Question

please help me answer the all question ..thanks a lot

2. Berikut adalah keputusan penganggaran persamaan regresi untuk mengkaji penentu tekanan darah sistolik. Below is the regression output showing the results of an examination into the determinants of systolic blood pressure SUMMARY OUTPUT Regression Statistics Multiple R R Square 0.9907 0.9815 4.5467 Standard Error Observations 20 ANOVA df MS Regression Residual Total 3 17560.0464 5853.3488 330.7536 20.6721 17890.8 16 19 Coefficients Standard Error tStat 12.9037 0.5581 Intercept Xt 7.2017 2.4077 0.1912 12.5933 X2 0.5629 0.2442 2.3051 -1.1514 X3 0.8512 1.3527 di mana where Y = tekanan darah sistolik (mm Hg)/ systolic blood pressure (mm Hg) X1umur (tahun) age (years) X2 berat badan (kg) / weight (kg) Xs-pengambilan gula sehari (g) sugar intake per day (g) a) Kirakan pekali penentuan terselaras dan terangkan maksudnya Calculate the adjusted R2 and explain its meaning (2 markah/marks) b) Uji keertian keseluruhan bagi model pada aras keertian 1% Test the overall significance of the model at 1% level of significance (4 markah/marks) ESEE2102 Uji hipotesis β1-2 melawan β1 #2 pada α :0.05 c) Test the hypotheses β1-2 versus β:1 2 at α-0.05. (3 markah/marks) d) Bina selang keyakinan 95% untuk pekali X2. Berdasarkan keputusan ini, uji hipotesis β2 = 0 melawan β. 0. Construct a 95% confidence interval for the coefficient of X2. Based on the result, test the hypotheses β,-0 versus β. 0. (4 markah/marks) . Uji hipotesis Ho:A -за melawan e) Diberikan Coy(B.A)s-00397 Ho:A -3A Test Given Cov(βί.A)--0.0397. H,:A*-3A at α-0.05. the hypotheses versus (4 markah/marks) (Jumlah markah: 17 Total marks: 17) 5. Jawab soalan berikut. Answer the following questions. a) Diberikan model serta output berikut: Given the following model and output: di mana where Y- bilangan pelanggan melanggani ABC Kabel TV I number of customers subscribe ABC Cable TV Xi- pendapatan per kapita (RM) / income per capita (RM) X2- yuran langganan bulanan (RM) / monthly subscribing fee (RM) Jadual 1 menunjukkan output regresi model. Table 1 shows the regression output of model. Jadual 1/ Table 1 Dependent Variable: Y Method: Least Squares Sample: 1 40 Included observations: 40 Coefficient Std. Error t-Statistic Prob Variable -49.21987 56.07677 -0.877723 0.3858 0.000346 0.006162 -0.056226 0.9555 10.48088 4.591805 2.282517 0.0283 X1 X2 0.634086 Mean dependent var 24.50850 Adjusted R-squared 0.587280 S.D. dependent var 33.53720 2.864719 0.069707 R-squared 193.8780 F-statistic Log likelihood Durbin-Watson stat 1.923773 Prob(F-statistic) Jadual 2 menunjukkan output ujian White yang telah dijalankan ke atas model itu Table 2 shows the White test conducted on the model. Jadual 21 Table 2 Dependent Variable: RESID2 Method: Least Squares Sample: 1 40 Included observations: 40 Variable Coefficient Std. Error t-Statistic Prob 33633.10 39286.98 -0.856088 0.3979 3.955417 8.421005 0.469708 0.6416 3852.628 5467.530 0.704638 0.4858 2.23E-05 0.000572 0.039098 0.9690 190.6436 290.8971 0.655365 0.5166 0.626635 0.576808 1.086385 0.2850 X2 X1A2 X22 XiX2 R-squared Adjusted R-squared Log likelihood Durbin-Watson stat 0.666847Mean dependent var 949.5825 0.544324 S.D. dependent var 2753.343 -369.4233 F-statistic 2.265359 1.361763 0.263010 Prob(F-statistic) i) Berdasarkan Jadual 2, adakah masalah heteroskedastisiti wujud di model ini? Gunakan ujian White pada a 0.05 Based on Table 2, does the problem of heteroscedasticity exist? Use White test at a 0.05 i) Cadangkan satu cara untuk mengatasi masalah heteroskedastisiti Suggest a way to mitigate the problem of heteroscedasticity (6 markah/marks) b) Diberikan model berikut berdasarkan data tahunan selama 30 tahun: Given the following model based on a 30-year annual data set Y 4.73+1.92X,+1.15x R 0.6175; Durbin-Watson: d-2.8783 i) Dengan ujian Durbin-Watson, apakah kesimpulan yang anda boleh buat mengenai ralat model ini? Uji pada 0.05 With a Durbin-Watson test, what conclusion would you draw about the residuals of the model? Test at a 0.05. ESEE2102 Kemudian, anda ingin menguji autokorelasi peringkat kedua berdasarkan model berikut: Then, you want to test for second order autocorrelation based on the following model: e, 1.58+1.13X, +2.04X, +0.98e--0.34e R-0.2954 Durbin-Watson: d 1.7128 ii) Dengan ujian Breusch-Godfrey LM, adakah wujud autokorelasi peringkat kedua dalam model ini pada a0.05? With a Breusch-Godfrey LM test, is there second order autocorrelation in the model at a 0.05? (7 markah/marks) c) Bilakah anda menggunakan ujian RESET? When do you use RESET test? (1 markah/mark) d) Bilakah anda menggunakan ujian Jarque-Bera? When do you use Jarque-Bera test? (1 markah/mark) (Jumlah markah: 15 Total marks: 15)

Answer 1

a)
adjusted R^2 formula = 1 - (1- R^2)(n-1)/(n-k-1)
= 1 - (1 - 0.9815)(19/16)
= 0.97803125

The adjusted R2 tells you the percentage of variation explained by only the independent variables that actually affect the dependent variable.
b)
F = MS regression / MS error
= 5853.3488/20.6721
= 283.1521

p-value = f.dist.rt( 283.1521,3,16)
= 0.0000

p-value < alpha (0.01)
hence we reject the null hypothesis
we conclude that the model is significant

c)
TS = (b^ - 2)/se(b^)
= (2.4077 - 2)/0.1912
= 2.13232

critical value at 0.05 alpha
= t.inv.2t(0.05,16)
=2.1199

since TS > critical value
we reject the null hypothesis

d)
95% confidence interval
(b^ - t * se , b^ + t * se)
t = 2.1199
b2^ = 0.5629
se = 0.2442

hence
(0.5629 - 2.1199* 0.2442 , 0.5629 + 2.1199* 0.2442 )
= ( 0.04522 , 1.080579)