chapter 8

A polynomial regression model is specified as:

A) Yi = β0 + β1Xi + β2X + ∙∙∙ + βrX + ui.

The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1 ln(Xi)+ ui is as follows:

A) a 1% change in X is associated with a β1 % change in Y.

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

A) allows the population effect on log earnings of being married to depend on gender

The exponential function

A) is the inverse of the natural logarithm function.

You have estimated the following equation: = 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

A) suggests a positive relationship between test scores and income for most of the sample.

In the model Yi = β0 + β1X1 + β2X2 + β3(X1 × X2) + ui, the expected effect is

A) β1 + β3X2.

In the model ln(Yi) = β0 + β1Xi + ui, the elasticity of E(Y|X) with respect to X is

A) β1X

The interpretation of the slope coefficient in the model Yi = β0 + β1 ln(Xi) + ui is as follows:

B) a 1% change in X is associated with a change in Y of 0.01 β1.

The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1Xi + ui is as follows:

B) a change in X by one unit is associated with a 100 β1 % change in Y.

In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β2

B) indicates the difference in the intercepts of the two regressions.

The following are properties of the logarithm function with the exception of

B) ln(a + x) = ln(a) + ln(x).

The best way to interpret polynomial regressions is to

B) 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.

To decide whether Yi = β0 + β1X + ui or ln(Yi) = β0 + β1X + ui fits the data better, you cannot consult the regression R2 because

B) the TSS are not measured in the same units between the two models.

In the log-log model, the slope coefficient indicates

B) the elasticity of Y with respect to X.

For the polynomial regression model,

B) the techniques for estimation and inference developed for multiple regression can be applied.

The following interactions between binary and continuous variables are possible, with the exception of

C) Yi = (β0 + Di) + β1Xi + ui.

An example of a quadratic regression model is

C) Yi = β0 + β1X + β2X2 + ui.

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

C) indicates the difference in the slopes of the two regressions.

A nonlinear function

C) 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.

Including an interaction term between two independent variables, X1 and X2, allows for the following except:

C) the interaction term coefficient is the effect of a unit increase in .

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by

C) △Y = f(X1 + △X1, X2,..., Xk)- f(X1, X2,...Xk).

In 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

D) F-statistic for the joint hypothesis that β2 = 0, β3= 0.

Consider the polynomial regression model of degree Yi = β0 + β1Xi + β2 + ...+ βr + ui. According to the null hypothesis that the regression is linear and the alternative that is a polynomial of degree r corresponds to

D) H0: β2 = 0, β3 = 0 ..., βr = 0, vs. H1: at least one βj ≠ 0, j = 2, ..., r

An example of the interaction term between two independent, continuous variables is

D) Yi = β0 + β1X1i + β2X2i + β3(X1i × X2i) + ui.

The binary variable interaction regression

D) allows the effect of changing one of the binary independent variables to depend on the value of the other binary variable.

In the case of regression with interactions, the coefficient of a binary variable should be interpreted as follows:

D) first 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 an expected value or as the difference between two or more expected values.

To test whether or not the population regression function is linear rather than a polynomial of order r,

D) use the test of (r-1) restrictions using the F-statistic.