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chapter 8
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Questions in this quiz (29)
1In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
- A△Y = f(X1 + X1, X2,... Xk).
- B△Y = f(X1 + △X1, X2 + △X2,..., Xk+ △Xk)- f(X1, X2,...Xk).
- C△Y = f(X1 + △X1, X2,..., Xk)- f(X1, X2,...Xk).
- D△Y = f(X1 + X1, X2,..., Xk)- f(X1, X2,...Xk).
2The interpretation of the slope coefficient in the model Yi = β0 + β1 ln(Xi) + ui is as follows:
- Aa 1% change in X is associated with a β1 % change in Y.
- Ba 1% change in X is associated with a change in Y of 0.01 β1.
- Ca change in X by one unit is associated with a β1 100% change in Y.
- Da change in X by one unit is associated with a β1 change in Y.
3The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1Xi + ui is as follows:
- Aa 1% change in X is associated with a β1 % change in Y.
- Ba change in X by one unit is associated with a 100 β1 % change in Y.
- Ca 1% change in X is associated with a change in Y of 0.01 β1.
- Da change in X by one unit is associated with a β1 change in Y.
4The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1 ln(Xi)+ ui is as follows:
- Aa 1% change in X is associated with a β1 % change in Y.
- Ba change in X by one unit is associated with a β1 change in Y.
- Ca change in X by one unit is associated with a 100 β1 % change in Y.
- Da 1% change in X is associated with a change in Y of 0.01 β1.
5In the case of regression with interactions, the coefficient of a binary variable should be interpreted as follows:
- Athere are really problems in interpreting these since the ln(0) is not defined.
- Bfor the case of interacted regressors, the binary variable coefficient represents the various intercepts for the case when the binary variable equals one.
- C) first set all explanatory variables to one, with the exception of the binary variables. Then allow for each of the binary variables to take on the value of one sequentially. The resulting predicted value indicates the effect of the binary variable.
- Dfirst compute the expected values of Y for each possible case described by the set of binary variables. Next, compare these expected values. Each coefficient can then be expressed either as expected value or as the difference between two or more expected values.
6The following interactions between binary and continuous variables are possible, with the exception of
- AYi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui.
- BYi = β0 + β1Xi + β2(Xi × Di) + ui.
- CYi = (β0 + Di) + β1Xi + ui.
- DYi = β0 + β1Xi + β2Di + ui.
7An example of the interaction term between two independent, continuous variables is
- AYi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui.
- BYi = β0 + β1X1i + β2X2i + ui.
- CYi = β0 + β1D1i + β2D2i + β3 (D1i × D2i) + ui.
- DYi = β0 + β1X1i + β2X2i + β3(X1i × X2i) + ui.
8Including an interaction term between two independent variables, X1 and X2, allows for the following except:
- Athe interaction term lets the effect on Y of a change in X1 depend on the value of X2.
- Bthe interaction term coefficient is the effect of a unit increase in X1 and X2 above and beyond the sum of the individual effects of a unit increase in the two variables alone.
- Cthe interaction term coefficient is the effect of a unit increase in √(X1 * X2)
- Dthe interaction term lets the effect on Y of a change in X2 depend on the value of X1.
9A nonlinear function
- Amakes little sense, because variables in the real world are related linearly.
- Bcan be adequately described by a straight line between the dependent variable and one of the explanatory variables.
- Cis a concept that only applies to the case of a single or two explanatory variables since you cannot draw a line in four dimensions.
- Dis a function with a slope that is not constant.
10An example of a quadratic regression model is
- AYi = β0 + β1X + β2Y2 + ui.
- BYi = β0 + β1ln(X) + ui.
- CYi = β0 + β1X + β2X2 + ui.
- DYi i^2 = β0 + β1X + ui.
11(Requires Calculus) In the equation test score = 607.3 + 3.85 Income – 0.0423Income2, the following income level results in the maximum test score
- A607.3.
- B91.02.
- C45.50.
- Dcannot be determined without a plot of the data.
12To decide whether Yi = β0 + β1X + ui or ln(Yi) = β0 + β1X + ui fits the data better, you cannot consult the regression R2 because
- Aln(Y) may be negative for 0<Y<1.
- Bthe TSS are not measured in the same units between the two models.
- Cthe slope no longer indicates the effect of a unit change of X on Y in the log-linear model.
- Dthe regression R2 can be greater than one in the second model.
13You have estimated the following equation:
test scores = 607.3 + 3.85 Income – 0.0423 Income2,
where TestScore is the average of the reading and math scores on the Stanford 9 standardized test administered to 5th-grade students in 420 California school districts in 1998 and 1999. Income is the average annual per capita income in the school district, measured in thousands of 1998 dollars. The equation- Asuggests a positive relationship between test scores and income for most of the sample.
- Bis positive until a value of Income of 610.81.
- Cdoes not make much sense since the square of income is entered.
- Dsuggests a positive relationship between test scores and income for all of the sample.
14For the polynomial regression model,
- Ayou need new estimation techniques since the OLS assumptions do not apply any longer.
- Bthe techniques for estimation and inference developed for multiple regression can be applied.
- Cyou can still use OLS estimation techniques, but the t-statistics do not have an asymptotic normal distribution.
- Dthe critical values from the normal distribution have to be changed to 1.962, 1.963, etc.
15To test whether or not the population regression function is linear rather than a polynomial of order r,
- Acheck whether the regression R2 for the polynomial regression is higher than that of the linear regression.
- Bcompare the TSS from both regressions.
- Clook at the pattern of the coefficients: if they change from positive to negative to positive, etc., then the polynomial regression should be used.
- Duse the test of (r-1) restrictions using the F-statistic.
16The best way to interpret polynomial regressions is to
- Atake a derivative of Y with respect to the relevant X.
- Bplot 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.
- Clook at the t-statistics for the relevant coefficients.
- Danalyze the standard error of the estimated effect.
17The exponential function
- Ais the inverse of the natural logarithm function.
- Bdoes not play an important role in modeling nonlinear regression functions in econometrics.
- Ccan be written as exp(ex).
- Dis ex, where e is 3.1415….
18The following are properties of the logarithm function with the exception of
- Aln(1/ x) = -ln(x).
- Bln(a + x) = ln(a) + ln(x).
- Cln(ax) = ln(a) + ln(x).
- Dln(xa) a ln(x).
19The binary variable interaction regression
- Acan only be applied when there are two binary variables, but not three or more.
- Bis the same as testing for differences in means.
- Ccannot be used with logarithmic regression functions because ln(0) is not defined.
- Dallows the effect of changing one of the binary independent variables to depend on the value of the other binary variable.
20 In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β3
- Aindicates the slope of the regression when D=1.
- Bhas a standard error that is not normally distributed even in large samples since D is not a normally distributed variable.
- Cindicates the difference in the slopes of the two regressions.
- Dhas no meaning since (Xi × Di) = 0 when Di = 0.
21In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β2
- Ais the difference in means in Y between the two categories.
- Bindicates the difference in the intercepts of the two regressions.
- Cis usually positive.
- Dindicates the difference in the slopes of the two regressions.
22In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the
- At-statistic separately for β2 = 0, β2 = 0.
- BF-statistic for the joint hypothesis that β0 = 0, β1 = 0.
- Ct-statistic separately for β3 = 0.
- DF-statistic for the joint hypothesis that β2 = 0, β3= 0.
23In the model Yi = β0 + β1X1 + β2X2 + β3(X1 × X2) + ui, the expected effect ΔY / ΔX1 is
- Aβ1 + β3X2.
- Bβ1.
- Cβ1 + β3.
- Dβ1 + β3X1.
24In the log-log model, the slope coefficient indicates
- Athe effect that a unit change in X has on Y.
- Bthe elasticity of Y with respect to X.
- CΔY / ΔX.
- DΔY / ΔX * Y/X.
25In the model ln(Yi) = β0 + β1Xi + ui, the elasticity of E(Y|X) with respect to X is
- Aβ1X
- Bβ1
- Cβ1X / β0 + β1X
- DCannot be calculated because the function is non-linear
26Assume that you had estimated the following quadratic regression model
test scores = 607.3 + 3.85 Income - 0.0423 Income2. If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test scores would be- A3.85
- B3.85-0.0423
- CCannot be calculated because the function is non-linear
- D2.96
27Consider the polynomial regression model of degree Yi = β0 + β1Xi + β2X i^2 + ...+ βrX i^r + ui. According to the null hypothesis that the regression is linear and the alternative that is a polynomial of degree r corresponds to
- AH0: βr = 0 vs. βr ≠ 0
- BH0: βr = 0 vs. β1 ≠ 0
- CH0: β3 = 0, ..., βr = 0, vs. H1: all βj ≠ 0, j = 3, ..., r
- DH0: β2 = 0, β3 = 0 ..., βr = 0, vs. H1: at least one βj ≠ 0, j = 2, ..., r
28Consider the following least squares specification between test scores and the student-teacher ratio:
test scores = 557.8 + 36.42 ln (Income). According to this equation, a 1% increase in income is associated with an increase in test scores of- A0.36 points
- B36.42 points
- C557.8 points
- Dcannot be determined from the information given here
29) 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
Yi = β0 + β1D1i + β2D2i + β3(D1i×D2i) + ui. The interaction term- Aallows the population effect on log earnings of being married to depend on gender
- Bdoes not make sense since it could be zero for married males
- Cindicates the effect of being married on log earnings
- Dcannot be estimated without the presence of a continuous variable
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- Nonlinear Regression Functions
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- kiran syed
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