Data sisaltaa 2 muuttujaa:
RealGDP: Quarterly values of Real GDP for the United States in Billions of Chained (2000) Dollars Seasonally Adjusted, Annual Rate.
TBillRate: Quarterly values of the rate on 3-month Treasury Bills. Quaterterly averages of daily rates in percentage points at an annual rate.
file<-"http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.csv" data<-read.table(file,skip=1,sep=",")
FILENAME myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.txt'; DATA USmacro; INFILE myurl firstobs=2; INPUT time $ gdpq tbill; RUN;
Olkoon Y(t) = log(RealGDP(t)) - log(RealGDP(t-1)) ja X(t) = TbillRate(t) - TbillRate(t-1)
Sovitetaan malli Y(t) = beta1 +beta2*X(t-1) + epsilon ja suoritetaan OLS-regressio. Luettele kertoimien pienimman neliosumman estimaatit. Suorita t-testit ja F-testi.
file<-"http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.csv" data<-read.table(file,skip=1,sep=",") gdp<-data[,2] r<-data[,3] n<-length(r) y0<-log(gdp[2:n])-log(gdp[1:(n-1)]) plot(y0,type="l") x0<-r[2:n]-r[1:(n-1)] plot(x0,type="l") T<-length(x0) y<-y0[2:T] x<-x0[1:(T-1)] plot(x,y) reg.model<-lm(y ~ x) summary(reg.model) plot(reg.model)
Saadaan tulos
Call: lm(formula = y ~ x) Residuals: Min 1Q Median 3Q Max -0.035938 -0.005788 0.000078 0.005344 0.031697 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.0084572 0.0006541 12.929 <2e-16 *** x 0.0017816 0.0009083 1.961 0.051 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.00992 on 228 degrees of freedom Multiple R-squared: 0.01659, Adjusted R-squared: 0.01228 F-statistic: 3.847 on 1 and 228 DF, p-value: 0.05104Ilman vakiotermia:
reg.model<-lm(y ~ 0+x) summary(reg.model) plot(reg.model) Call: lm(formula = y ~ 0 + x) Residuals: Min 1Q Median 3Q Max -0.027477 0.002648 0.008503 0.013781 0.040151 Coefficients: Estimate Std. Error t value Pr(>|t|) x 0.001860 0.001193 1.559 0.12 Residual standard error: 0.01303 on 229 degrees of freedom Multiple R-squared: 0.0105, Adjusted R-squared: 0.006184 F-statistic: 2.431 on 1 and 229 DF, p-value: 0.1203
Kokeillaan SAS:ia.
FILENAME myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.txt'; DATA USmacro; INFILE myurl firstobs=2; INPUT time $ gdpq tbill; loggdpq = log(gdpq); y = loggdpq - lag1(loggdpq); x0 = tbill - lag1(tbill); x = lag1(x0); RUN; proc reg data = USmacro; model y = x; run; proc reg data = USmacro; model y = x / noint; run;