Kinh tế lượngTrắc nghiệm

180 câu trắc nghiệm Kinh tế lượng – Phần 3

Chapter 8: Nonlinear Regression Functions

KTL_001_C8_1: The interpretation of the slope coefficient in the model \(\ln ({Y_i}) = {\beta _0} + {\beta _1}\ln ({X_i}) + {u_i}\) is as
follows: a
● 1% change in X is associated with a \({\beta _1}\) % change in Y.
○ change in X by one unit is associated with a \({\beta _1}\) change in Y.
○ change in X by one unit is associated with a 100\({\beta _1}\)% change in Y.
○ 1% change in X is associated with a change in Y of 0.01\({\beta _1}\).

KTL_001_C8_2: A nonlinear function
○ makes little sense, because variables in the real world are related linearly.
○ can be adequately described by a straight line between the dependent variable and one of the explanatory variables.
○ is a concept that only applies to the case of a single or two explanatory variables since you cannot draw a line in four dimensions.
● is a function with a slope that is not constant.

KTL_001_C8_3: A polynomial regression model is specified as:
● \({Y_i} = {\beta _0} + {\beta _1}{X_i} + {\beta _2}X_i^2 + … + {\beta _r}X_i^r + {u_i}\).
○ \({Y_i} = {\beta _0} + {\beta _1}{X_i} + \beta _1^2{X_i} + … + \beta _1^r{X_i} + {u_i}\).
○ \({Y_i} = {\beta _0} + {\beta _1}{X_i} + {\beta _2}Y_i^2 + … + {\beta _r}Y_i^r + {u_i}\).
○ \({Y_i} = {\beta _0} + {\beta _1}{X_i} + {\beta _1}{X_{1i}} + {\beta _2}{X_2} + {\beta _3}({X_{1i}} + {X_{2i}}) + {u_i}\).

KTL_001_C8_4: The best way to interpret polynomial regressions is to
○ take a derivative of Y with respect to the relevant X.
● plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X.
○ look at the t-statistics for the relevant coefficients.
○ analyze the standard error of estimated effect.

KTL_001_C8_5: In the log-log model, the slope coefficient indicates
○ the effect that a unit change in X has on Y.
● the elasticity of Y with respect to X.
○ \(\frac{{\Delta Y}}{{\Delta X}}\).
○ \(\frac{{\Delta Y}}{{\Delta X}}\frac{Y}{X}\)

KTL_001_C8_6: In the model \(\ln ({Y_i}) = {\beta _0} + {\beta _1}{X_i} + {u_i}\), the elasticity of E(Y|X) with respect to X is
● \({\beta _1}X\)
○ \({\beta _1}\)
○ \(\frac{{{\beta _1}X}}{{{\beta _0} + {\beta _1}X}}\)
○ cannot be calculated because the function is non-linear

KTL_001_C8_7: Assume that you had estimated the following quadratic regression model
\({\hat Y}\) = 607.3 + 3.85Income – 0.0423 \(Incom{e^2}\) . If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test scores would be
○ 3.85
○ 3.85-0.0423
○ Cannot be calculated because the function is non-linear
● 2.96

KTL_001_C8_8: Consider the polynomial regression model of degree r,
\({Y_i} = {\beta _0} + {\beta _1}{X_i} + {\beta _2}X_i^2 + … + {\beta _r}X_i^r + {u_i}\). According to the null hypothesis that the regression is linear and the alternative that is a polynomial of degree r corresponds to
○ \({H_0}:{\beta _r} = 0\begin{array}{ccccccccccccccc}{}&{vs.}&{{H_1}:{\beta _r} \ne 0}\end{array}\)
○ \({H_0}:{\beta _1} = 0\begin{array}{ccccccccccccccc}{}&{vs.}&{{H_1}:{\beta _1} \ne 0}\end{array}\)
○ \({H_0}:{\beta _2} = 0,{\beta _3} = 0,…,{\beta _r} = 0\begin{array}{ccccccccccccccc}{}&{vs.}&{{H_1}:all\begin{array}{ccccccccccccccc}{}&{{\beta _i} \ne 0}\end{array}}\end{array},i = 2,…,r\)
● \({H_0}:{\beta _2} = 0,{\beta _3} = 0,…,{\beta _r} = 0\begin{array}{ccccccccccccccc}{}&{vs.}&{{H_1}:at\begin{array}{ccccccccccccccc}{least}&{one}\end{array}\begin{array}{ccccccccccccccc}{}&{{\beta _i} \ne 0}\end{array}}\end{array},i = 2,…,r\)

KTL_001_C8_9: Consider the following least squares specification between test scores and the studentteacher ratio: \({\hat Y}\) = 557.8 + 36.42ln(Income) . According to this equation, a 1% increase income is associated with an increase in test scores of
● 0.36 points
○ 36.42 points
○ 557.8 points
○ cannot be determined from the information given here

KTL_001_C8_10: Consider the population regression of log earnings [Yi, where Yi = ln(Earningsi)] against two binary variables: whether a worker is married (D1i, where D1i=1 if the ith person is married) and the worker’s gender (D2i, where D2i=1 if the ith person is female), and the product of the two binary variables \({Y_i} = {\beta _0} + {\beta _1}{D_{1i}} + {\beta _2}{D_{2i}} + {\beta _3}({D_{1i}}x{D_{2i}}) + {u_i}\). The interaction term
● allows the population effect on log earnings of being married to depend on gender
○ does not make sense since it could be zero for married males
○ indicates the effect of being married on log earnings
○ cannot be estimated without the presence of a continuous variable

Previous page 1 2 3 4Next page

Back to top button