Lecture #10.ppt

Therefore, we might expect ?i2 = Zi2?2 Zi2 = X2i2 =Zi =X2i These plots suggest variance is increasing proportional to X2i2. The scattered plots spreading out as nonlinear pattern. = Yi* = ?1 X0* + ?2 X1* + ?3 + ?* Now this becomes the intercept coefficient If the residuals plot against X2i are as following : X2 ?i + 0 - ^ X2 ?2 ^ Yi 1 X1i X2i ?i X2i X2i X2i X2i X2i = ?0 + ?1 + ?2 + Hence, the transformed equation becomes Where ?*i satisfies the assumptions of classical OLS Example: Studenmund (2006), Eq. 10.24, pp.374 C.V.=0.3392 The correction is built in EVIEWS Use the weight (1/REG) to remedy the heteroscedasticity Refers to Studenmund (2006), Eq.(10.28), pp.376 OLS result WLS result FC(0.05, 5, 44) = 2.45 ?2(0.05, 5) = 11.07 ?2(0.10, 5) = 9.24 W= Decision rule: W ?2df == not reject Ho Now, after the reformulation The test statistic value indicates that the heteroscedasticity is not existed. Alternative remedy of heteroscedasticity: reformulate with per capita W= Now, after the reformulation The test statistic value indicates that the heteroscedasticity is not existed. FC(0.05, 5, 44) = 2.45 ?2(0.05, 5) = 11.07 ?2(0.10, 5) = 9.24 Decision rule: W ?2df == not reject Ho W ?2df = not reject Ho This plot suggests a variance is increasing proportional to X2i. The scattered plots spreading out as a linear pattern If the residuals plot against X2i are as following : X2 ?i + 0 - ^ X2 ?2 ^ Therefore, we might expect ?i2 = Zi?2 hi2 = X2i = hi = X2i = Yi* = ?1 X0* + ?2 X1* + ?3 X2* + ?* = ?0 + ?1 + ?2 + Yi 1 X1i X2i ?i ?X2i ? X2i ? X2i ? X2i ? X2i The transformed equation is Transformation: divided by the squared root term --“@sqrt(X)” = ?0 + ?1 + ?2 + Yi 1 X1i