Question

please show Work and graphs

S&W, Chapter 8-Nonlinear Regression Functions Regressor 1.020.67 (0.37) (0.27) 124 172-0.69* -0.64 (0.50) (027) (027) (14.0) Student-teacher ratio STR) 0680 (0.737) 0011 (0.013) STR -04110437 0.434 (0.306)(0.303) (0.300) % English learners % Englishlearners median? (Binary, HIEL) -12.6 (9.8) "EL × STR 0.80 (0.56) Eligible for free lunch 0521 05820587 -0.7090653 (0.077) (0.097) (0,104)(0.091)(0.72) District income (logarithm) 16.53 (3.15) District income -3.07 (233) 3.38 (249) 3.87 (2.49) 3.22 (2.31) District income 0184 0.165 0.164 0.174 (0085)(0089)(0.090)rass) District income 0.00220.0023 0.0023 0022 (0.0010)(0.0010) (0.0010) (00010) 7396 6824 744.0 (115) 665.5- 759.97474 (20.3) (8.6) (21.3) Tahle 92 ontind) F-Statisties and p-Values Testing Exclusion of Groups of Varlables Al STR variables and 4.01 interactionsD (0.038)(0.020) STR.STR 0.45 (0,641) Income-, Income 7.74 (< 0001) 7.75 5.85 (0.003) 6.55 (0.002) (c 0.001) lliEL. HiEL× STR (0.208) SER 14.64 8.61 8,63 8,62 0.0630.6700.676 0.675 0.675 0.674 These regressions were estimated using the data on Massachusetts elementary school districts described in Appendix 9.1. Stan- dard errors are piven in parentheses under the coefficients, and p-values are given in parentheses under the F-statistics Individ- ual coefficients are statistically spnificant at the .5% level or "1% ke.

Answer 1

18.

From the output, we see that the regression 3 contains the quadratic terms of Income - Income² and Income³. The regression 3 estimates the non-linear regression model based on Income variable.

The evaluation to be made by using the two versions of the model is whether the non-linear terms Income² and Income³ are statistically significant in the model. The appropriate hypotheses are,

H0:

Income? Income

Ha: H0 is False.

F statistics is used in making the evaluation. F statistic for the hypothesis test is 7.74 and p-value is less than 0.001.

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that Income² and Income³ are statistically significant in the model 3.