F- Test ApplicationsTime Series ApplicationsSlide 3Slide 4Slide 5Actual, Fitted, Residual graphThe Gann InitiativeSlide 8Slide 9Slide 10RegressionSlide 12Slide 13F-TestSlide 15F density for 2 and 36 Degrees of FreedomCan you go from 2 parameters to 4 parameters?Alternatively, can you estimate a single time trend instead of two time trends?Slide 19Wald TestSlide 21Slide 22Slide 23Slide 2411F- Test ApplicationsF- Test Applications22Time Series ApplicationsTime Series ApplicationsChow Test for structural changeChow Test for structural change33445566-1.0-0.50.00.51.01.54567870 75 80 85 90 95 00 05Residual Actual FittedActual, Fitted, Residual graphActual, Fitted, Residual graph77The Gann InitiativeThe Gann Initiative1977-Limit Government in Real Terms Per 1977-Limit Government in Real Terms Per CapitaCapitaTwo periodsTwo periods1968-69 through 1977-781968-69 through 1977-781978-79 through 2007-081978-79 through 2007-0888Genr periodone=0, type in onesGenr periodtwo=1, type in zeros99Genr timeone=periodone*timeGenr timetwo=periodtwo*time10101111RegressionRegressionRatio = c(1)*periodone + c(2)*timeone + Ratio = c(1)*periodone + c(2)*timeone + c(3)*periodtwo + c(4)*timetwo +e(t)c(3)*periodtwo + c(4)*timetwo +e(t)12121313-1.5-1.0-0.50.00.51.04567870 75 80 85 90 95 00 05Residual Actual Fitted1414F-TestF-TestFF2, 36 2, 36 = [SSR= [SSR2 2 - SSR- SSR4 4 ]/2 ]/2 ÷ SSR÷ SSR44/(40-4)/(40-4)FF2, 36 2, 36 = [13.31 – 7.40]/2 ÷ 7.40/36= [13.31 – 7.40]/2 ÷ 7.40/36FF2, 36 2, 36 = 2.96/0.206 = 14.4= 2.96/0.206 = 14.41515Genr: Fvar=@rfdist(2, 36)Genr: Density=@dfdist(Fvar, 2, 36)16160.00.20.40.60.81.00 2 4 6 8 10FVARDENSITYF-density for 2 and 36 degrees of freedomF density for 2 and 36 Degrees of F density for 2 and 36 Degrees of FreedomFreedom3.275%14.41717Can you go from 2 parameters to 4 Can you go from 2 parameters to 4 parameters?parameters?Yes, there is a significant increase in Yes, there is a significant increase in explained variance, indicating a structural explained variance, indicating a structural change after the passage of the Gann change after the passage of the Gann Initiative in 1977Initiative in 19771818Alternatively, can you estimate a Alternatively, can you estimate a single time trend instead of two single time trend instead of two time trends?time trends?No, two time trends fits the data No, two time trends fits the data significantly bettersignificantly better19192020Wald TestWald
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