課程名稱︰計量導論
課程性質︰財金系必修
課程教師︰王衍智
開課學院：管理學院
開課系所︰財金系
考試日期（年月日）︰110.06.23
考試時限（分鐘）：100
試題 :
Multiple choices questions (72%, 4 points for each). Note that each question m-
ight have more than one answer (e.g., A, B, and D).
1. In a multiple regression with two explanatory variables, the total sum of s-
quares SST = 100 and the mean square error MSE = 30. There are 13 observations.
What is the value of R-squared?
A) 0.30
B) 0.70
C) 0.50
D) 0.96
E) None of the above
2. A researcher collects 100 NTU students for following study. An unrestricted
regression is performed as y = a_0 + a_1x_1 + a_2D + a_3x_1D + e. Dependent va-
riable y is the salary of NTU student. X is his/her GPA average. D is a dummy
variable that equal to one if the person is male. A restricted regression is p-
erformed as y = a_0 + a_1x_1 + e. We have known that sum of squared residual
SSR of the unrestricted model is 78, and sum of squared residual SSR of the re-
stricted model is 85. Please compute F-value that tests the effect of gender on
the relationship between GPA and salary, with null hypothesis H0: a_2 = a_3 = 0.
A) 2.87
B) 4.31
C) 4.35
D) 5.21
E) 8.62
3. Running two regressions below. Model 1: MBR = a_0 + a_1CR + e, and Model 2:
MBR = b_0 + b_1CR_1 + b_2CR_2 + b_3CR_3 + e. MBR is the Municipal bond rate. CR
is the rating of bond (with values from 1 to 4). CR_11 is a dummy, which is eq-
ual to one if CR = 1; zero otherwise. CR_2 to CR_4 are dummies designed similar
to CR1. Which of following one(s) is right statement(s).
A) R-sq of model 1 is larger than or equal to R-sq of model 2.
B) R-sq of model 1 is smaller than or equal to R-sq of model 2.
C) Coefficient b_0 implies the effect of CR_4.
D) Intercepts a_0 = b_0.
E) Mean squared residuals of two models are the same.
4. To perform a multiple regression ln(y) = a_0 + a_1x + e (given the populati-
on ln(y) = b_0 + b_1x + b_2z + u). What condition(s) could make a_1 estimator
be unbiased?
A) Mean of z is zero
B) Variance of y is a constant
C) x and z are uncorrelated
D) Variance of z is zero
E) Ln(y) is non-negative
5. Which of following tests are for heteroscedasticity?
A) Breusch-Pagan test
B) White test
C) Chow test
D) QQ plot
E) Ramsey Regression Equation Specification Error Test
6. Which of following method(s) could be the way to reduce the impact from out-
liers of dependent variable Y.
A) Trimming outliers
B) Taking logarithm of Y
C) Taking exponential of regression model: exp(a_0 + a_1X_1 +…+ a_kX_k + e)
D) Changing distribution of the error term to Poisson
E) Estimate the coefficients by Least Absolute Deviations Estimation (LAD)
7. In the multiple linear regression analysis, why do we need to compute beta
coefficient?
A) We can compare two coefficients in two regression systems with the same dep-
endent variable.
B) We can compare two coefficients in a regression system.
C) It makes hypothesis more robust.
D) We can know the economic significance.
E) Beta coefficient is more statistically powerful.
8. As errors-in-variable problem could be true, measurement errors problem in
the regression.
A) leads to inconsistent estimator when measurement error exists in right hand
side variable.
B) leads to inconsistent estimator when measurement error exists in left hand
side variable.
C) in the independent variable necessarily causes downward inconsistent estima-
tor.
D) in the independent variable necessarily causes upward inconsistent estimator.
E) in the independent variable does not necessary cause downward inconsistent
estimator.
9. Which of following statement about the heteroscedasticity is INCORRECT?
A) Regression with White (1980) heteroskedasticity-robust OLS standard error s-
hows different coefficient estimates against that of OLS
B) Regression with Weighted Least Squared (WLS) method shows different coeffic-
ient estimates against that of OLS
C) Regression with WLS method has better statistical efficiency than does OLS
D) WLS is a special case of generalized least squares (GLS)
E) Linear Probability Model can be estimated by WLS to deal with its heterosce-
dasticity problem.
10. In a regression analysis of oxygen uptake, we gain computer output and note
that the t-ratio for the variable RunPulse is -3.04 with a P-value of 0.0056
and the t-ratio for the variable age is 5.12 with a P-value of 0.042. What is
possible interpretation(s) of this result?
A) The small P-value suggests that variable "RunPulse" is not a significant pr-
edictor of Oxygen Uptake.
B) There is weak evidence that "RunPulse" is an important variable.
C) When assessing the value of variables for predicting "Oxygen Uptake", using
one variable “RunPulse” is enough.
D) The small P-value suggests that the variable "RunPulse" is statistically si-
gnificant when all the other predictor variables are included in the regres-
sion equation.
E) The regression equation should include "Age", otherwise its coefficient
-3.04 is very likely to be inconsistent.
11. Given this figure, please find out the wrong numbers in these statistics.
https://imgur.com/VFLqFGv
A) R-sq
B) Adj. R-sq
C) T-value of variable "Flour"
D) F-value in ANOVA
E) P-value of variable "Size"
12. A multiple regression y = a_0 + a_1x + a_2z + e, y is a dummy variable; wh-
at would be the weighted function h if we plan to conduct FGLS to deal with the
heteroscedasticity?
A) h = x
B) h = z
C) h = (fitted y)
D) h = (fitted y)(1- fitted y)
E) None of the above
13. We proxy a latent variable X* by the proxy X, then errors-in-variable prob-
lem is
A) zero covariance between a latent variable and error terms from the differen-
ce between proxy variable and the latent variable.
B) non-zero covariance between a latent variable and error terms from the diff-
erence between proxy variable and the latent variable.
C) a problem that makes coefficient estimation less efficient when X is the in-
dependent variable.
D) more severe when the regression model is a quadratic form of X.
E) not a concern if y follows normal distribution.
14. Based on a sample of the salaries of professors at a major university, you
have performed a multiple linear regression relating salary to years of service
and gender (male for 1). The estimated multiple linear regression model is Sal-
ary = 45 + 3*(Years) + 2*(Gender) + 1*(Years)*(Gender). Salary is in thousand
dollars. Using the multiple linear regression equation, what would you estimate
the average difference in the salaries of a male professor with three years of
service and a female professor with three years of service to be?
A) $3000
B) $4000
C) $5000
D) $7000
E) $8000
15. Which of following problem(s) leads to inconsistent estimator of coefficie-
nts in a linear regression model?
A) Omitted important variable
B) Adding irrelevant variables
C) Measurement error exists in the dependent variable
D) Measurement error exists in the independent variable
E) Heterogeneous variables
16. To examine the six assumption in the multiple linear regression (MLR 6), w-
hich one could be adopted in verifying the normality assumption?
A) LM test
B) White test
C) QQ plot
D) Residual plot
E) ANOVA table
17. A regression y = a_0 + a_1x + a_2z + e. Dependent variable y is a dummy th-
at equals one if the person passes the exam. X is the hours spent on study. Z
is the SAT score. Please verify multiple linear regression assumptions below,
and mark which one(s) is incorrect.
A) Y follows normality
B) Random sample could be met
C) The model meets the assumption of linearity
D) No perfect collinearity is very possible
E) The regression could be conditional heterogeneous
18. Two regression models are nested, which of following test(s) can compare t-
he two models for their model specifications.
A) Breusch-Pagan test
B) White test
C) T test
D) LM test
E) Ramsey Regression Equation Specification Error Test
Calculations- Part I (20%, 4 points for each). Please insert your answer by th-
ree digits after the decimal point.
Note that the orders of questions (1) to (5) are randomly made.
Q1:
https://imgur.com/4zyKRCg
Q2:
https://imgur.com/gYUuCfZ
Q3:
https://imgur.com/Hq2NV6p
Q4:
https://imgur.com/jexWUf6
Q5:
https://imgur.com/btGQJeH
Calculations- Part II (8%, 4 points for each). Please insert your answer by th-
ree digits after the decimal point. Note that the orders of questions (1) to
(2) are randomly made.
Q1:
https://imgur.com/Bi6RCLk
Q2:
https://imgur.com/9oUu0l3