
(ii) No. A lot of other variables like health facilities
available to the mother may also affect birth
weight.
A regression equation simply shows the impact of
one variable on another, thus does not
necessarily indicate causality.
QUESTION 4
i.
The intercept implies that when inc=0,
consumption=-124.84. This obviously is
not true as consumption can not be
negative.
ii. Cons(hat)=-124.84+0.853*30000=
$25465.16
MPC,
APC
MPC=slope coefficient
APC=-124.84/INC + 0.853
MPC
0.853
APC
1000
2000
3000
4000
INC
QUESTION 5
i.
A percentage increase in the distance of the
house from a recently built garbage incinerator,
increases the price of the house by 0.312%,
keeping everything else constant.
Yes. A house further away from incinerator is
worth more.
ii.
NO. There might be other variables correlated
with ‘dist’ leading to a biased estimate of the
elasticity of price with respect to dist.
iii.
Area, Quality of house, size of the house,
number of bedrooms, attractiveness of the
neighborhood etc. Some of these variables
may be correlated with distance.
QUESTION 6
(question 5 from Studenmund)
i.
The intercept and slope coefficients are being
estimated. The squared residuals are being
minimized.
ii.
If R² =0, then RSS=TSS meaning the
independent variables included in the model do
not help explain variation in the dependent
variable. ESS=0. In our usual OLS regression
model, R² can not be negative as everything is
being squared.
iii.
Model T has estimated signs that meet our
expectations. A higher R² does not
automatically mean that an equation is
preferred. Model T is preferred as it includes an
important variable missing in Model A.
QUESTION 7
ATT  +IVE; PS  +IVE
Going to classes and doing problem sets
should improve student’s grade.
ii. Yes. Refer to part i.
iii. 25 hours of lecture & 50 hours to complete PS
1 hour0.04 lecture; 1 hour0.02 PS
1.74*0.04=0.0696: gain in grade by
spending an extra hour on lectures
0.6*0.02=0.012: gain in grade by spending
an extra hour on PS.
gain from lectures > gain from PS
SO, going to class pays off more.
i.
50 Hours of lecture & 10 hours of problem set.
1 hour0.02 lecture; 1 hour0.1 PS
0.02*1.74 > 0.1*0.6
0.0348
> 0.06 this time doing
problem sets pays off more.
Since the units of variables can differ
dramatically, coefficient size does not measure
importance.
v. 33% of variation in the grade received by a
student is explained by the regression
equation.
vi. No. other factors such as students ability may
be included.
iv.
QUESTION 8
i.
ii.
iii.
iv.
Yes
Yes.
1 book$230;
Two excellent articles2*(102+18)=$240
Three dissertations 3*489=1467
writing dissertation leads to a higher
increment in salary. Thus preferred.
The coefficient D seems to be too high. May
be absorbing the impact of omitted variables
e.g. students may choose a dissertation
advisor on the basis of reputation or
qualification.