need the commands in R to complete the following question.

The question is from chapter 7 of Introductory Econometric 5th edition, Wooldridge.

C9) There has been much interest in whether the presence of 401(k) pension plans, available

to many U.S. workers, increases net savings. The data set 401KSUBS.RAW contains

information on net financial assets (nettfa), family income (inc), a binary variable for

eligibility in a 401(k) plan (e401k), and several other variables.

(i) What fraction of the families in the sample are eligible for participation in a

401(k) plan?

(ii) Estimate a linear probability model explaining 401(k) eligibility in terms of

income,

age, and gender. Include income and age in quadratic form, and report

the results in the usual form.

(iii) Would you say that 401(k) eligibility is independent of income and age? What

about gender? Explain.

(iv) Obtain the fitted values from the linear probability model estimated in part (ii).

Are any fitted values negative or greater than one?

(v) Using the fitted values e?401k i from part (iv), define ?e401ki 5 1 if ? e401k $ .5 and ?401k 5 0 if ? e401k ? .5. Out of 9,275 families, how many are predicted to be

eligible

for a 401(k) plan?

(vi) For the 5,638 families not eligible for a 401(k), what percentage of these are predicted

not to have a 401(k), using the predictor ? e401ki? For the 3,637 families

eligible for a 401(k) plan, what percentage are predicted to have one? (It is helpful

if your econometrics package has a "tabulate" command.)

(vii) The overall percent correctly predicted is about 64.9%. Do you think this is a complete

description of how well the model does, given your answers in part (vi)?

(viii) Add the variable pira as an explanatory variable to the linear probability model.

Other things equal, if a family has someone with an individual retirement account,

how much higher is the estimated probability that the family is eligible for a

401(k) plan? Is it statistically different from zero at the 10% level?

9 Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model y = Bo + dod + Biz+ 8d. z+ u; this is a general version of a model with an interaction between a dummy variable and a quantitative variable. [An example is in equation (7.17).] (i) Since it changes nothing important, set the error to zero, u = 0. Then, when d = 0 we can write the relationship between y and z as the function fo(z) = Bo + Biz. Write the same relationship when d = 1, where you should use fi(z) on the left-hand side to denote the linear function of z. (ii) Assuming that 8, # 0 (which means the two lines are not parallel), show that the value of z* such that fo(z*) = fi(z*) is z* = -8/8,. This is the point at which the two lines intersect [as in Figure 7.2(b)]. Argue that z* is positive if and only if 8, and 8, have opposite signs. (iii) Using the data in TWOYEAR.RAW, the following equation can be estimated: log(wage) = 2.289 - .357 female + .50 totcoll + .030 female . totcoll (0.011) (.015) (.003) (.005) 1 = 6,763, R- = .202. where all coefficients and standard errors have been rounded to three decimal places. Using this equation, find the value of torcoll such that the predicted values of log(wage) are the same for men and women. (iv) Based on the equation in part (iii), can women realistically get enough years of college so that their earnings catch up to those of men? Explain