自相关

表5-3显示了1970-1994年25年间，日本工薪家庭实际消费支出Y与实际可支配收入X的变化。

(1)对下面的回归模型进行OLS检验，并计算t值和决定系数\(R^2\)。 \[Y_t = \beta_1+\beta_2X_t+\varepsilon_t\] (2)用(1)的估计结果，计算OLS的残差 ，并求杜宾-沃特森统计量DW。

(3)利用(2)的DW值，进行 ，显著性水平为5%的单侧检验。

回归结果

## 
## Call:
## lm(formula = y ~ x, data = dat1)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.527 -2.615 -1.352  1.724  8.350 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 50.87454    8.29106   6.136 2.93e-06 ***
## x            0.63744    0.02124  30.008  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.509 on 23 degrees of freedom
## Multiple R-squared:  0.9751, Adjusted R-squared:  0.974 
## F-statistic: 900.5 on 1 and 23 DF,  p-value: < 2.2e-16
## % latex table generated in R 3.3.3 by xtable 1.8-2 package
## % Wed Jun 27 22:33:00 2018
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrr}
##   \hline
##  & Estimate & Std. Error & t value & Pr($>$$|$t$|$) \\ 
##   \hline
## (Intercept) & 50.8745 & 8.2911 & 6.14 & 0.0000 \\ 
##   x & 0.6374 & 0.0212 & 30.01 & 0.0000 \\ 
##    \hline
## \end{tabular}
## \end{table}

自相关简单–Durbin Waton检验

## 
##  Durbin-Watson test
## 
## data:  lm1
## DW = 0.35276, p-value = 4.517e-09
## alternative hypothesis: true autocorrelation is greater than 0
summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

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