Question

Question 3. According to the estimation of econometric model shown in below Table. I, please answer the following questions. The data for the all variables collected from World Bank over 2010- 2015. (60 pts) 1. Make a mathematical model of theory. (5 pts) 2. Make an econometric model of theory. (5 pts) 3. Hypothesis testing of (intercept, coefficients, model). Make and write a hypothesis for each of them and test your hypothesis based on 190, 5%, and 10% significance level. (30 pts) 4. What is the R square (R3) of estimated econometric model. Does your model explain the variation of GDP per capita? (10 pts) s, what will be the value of GDP per capita in 2016, if the future value of Domestic Credit (% GDP- 178 37: Total Investment (% GDP)-28.42; Tax revenue (% GDP)-22.17; Net Export (% GDP)-.1.32. (10 pts) Table 1: Regression Estimation Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA 0.37 0.49 0.47 0.09 20 Regression Residual Total MS 0.28 39.21 0.01 Significance F 0.09 1.14 0.01 1.15 Coeficdents StanddBror StatPvalue Domestic Credit (% GDP) Total Investment 0% GDP) Tax revenue (% GDP) Net Export (% GDP) 5.47 0.05 0.35 -0.52 0.71 0.02 0.22 0.15 0.07 -2.71 0.07 4.73 0.09 3.29 0.09 -2.10 0.08 4.64 0.05 0.78 Good Luck!

Answer 1

$Let~x_1=Domestic~credit,~x_2=Total~investment,~x_3=Tax~revenue,\\ ~x_4=Net~export,~y=GDP~per~capita\\ 1.~y=\alpha+\beta_1x_1+\beta_2x_2+\beta_3 x_3+\beta_4x_4\\ where,~\alpha=intercept,~\beta_i=regression~coefficient~of~x_i,~i=1,2,3,4\\ 2.~\hat{y}=estimate~of~y=-5.47+0.05x_1+0.35x_2-0.52x_3+0.78x_4\\ 3.~Since~p-value~corresponding~\alpha~and~\beta_i's,~model~fall~in~the~interval~(0.05,~0.1).\\ All~(intercept,~coefficients)~are~significantly~different~from~0~at~10\%~level.\\ However~they~are~insignificant~at~1\%~and~5\%~level.~Similarly~model~is~significant\\ at~10\%~level~however~it~is~insignificant~at~1\%~and~5\%~levels.\\ 4.~R^2=0.49.~The~model~explains~49\%~of~total~variation~of~GDP~per~capita.\\ 5.~When~x_1=178.37,~x_2=28.42,~x_3=22.17,~x_4=-1.32~\\ hat{y}=-5.47+0.05*178.37+0.35*28.42-0.52*22.17+0.78*(-1.32)\\ =0.8375\approx 0.84$