Posted: February 28th, 2022

Stastic Exam (May Be Required Using R) essay

GBA6230, Midterm Exam. Deadline: three/21 eight:00 PM. Please submit
your solutions in a single pdf file alongside along with your R code file by way of Blackboard.
In case you are utilizing different software program than R-studio, please additionally submit your code
to your software program.
1. True or False. Clarify your reply intimately. Your rating will likely be primarily based in your
clarification.
(a) E(u|X1, X2) = zero implies E(u) = zero. It additionally implies that (1) u is uncorrelated with X1 and X2; and (2) X1 and X2 is uncorrelated. (5 pt)
(b) To ensure that our regression estimators to be unbiased, we want the variance
of X to be as small as doable. In the very best state of affairs, we wish the variance
of X to be zero. (5 pt)
(c) R2 measures how a lot of the variation in information could be defined by linear
regression mannequin, and it by no means will increase once we attempt to management extra X in
the mannequin. (5 pt)
(d) E(u|X1, X2) = zero implies E(u) = zero. It additionally implies that u is uncorrelated
with X1 and X2 and X1 and X2 is uncorrelated. (5 pt)
(e) Suppose we’re fascinated with testing the null speculation: H0 : β1 =
zero and β2 = zero, we will apply t take a look at and take a look at H0 : β1 = zero and H0 : β2 = zero
individually. (5 pt)
(f) When there are three teams within the pattern, we should always outline three dummy variables and use all of them within the regression mannequin to regulate all of the group
variations. (5 pt)
2. Contemplate the next two fashions relates training to wage:
log(wage) = β0 + β1educ + u
log(wage) = β0 + β1educ + β2sibs + e
the place wage denotes month-to-month wage; educ is the training degree measured by
yr; and sibs is the variety of siblings. Let βe1 denotes the estimator of β1
from the straightforward regression, and βb1 denotes the estimator from the a number of
regression.
1
(a) Suppose educ and sibs are positively correlated within the pattern, and sibs
has unfavourable results on log(wage), would you anticipate βe1 and βb1 to be very
completely different? If sure, which one will likely be bigger? Clarify your reply intimately.
(5 pt)
(b) Suppose educ and sibs are positively correlated within the pattern, and sibs has
no results on log(wage), would you anticipate βe1 and βb1 to be very completely different?
If sure, which one will likely be bigger? Clarify your reply intimately. (5 pt)
(c) In the identical circumstance partially (b), would you anticipate se(βe1) and se(βb1)
to be very completely different? If sure, which one will likely be bigger? Clarify your reply
intimately. (5 pt)
three. Use wage1 information for this Question Assignment. Contemplate the next mannequin,
log(wage) = β0 + β1educ + β2exper + β3tenure + β4educ ∗ tenure + u
(a) Holding different elements mounted, what’s the marginal impact of educ to log(wage)
primarily based on the estimation consequence? (5 pt)
(b) State the null speculation that the educ has no impact on log(wage) towards
the choice speculation that it has impact. (5 pt)
(c) Check the speculation partially (b). Clarify your reply intimately. (5 pt)
four. Use ceosal1 information for this Question Assignment. Contemplate the next mannequin that hyperlinks
CEO’s wage to the kind of trade, firm’s gross sales and roe,
log(wage) = β0 + β1f inance + β2consprod + β3utility + β4sales + β5roe + u
the place now we have four sorts of trade within the information: industrial, monetary, shopper
merchandise, and utilities industries. f inance, consprod, and utility are binary
variables indicating the monetary, shopper merchandise, and utilities industries.
(a) Which trade is the bottom group? (5 pt)
(b) Compute the approximate share distinction in estimated wage between the commercial and utilities industries, holding gross sales and roe mounted. Is
the distinction statistically vital on the 1% degree? (5 pt)
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(c) Compute the approximate share distinction in estimated wage between the utilities and finance industries, holding gross sales and roe mounted. (5
pt)
(d) Check whether or not the distinction partially (c) is important at 5% degree. Clarify
your reply intimately. (5 pt)
5. Use hprice1 information for this Question Assignment. Contemplate the next mannequin that hyperlinks
home worth to its sq. ft, lot dimension, and variety of bedrooms,
worth = β0 + β1sqrf t + β2lotsize + β3bdrms + u
(a) Check whether or not sqrf t has the identical impact as lotsize on worth at 5% degree.
Report the outcomes below conventional customary error and strong customary
error. Do you discover completely different conclusions? Clarify your reply intimately. (5
pt)
(b) We now have two sorts of home within the information, colonial model and non-colonial
model. Outline colonial as a dummy variable for colonial model home. Contemplate the next mannequin,
worth = β0 + δ0colonial + β1sqrf t + δ1sqrf t ∗ colonial + β2lotsize
+δ2lotsize ∗ colonial + β3bdrms + δ3bdrms ∗ colonial + u
Clarify what does the null speculation, H0 : δ0 = δ1 = δ2 = δ3 = zero suggest?
(5 pt)
(c) Check the null speculation in (b). Report the outcomes from conventional F-test
and the strong F-test. Do you discover completely different conclusions? Clarify your
reply intimately. (5 pt)
(d) Carry out Breusch-Pagan and White exams on the mannequin partially (b). What
are your conclusions primarily based on these two exams? (5 pt)
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