In the probit model given in the following table the disturbance ui has this variance where f i is the standard normal density function evaluated at F1(Pi) a Given the preceding variance of ui, how would you transform the model in Table 15 10 to make the resulting error term homoscedastic i li F 1 (P Igrave i ) 0 20 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 8416 0 24 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 7063 0 30 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 5244 0 35 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 3853 0 45 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 1257 0 51 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 0251 0 60 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 2533 0 66 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 4125 0 75 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 6745 0 80 brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar brvbar 0 8416 b Use the data in Table 15 10 to show the transformed data c Estimate the probit model based on the transformed data and compare the results with those based on the original data Dependent Variable I Coefficient Variable Std Error Probability 1 0397E 07 4 8547E 08 t Statistic 0 0572 0 00247 1 0166 0 04846 17 7473 Income 19 5585 R 0 97951 Durbin Watson statistic 0 91384 P (1 P ) Nif 2 r2

Question: In the probit model given in the following table the disturbance ui has this variance: where f i is the standard normal density function evaluated

In the probit model given in the following table the disturbance ui has this variance:

Dependent Variable: I Coefficient Variable Std. Error Probability 1.0397E-07 4.8547E-08 t-Statistic 0.0572 0.00247 -1.01

P;(1 – P.) Nif? .2 r2

where f_i is the standard normal density function evaluated at Fˆ’1(Pi).

a. Given the preceding variance of ui, how would you transform the model in Table 15.10 to make the resulting error term homoscedastic?

i li = F^ˆ’1(PÌ‚_i)

0.20 €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦. ˆ’0.8416

0.24€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.€¦. ˆ’0.7063

0.30€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.€¦. ˆ’0.5244

0.35€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.. ˆ’0.3853

0.45€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.. ˆ’0.1257

0.51€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦..€¦.. 0.0251

0.60€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦..€¦.. 0.2533

0.66€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦. 0.4125

0.75€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.. ..0.6745

0.80€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦ 0.8416

b. Use the data in Table 15.10 to show the transformed data.

c. Estimate the probit model based on the transformed data and compare the results with those based on the original data.

Dependent Variable: I Coefficient Variable Std. Error Probability 1.0397E-07 4.8547E-08 t-Statistic 0.0572 0.00247 -1.0166 0.04846 -17.7473 Income 19.5585 R? = 0.97951 Durbin-Watson statistic = 0.91384 P;(1 P.) Nif? .2 r2

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