:
3
:
. -. .
, , . , 1- 2006 31 2011. R MS EXSEL.
, , , :
vyt =-1486.5342 + 1.3777 zp + 0.2821 pr - 0.1835 doh + 0.4960 tr,
vyt - , zp - , pr , doh - , tr .
³ :
Residuals:
Min 1Q Median 3Q Max
-11262.3 -2272.3 117.1 2608.5 10014.0
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1486.5342 4429.7041 -0.336 0.7411
zp 1.3777 0.2186 6.303 6.09e-06 ***
pr 0.2821 0.1471 1.917 0.0712.
doh -0.1835 0.1979 -0.927 0.3660
tr 0.4960 0.1845 2.688 0.0150 *
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 5178 on 18 degrees of freedom
Multiple R-squared: 0.992, Adjusted R-squared: 0.9902
F-statistic: 557.3 on 4 and 18 DF, p-value: < 2.2e-16
1, . ( >99,9%), (>90%) (>95%). , p-value .
. 1
. 2
. , 1. .
:
(1.3777-1)/0.2186 = 1.727813
qt(0.95,18) = 1.734064
, 95% , 1.
. , , 2, .
:
t=matrix(0,ncol = 5)
t[1,2]=1
t[1,3]=1
x=matrix(nrow=23,ncol=5)
for(i in 1:23)for(j in 2:5) {x[i,j]=sh1[i,j+1]}
x[,1]=1
b=matrix(nrow=1,ncol=5)
b[,1]=-1486.5342
b[,2]= 1.3777
b[,3]= 0.2821
b[,4]= -0.1835
b[,5]= 0.4960
fpr=(t(t%*%t(b)-2)%*%solve(t%*%solve(t(x)%*%x)%*%t(t))%*%(t%*%t(b)-2))*18/ sum(residuals(fm1)^2) = 5.191101
qf(0.05,1,18) = 0.004043292
t , , b . , 95% .
|
|
. ᒺ , 1 2006 4 2008 (12 ) 1 2009 3 2011 (11 ). , , .
:
vyt1=sh1[1:12,2]
vyt2=sh1[13:23,2]
zp1=sh1[1:12,3]
pr1=sh1[1:12,4]
doh1=sh1[1:12,5]
tr1=sh1[1:12,6]
zp2=sh1[13:23,3]
pr2=sh1[13:23,4]
doh2=sh1[13:23,5]
tr2=sh1[13:23,6]
fm01=lm(vyt1~zp1+pr1+doh1+tr1)
fm02=lm(vyt2~zp2+pr2+doh2+tr2)
summary(fm01)
lm(formula = vyt1 ~ zp1 + pr1 + doh1 + tr1)
Residuals:
Min 1Q Median 3Q Max
-3151.73 -886.58 -96.53 1363.20 3113.31
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3398.0518 3323.9132 -1.022 0.34066
zp1 1.2100 0.2529 4.784 0.00200 **
pr1 0.1287 0.1248 1.031 0.33684
doh1 -0.1480 0.8798 -0.168 0.87116
tr1 0.7831 0.2154 3.636 0.00833 **
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 2343 on 7 degrees of freedom
Multiple R-squared: 0.9975, Adjusted R-squared: 0.9961
F-statistic: 710.9 on 4 and 7 DF, p-value: 3.297e-09
summary(fm02)
lm(formula = vyt2 ~ zp2 + pr2 + doh2 + tr2)
Residuals:
Min 1Q Median 3Q Max
-10519 -4547 2011 5019 7881
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2990.8815 26524.4902 -0.113 0.9139
zp2 1.3678 0.5578 2.452 0.0496 *
pr2 0.3568 0.3199 1.115 0.3074
doh2 -0.1925 0.3542 -0.543 0.6064
tr2 0.4918 0.6442 0.763 0.4742
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 8123 on 6 degrees of freedom
Multiple R-squared: 0.968, Adjusted R-squared: 0.9466
F-statistic: 45.31 on 4 and 6 DF, p-value: 0.0001284
rss1=sum(residuals(fm01)^2)
rss2=sum(residuals(fm02)^2)
rss=sum(residuals(fm1)^2)
(rss-rss1-rss2)/5*13/(rss1+rss2) = 0.2895121
qf(0.95,5,13) = 3.025438
, 95% , .
, . 3 , , 1 . :
fmz=lm(vyt~zp+pr+doh+tr+q2+q3+q4)
summary(fmz)
Residuals:
Min 1Q Median 3Q Max
-7376 -1388 648 2014 4932
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.003e+03 4.226e+03 2.131 0.050088.
zp 1.087e+00 1.839e-01 5.912 2.85e-05 ***
pr 1.114e+00 2.629e-01 4.236 0.000719 ***
doh -3.128e-01 1.611e-01 -1.942 0.071198.
tr 4.939e-01 1.354e-01 3.648 0.002381 **
q2 -7.772e+03 2.260e+03 -3.439 0.003656 **
q3 -2.260e+04 5.799e+03 -3.897 0.001429 **
q4 -8.572e+03 2.943e+03 -2.913 0.010707 *
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 3736 on 15 degrees of freedom
Multiple R-squared: 0.9965, Adjusted R-squared: 0.9949
F-statistic: 614.4 on 7 and 15 DF, p-value: < 2.2e-16
, , , 90% . , , .
. 3
. 4
. , :
|
|
(22-(8+5)/6)*4.68 = 92.82
qchisq(0.95,6) = 12.59159
, , , . , , . , (23) .
, , .
fml=lm(vyt~ zp + pr + tr)
summary(fml)
Residuals:
Min 1Q Median 3Q Max
-10375.7 -2736.5 433.9 2947.7 10347.2
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 339.1386 3953.6259 0.086 0.9325
zp 1.3375 0.2134 6.267 5.12e-06 ***
pr 0.2894 0.1464 1.978 0.0627.
tr 0.4943 0.1838 2.689 0.0145 *
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 5159 on 19 degrees of freedom
Multiple R-squared: 0.9916, Adjusted R-squared: 0.9903
F-statistic: 748.2 on 3 and 19 DF, p-value: < 2.2e-16
(0.992-0.9916)/(1-0.992)*19 = 0.95
qf(0.05,1,19) = 0.004037369
, , , , , .
. ³ :
gqtest(fm1,fraction=0.15)
Goldfeld-Quandt test
data: fm1
GQ = 12.4976, df1 = 5, df2 = 4, p-value = 0.01489
, 95% .
:
bptest(fm1,~ I(zp^2)+I(pr^2)+I(doh^2)+I(tr^2)+zp*pr+zp*doh+zp*tr+pr*doh+pr*tr+tr*doh)
studentized Breusch-Pagan test
data: fm1
BP = 17.8776, df = 14, p-value = 0.2124
, <80% .
vytf=vyt/abs(residuals(fm1))
zpf=zp/abs(residuals(fm1))
prf=pr/abs(residuals(fm1))
dohf=doh/abs(residuals(fm1))
trf=tr/abs(residuals(fm1))
fmf=lm(vytf~zpf+prf+dohf+trf)
summary(fmf)
Residuals:
Min 1Q Median 3Q Max
-1.8600 -0.9368 0.1350 0.9040 1.5722
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.08353 0.29930 -0.279 0.7834
zpf 1.29634 0.10171 12.746 1.90e-10 ***
prf 0.28973 0.05015 5.777 1.78e-05 ***
dohf -0.17229 0.09119 -1.889 0.0751.
trf 0.56513 0.09567 5.907 1.36e-05 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 1.168 on 18 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 3.72e+05 on 4 and 18 DF, p-value: < 2.2e-16
bptest(fmf,~ I(zpf^2)+I(prf^2)+I(dohf^2)+I(trf^2)+zpf*prf+zpf*dohf+zpf*trf+prf*dohf+prf*trf+trf*dohf)
studentized Breusch-Pagan test
data: fmf
BP = 22.1533, df = 14, p-value = 0.07552
, >90% . , 1, .
. 5
. 6
.
dwtest(fmf)
Durbin-Watson test
data: fmf
DW = 1.4838, p-value = 0.08989
alternative hypothesis: true autocorrelation is greater than 0
, >90% .
, , AR(1) :
ro=sum(residuals(fmz)[2:23]*residuals(fmz)[1:22])/sum(residuals(fmz)[1:22]^2)
> vyta[1]=(1-ro)^(1/2)*vytf[1]
> zpa[1]=(1-ro)^(1/2)*zpf[1]
> pra[1]=(1-ro)^(1/2)*prf[1]
|
|
> doha[1]=(1-ro)^(1/2)*dohf[1]
> tra[1]=(1-ro)^(1/2)*trf[1]
> for (i in 2:23) {vyta[i]=vytf[i]-ro*vyta[i-1]}
> for (i in 2:23) {zpa[i]=zpf[i]-ro*zpa[i-1]}
> for (i in 2:23) {pra[i]=prf[i]-ro*pra[i-1]}
> for (i in 2:23) {doha[i]=dohf[i]-ro*doha[i-1]}
> for (i in 2:23) {tra[i]=trf[i]-ro*tra[i-1]}
> fma=lm(vyta~zpa+pra+doha+tra)
> summary(fma)
Residuals:
Min 1Q Median 3Q Max
-2.0618 -0.5750 0.1395 0.8945 1.4579
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.03733 0.26363 0.142 0.8890
zpa 1.27904 0.09493 13.473 7.66e-11 ***
pra 0.29649 0.04493 6.599 3.38e-06 ***
doha -0.20274 0.08148 -2.488 0.0229 *
tra 0.58309 0.08952 6.514 4.00e-06 ***
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 1.093 on 18 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 3.937e+05 on 4 and 18 DF, p-value: < 2.2e-16
dwtest(fma)
Durbin-Watson test
data: fma
DW = 1.6542, p-value = 0.2564
alternative hypothesis: true autocorrelation is greater than 0
, , , .
. 7
. 8